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At the urging of Planned Parenthood, the Nevada state Assembly approved an amendment in April 2003 to stop pharmacists with religious objections from refusing to fill prescriptions for any drug, including abortifacient contraceptives and the so-called "morning after" pill. New York City hospitals now require abortion training for all their OB/GYN resident doctors unless they invoke a narrowly written conscience clause. The Oregon Nursing Association has issued guidelines for assisted suicide that prohibit nurses from making "unwarranted, judgmental comments or actions" to patients, families or other colleagues when patients decide to kill themselves with doctor-prescribed lethal overdoses.
Slowly but surely, more and more pro-life doctors, nurses and other healthcare professionals are getting the message that they and their views are unwelcome in today's health care system. But these public items tell only a small part of the story. Intimidation, harassment and coercion are becoming increasingly common as pro-life health care providers try to advocate for both their patients and their professional ethics. For example, a nurse was threatened with firing after she refused to follow a doctor's verbal order to increase an intravenous morphine drip "until he stops breathing" on a patient who continued to survive despite having a ventilator removed. An OB/GYN physician was told by other doctors that they would no longer refer patients to him if he continued to sign an annual pro-life ad. Three California nurses were suspended after they reported a doctor who later admitted giving a lethal injection to a child. An insurance company executive speaking on ethics committees at a conference recommended that such committees avoid appointing "family values" members. Unfortunately, these reprehensible acts are not confined to just secular health care institutions. A dedicated nurse who cared for elderly nuns in a Catholic facility for over a decade was told she could resign when she objected to the slow starvation and dehydration deaths of two of her beloved nuns. Several doctors and nurses working at Catholic hospitals have personally told me about similar incidents, including other supposedly prohibited actions such as sterilizations, referrals to Planned Parenthood and even some abortions. Amazingly, hospital administrators often told them that these procedures were ethically allowed according to some prominent Catholic ethicists. Years ago when I was the co-chair of the St. Louis Archdiocesan Pro-Life Committee, I was asked by the late Archbishop May why I didn't work as a nurse at a Catholic institution. He was shocked when I told him that I felt safer at a secular institution that at least understood the implications of conscience rights rather than at a Catholic institution, which could try to talk me out of them. I wasn't kidding.
Before the invention of the Pill and the legalization of abortion, medical ethics principles were relatively simple, unambiguous and, with few exceptions, followed by doctors and nurses. The Hippocratic oath prohibiting abortion and euthanasia was a mainstay of medical education.
However, the beginnings of a drastic change started with the furor over the invention of the Pill and accelerated when the American College of Obstetricians and Gynecologists (ACOG) allowed the redefinition of conception from fertilization to the later implantation of the embryo into a woman's uterus, thus blurring the distinction between contraception and abortion by ignoring scientific fact. The American Medical Association (AMA) softened its long-standing opposition to abortion as state laws on abortion were being relaxed in the 1960s and 1970s. After the 1973 Roe v. Wade decision, the AMA declared abortion to be an ethical healthcare procedure and now opposes almost any restrictions on abortion practice. With legality rather than principle becoming a deciding factor in medical ethics, the standard of the Hippocratic oath had to be revised and now it is rarely used at all. Both the prohibition of abortion and euthanasia in the oath as well as the sacred commitment of the doctor to the individual patient were seen as obstacles to a more "enlightened" and modern healthcare system. Healthcare is now seen by many as an important part of societal reform to a more "inclusive" and less "judgmental" culture. Thus, it is not surprising that pro-life health care providers are now portrayed as divisive to their professions and even a threat to patients' rights when they refuse to conform to the Culture of Death. When the infamous Roe v. Wade decision on abortion was handed down, it was assumed that healthcare providers would not be forced to participate in abortion. However, the reality of legalizing abortion soon led many states to pass conscience rights legislation on abortion to protect doctors and nurses who object. Unfortunately, this still has not adequately protected doctors and nurses from intimidation, harassment or from obstacles to career advancement because they do not provide what is now called "full service" on "reproductive rights". Many pro-life healthcare providers thought they would be safe if they chose a specialty other than OB/GYN or labor and delivery. But with the court decisions and laws legalizing the withdrawal of basic medical treatment, the acceptance of terminal sedation as comfort care, the legalization of assisted suicide in Oregon and the push for such laws in other states, etc., there is now almost no area of medicine where a pro-life healthcare provider can avoid ethical dilemmas.


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or call us on 0800 781 4893
This tour offers a once in a lifetime opportunity to see the Big Five on safari at the famous Kruger National Park, soak up the unforgettable scenery along Chapman's Peak Drive, explore cosmopolitan Cape Town and discover the beautiful Winelands region.
Depart London on your scheduled, overnight flight via Johannesburg to Cape Town.
On arrival the following day, you will be met and transferred to your hotel.
Embark on a fantastic full day tour around the Cape Peninsula. Joining one of the most spectacular coastal drives in the world - Chapman's Peak Drive - travel to the World Heritage Site of The Cape of Good Hope Nature Reserve and then on to Cape Point where the mighty Atlantic and Indian Oceans meet. You will also visit the beautiful marine protected area of Boulders Beach where the sandy shores are home to a breeding colony of over 2,000 endangered penguins.
Enjoy day four in Cape Town at leisure, in which you can unwind upon its surrounding beaches or experience this city's lively cultural scene.
Optional excursions (payable locally): Helicopter ride over Cape Town and Cable Mountain, Half day West Coast Ostrich Farm tour.
Today, tour the breathtakingly beautiful Cape Winelands, first stopping at the town of Franschoek, then onto Stellenbosch. Take some time to explore these delightful towns before enjoying a cellar tour and wine tasting at the award-winning Boschendal Estate.
Take a scenic drive into the heart of the gorgeous Garden Route and into the picturesque coastal town of Knysna. Spend the remainder of the afternoon at leisure.
This morning, take a ferry across Knysna lagoon to the Featherbed Nature Reserve. Stopping at some magnificent viewpoints, your guide will describe the area's fauna, flora, history and shipwrecks followed by a leisurely guided walk.
Depart for Tsitsikamma, a section of the Garden Route famed for luscious forests and dramatic coastlines. In the afternoon head to Port Elizabeth, a city known for its laid-back coastal ambience and bold colonial architecture.
Fly from Port Elizabeth to Johannesburg, where you will be transferred to the town of Mpumalanga. Your retreat within this idyllic space will serve as the perfect base from which to explore Kruger National Park.
Undoubtedly one of the highlights of the tour; a guided safari drive in Kruger National Park. One of the biggest, oldest and quite simply one of the best wildlife parks in the world, Kruger boasts the greatest variety of animals including the famed Big Five.
Today is at leisure alternatively, optional excursions are available, including a unique safari on elephant-back (at a fee).
Today, travel along the magnificent Panorama Route, one of South Africa's most stunning scenic drives. With awe-inspiring vistas, the route follows the impressive Blyde River Canyon, before arriving in the city of Johannesburg.
Enjoy a short sightseeing tour of the city, with a stop at the Apartheid Museum for a fascinating insight into South Africa's cultural struggles. Later in the afternoon, head to the airport for your scheduled flight back to the UK.
British passport holders are not currently required to obtain a visa in order to travel to South Africa. This will be granted on arrival. Further visa advice should be sought from the applicable tourist authority for other nationalities and for general queries. We strongly advise you to check with your destinations' Tourist Board or Embassy for the most up-to-date guidelines regarding required passport validity.
We strongly recommend that you and all members of your party are suitably insured as soon as you book your holiday. It is a condition of booking that you must have suitable travel insurance. It is important that you purchase travel insurance that suitably covers your participation in whatever activities you may undertake at the time that you make your booking. To assist you with this, we have arranged travel insurance in partnership with Holiday Extras. To arrange your travel insurance with Holiday Extras, please call 0800 781 4237 and quote 'WK830' for preferential rates. Please ensure you provide us with the name of your insurer, policy number and their 24-hour emergency contact number as soon as possible. Mercury Holidays will not be liable for any costs incurred by you due to your failure to take out suitable travel insurance from the date of booking.
If booking more than 10 weeks before departure a deposit of £250pp will need to be paid at the time of booking with the full amount payable at 10 weeks prior to departure. The deposit applies to adults and children. If you are within 10 weeks of travel then the full balance of the holiday will be payable.
Your flight is to Johannesburg Airport is with South African Airways (SA), departing from London Heathrow Terminal 2. Each passenger is entitled to 23kg of hold luggage and hand luggage that you are permitted to carry one item of hand baggage (Max 8kg - 56cm/36cm/ 23cm) in addition to one small personal item on-board the aircraft. Weight restrictions will be finalized on E-ticket receipt. Should you wish to take additional luggage you will need to pay extra at check-in. Check-in should be at least 3 hours before departure.
It is your responsibility to check any health and vaccination requirements applicable to your booked arrangements. We can only provide general information about this. Health and hygiene facilities and disease risks vary from country to country. You should take health advice about your own needs as early as possible and in good time before your departure. Sources of information include; www.fco.gov.uk, http://travelhealthpro.org.uk/, www.hpa.org.uk, your General Practitioner or a specialist clinic.
This tour is accessible to most people with an average level of fitness and normal mobility. It involves full days of sightseeing, often on foot and includes some climbing of stairs and getting on and off coaches. This tour is not suitable for anyone with walking difficulties.
The minimum number of travellers in your group will be 10, and the maximum will be 35. If in the unlikely event there are less than 10 people booked on your tour date, we will endeavour to reduce any disruption to your holiday and try to operate your tour with lower passenger numbers. If we are not able to operate your departure date then you may be asked to change to a different date and a full refund will be made available to you should this alternative not be suitable.
This is a fully escorted tour, meaning that you will be met on arrival by your national guide who will remain with you for the duration of the tour, ensuring that you have first-hand knowledge at all times.
The currency in South Africa is the South African Rand and we recommend you change some currency before you leave the UK. Cash machines will also be available throughout the tour in order to withdraw money in your local currency.
You will need to take money with you to cover any personal purchases such as souvenirs, laundry and extra drinks and snacks. Approximately £300 - £400 will be sufficient for the durations of the tour, depending on how much of a bargain-hunter you are!
|Depart UK
|Arrive UK
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|2018 Dates
|07 Nov 2018
|19 Nov 2018
|2019 Dates
|15 Jan 2019
|27 Jan 2019
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|19 Feb 2019
|03 Mar 2019
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|19 Mar 2019
|31 Mar 2019
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|16 Apr 2019
|28 Apr 2019
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|14 May 2019
|26 May 2019
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|11 Jun 2019
|23 Jun 2019
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|09 Jul 2019
|21 Jul 2019
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|13 Aug 2019
|25 Aug 2019
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|17 Sep 2019
|29 Sep 2019
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|08 Oct 2019
|20 Oct 2019
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|05 Nov 2019
|17 Nov 2019
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|03 Dec 2019
|15 Dec 2019
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Unfortunately, we do not have any places with no single supplements on this tour. However, if you are happy to share with another passenger of the same gender, then let us know at the time of booking and we will endeavour to find you a travelling partner. Alternatively, please ask about our single supplement prices in order to book your own twin room
If the group departure dates are not suitable for you and you would prefer a more personal and flexible experience then you can choose to book a private guide for your tour at a reasonable supplement.
South African Rand
12 hours
Weather can vary quite considerably throughout the year, so please familiarise yourself with the climate charts below.
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Fabulous Inclusive tour.
0800 781 4893 (free)
0333 321 3144 (mobile friendly)
Spend 5 nights in South Africa's eastern coastal city of Durban located in the KwaZulu-Natal province.
Spend 7 nights in South Africa's eastern coastal city of Durban located in the KwaZulu-Natal province.
Travel to Zimbabwe and witness the awe-inspiring beauty and grandeur of the 'Smoke that Thunders' on this three night extension to Victoria Falls; one of the world's most sensational natural wonders.
Uncover Morocco's colourful cultural offerings as you explore ancient medinas, spice-filled souks and dramatic Moorish architecture.
Ancient shrines adorned with hieroglyphics and vast temple complexes built for the gods lie beside the iconic archaeological wonders of the Giza Pyramids in Egypt, a country rich in history, mysticism and centuries-old culture.
A leisurely journey along South Africa's breathtaking Garden Route, this itinerary combines scenic drives through undulating vine-clad valleys, a chance to meet an ostrich, the world's largest flightless bird and a rewarding hike along the stunning Cliff Path to spot whales from the shoreline.

subset: commoncrawl


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- Online Store
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- Motion Raceworks Manufactured Parts
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- Steering Column
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- Double push button steering wheel bracket with your choice red/green push buttons and Hardware
Double push button steering wheel bracket with your choice red/green push buttons and Hardware
Steering Wheel Not Included! Must Purchase separately.
Double Pushbutton with bracket assembly. This bracket is laser cut from aluminum, and anodized. This is a universal bracket for both aftermarket as well as stock steering wheels. The design allows for the button to be in the perfect position to reach the button while keeping your full hand positively and comfortably on the steering wheel (see pictures). Included: (2) Red Motion Raceworks Momentary Buttons (Red) and hardware (2) 6/32 stainless button head screws/nylon lock nuts (1) Black anodized double button bracket 10 amp Momentary Red Pushbutton Switch custom made for Motion Raceworks. This unit is an Aerospace grade quality switch MADE IN THE USA! Great for use for a line lock, transbrake, boost scramble, boost descramble, bump box, nitrous purge, and many more. This switch is a sealed unit with a 6 foot long rectractable cord (length when full pulled tight) with two 18 ga wires inside an outer covering. Comes with lock nut and washer to securely fashion. Your choice of red or green buttons


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Birds of Prey
Saturday, May 5th 9am
Cisterna Park – 1001 Garrison Ave
Birds of Prey Show is fun and educational for the whole family. While there is no cost or admission, donations to the Arkansas Native Plant and Wildlife Center are appreciated and you can have your photo taken with the birds. From owls to hawks to falcons, see and learn about these majestic creatures up close!
Tommy Young is the director of the wildlife center and holds degrees in Ornithology and Wildlife Medicine from Cornell University. He has helped rehabilitate and release back into the wild thousands of animals including 36 bears, 10,000 hawks, 9,000 owls, 22,000 mammals, 44 American Bald Eagles, 36 Golden Eagles. The wildlife center is located near Mena, AR, which makes for a good day-trip motorcycle ride from Fort Smith, AR.


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Leaving Staroia, a woman named Katerin approached Dalinar. Her husband, Harken, was an old shipmate of Dalinar's. He'd been captured by a pirate, Captain Jarzon. Jarzon had sailed the waters as a trader but had turned pirate some time ago. She implored Dalinar to help find his old shipmate… Jarzon's piracy had accelerated and taken a darker turn. He was no longer ransoming captives, but holding them, for some reason. Using the small ship she had available, Katerin dropped off Dalinar, accompanied by Garet, Umberto, Valius, and Berenike on the island Jarzon frequented. The forbidding reefs and rocky shores challenged her sailing and forced her to the far side of the island away from Jarzon's cove.
The group set off, crossing the rocky island. Garet scouted ahead, noticing a group of pirates in a group of cottages. They were led by a strange looking pirate who had a strange tenticular beard with a massive axe and a wild look in his eye. One of the pirates was standing near a large brass ship's bell. After some stealthing, Garet snuck up to try to deal with the pirate with the bell. Everyone else approached. Garet shot the bell-ringer. Several of the other pirates charged forward, but two remained behind, shooting arrows. Valius fireballed a group and the berserk pirate charged forward. A brutal fight ensued, with Dalinar and Umberto getting locked in a melee with the berserker. Eventually the pirates were dispatched, but not before the bell was rung. Garet scouted ahead to try to determine if anyone had noticed the bell. He found that there was a strange looking bird scouting around. Valius' hawk familiar and an arrow finished it off. Everyone took a rest, though, not quite sure what's happening, though Dalinar felt something ominous was going on.
Garet scouted ahead, proceeding down to the cove ahead of the group. He snuck into the caves that the pirates inhabited. Everyone else pushed on to attack, not knowing where Garet had gone. Berenike used a Bless spell, singing songs of the valor of the Gods. The battle started with Valius' Fireball, which fried several of the pirates. Umberto and Dalinar charged forward and attacked the sentry by the bell and another of the tenticularly-mutated berserkers. Between Berenike's Vicious Mockery and arrows, smites from Dalinar, and stabs from Umberto, along with Flaming Sphere and Firebolts from Valius, pretty soon the pirates were dispatched or driven off.
There was a door to the north as well as one to the east, heading deeper in. The east door appeared to be heavy wood and iron and Dalinar could sense that beyond it was something ominous. Expecting it to be locked he tried it, finding that it had been opened, presumably by Garet.On the other side of the door were two of the berserker pirates. Garet was hiding from them under the table. Valius used the Flaming Sphere and Firebolts to fry one, and Dalinar and Umberto quickly advanced, focusing on one of the berserkers. A concerted effort brought him down, though he wounded Umberto first. The other berserker moved up to attack but he too was dispatched, suffering under blades, arrows, and spells.
Meanwhile Garet moved to a curtain which was blocking the view of the outside and dropped a mine, taking up a ready position to prevent any counterattack. However, no foe emerged and Garet saw that one of the berserkers was doing the same on the other side of the curtain. Garet used his bow to pull back the curtain when Valius was ready, allowing the elven mage to throw a Fireball into the midst of the cultists, who had two captives, a young girl and Dalinar's friend. While the cultists thought that would stay the hand of any spell caster, the were wrong: Valius' ability to sculpt spells kept the two captives safe from the fire. Some of the cultists dropped under the fire while others were wounded. The cult leader Captain Jarzon, dressed in a bizarre regalia, appeared unmoved and cast a spell, shrouding himself in frost.
Umberto readied a shot with his reloaded pistol and put it right between the eyes of one of the cultists, killing him. A melee between Dalinar and the berserker developed, with Umberto joining. Berenike shot arrows after refreshing Bless. While Dalinar, Umberto, and Berenike pressed forward, Valius and Garet stayed behind, feeling that whatever ritual the cultists enacted—-summoning a kraken from the Ether—-wouldn't bother them on land. However, Dalinar felt that the beast, an enemy of the gods, must be dispatched and driven out of the world. He pressed forward, facing some Eldritch Blasts from Jarzon for his trouble.
Umberto ran forward to attack Jarzon but was frozen by the rime of frost protecting him, much to everyone's surprise! However, Berenike and Dalinar revived him and later Umberto rescued the hostages while Dalinar faced the kraken and Valius and Garet sniped at it from cover. The kraken, annoyed at Valius, who thought to stand out in the open, shot Valius with lightning, but proceeded to attack the surprised Jarzon, who had failed in summoning the kraken properly! However, Jarzon used the Dimension Door spell to escape.
The kraken then started attempting to savage Dalinar, who returned blows using the Spear of Athene and smiting strikes. The kraken proved to be a mighty foe but was inaccurate and smashed up the landscape more than it damaged Dalinar. However, finally the Kraken's blows told and knocked the mighty Dalinar down, pulling the paladin towards its maw after taunting him telepathically. Umberto picked up the Spear of Athene and stabbed into its tentacle, severing it and driving the beast back into the Ether from whence it came.


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After the NCAA championship game last season, Duke coach Mike Krzyzewski suggested that Butler should be considered a 2011 contender.
The perception of the Bulldogs went from favorites to unfortunates after they started the season 4-4 and suffered through a rough winter slump in Horizon League play.
Of course, coach Brad Stevens cares as much about perception as Blue the bulldog mascot cares about his appearance. Stevens employs a straightforward strategy to deal with this.


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Today, a large number of small and middle size of business ventures often use the option of virtual support, particularly, to perform a few specific tasks, including online promotion, client communication and social media management.
Virtual assistants are now in a huge demand among entrepreneurs and business ventures because they need help to accomplish daily tasks but do not want or afford to bring on staff in the specific office locations. Irrespective of the tasks on head, type of business venture or reason behind approaching VAs, services offered by virtual assistants are beneficial for companies or individual business ventures. These include-
Involves Less Investment
Hiring of Virtual Assistants involves low investments in furniture items and other valuable office assets, because virtual assistants perform their functions remotely simply from their personal offices or homes.
Saves Time and Money related to Recruitment
Every time, companies have to spend a big amount of money and dedicate many hours on creating lists of job posts, make payments to employment agencies and several other procedures while conducting the recruitment of employees. However, with Virtual Assistants, a large number of companies and businesses may save their valuable money and time involved in recruitment, selection and staffing procedures.
Reduces a Company's Expenses
Virtual tasks will take care of almost every type of office skill tasks done on a daily basis. In this way, you may easily avoid expenses associated with hiring of traditional employees. For instance, you are not bound to pay for insurance premiums, health benefits, holidays, payroll taxes and vacations to VAs, as you have to pay for any traditional employee. Instead, you only have to make payments based on the services they deliver for your company as per the terms present in the previously signed contract.
Eliminates the Need to Hire Temporary Employees
Companies opt to avail services from Virtual Assistants will eliminate the requirement to hire employees on a temporary basis in case of illness or vacations of staffs.
Easily Accessible for the Job
Companies may easily access Virtual Assistants with the help of different communication mediums, such as emails, phones, Skype and various other types of remote communication.
Flexibility in Working Hours
Unlike regular employees, you as a company owner may approach Virtual Assistants even after the regular business hours, so that they accommodate your work schedule. In simple words, Virtual Assistants are independent contractors providing their valuable administrative solutions and other essential support to a large number of individuals, entrepreneurs, consultants and various small plus medium size business ventures with the help of internet.
Helps to Off-load Specific Difficult Tasks
Virtual assistants incorporate good knowledge and countless innovative skills in various areas. This helps you a lot to increase your business efficiency, as you may now off-load your specific difficult tasks and let VAs to handle them in an efficient way.
Therefore, with Virtual Assistants, you as a company or a business owner, gain access to various professionally trained and high skilled individuals vesting their valuable interests in the long-term success and survival of your business.


text: Ok, i have a youtube bot i use, but it looks like Youtube have changed their subscribe button and now my bot isnt auto subscribing when it runs, so im looking for someone who could maybe fix it, or make me a new bot that will work with the new subscribe button. If you can do this, please contact asap. thanks in advance


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Your business should act as a funnel. Your customers enter at the top at your website and then your design, autoresponders, videos, and sales copy allow them to slide all the way down and come out the end as satisfied customers. All you have to do is ensure that they get to the top of that funnel.
Things which will already be pulling customers to your site are Google Maps, search engine optimization and social media. Your final step is to multiply that traffic and position yourself as an expert at the same time. Perhaps you shy away from attention, and don't like to think of yourself as an expert or 'guru'. However, you should pay attention to what I am about to explain, as one success story here can have a huge impact on your business and ultimately your bank account.
As you have probably gathered from the heading of this post, this is all about press releases. You may have heard that a press release marketing is a way to get links to your website; however, that is not the main reason you should be writing and distributing them.
When you write a press release, your aim is to get noticed by a reporter who will then create a story about you and your business to be reported in the newspaper, in magazines or on TV. This is great free publicity for you and also creates the sort of 'Halo Effect' we talked about before. If you are being seen as worthy of a story in the media, this creates an aura around you which positions you as someone who has authority in your niche.
Once you are picked up by a reporter, you needn't fear having your face spread over every news broadcast in the country. That kind of national coverage is quite rare. What you will experience is an editorial in an industry publication or some local newspaper or radio coverage. If that level of exposure worries you, you can always have one of your employees or a business partner become the face of your business.
Looking for expert advice on how to do your press release marketing? Take a look at my internet marketing consulting service by clicking here.


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In species subject to individual and social learning, each individual is likely to express a certain number of different cultural traits acquired during its lifetime. If the process of trait innovation and transmission reaches a steady state in the population, the number of different cultural traits carried by an individual converges to some stationary distribution. We call this the trait-number distribution. In this paper, we derive the trait-number distributions for both individuals and populations when cultural traits are independent of each other. Our results suggest that as the number of cultural traits becomes large, the trait-number distributions approach Poisson distributions so that their means characterize cultural diversity in the population. We then analyse how the mean trait number varies at both the individual and population levels as a function of various demographic features, such as population size and subdivision, and social learning rules, such as conformism and anti-conformism. Diversity at the individual and population levels, as well as at the level of cultural homogeneity within groups, depends critically on the details of population demography and the individual and social learning rules.
1. Introduction
In evolutionary biology, demographic factors of a population include its size, the degree to which population size changes over time, or the level of population subdivision, whether by sex, age or geography. All of these are expected to affect the evolutionary dynamics of phenotypes. This is true for any phenotype and whether the sources of phenotypic variation under study are genetic [1–3], cultural [4–6] or both.
The level of standing phenotypic variation and how this changes over time, as well as the degree of similarity between randomly chosen individuals, are all expected to be functions of demographic factors. In turn, the demographic properties of a population are affected by variation in phenotypes, which leads to a coupled dynamic that has received a lot of attention in the biological literature (e.g. [7,8]). There is much less theory on how cultural variation affects demography or how demography affects cultural diversity.
How do demographic factors, such as population size, population subdivision and migration rates between subgroups, affect cultural diversity? In population genetics, population size, in partnership with rates of genetic mutation, plays a central role in the structuring of genetic diversity. Indeed, the product NU of population size (N) and mutation rate (U) was shown by Kimura & Crow [9] to be a key element of the neutral theory of genetic evolution, and it determines Ewens' [10] distribution of the number of representatives of each allele in a population, the so-called configuration distribution, which was derived in a one-trait population genetic setting (i.e. a single gene). The neutral model has come into prominence not only in population genetics, but also in ecology [11] and archaeology [12] as the null model that describes diversity in the absence of selective differences (among alleles), ecological advantage (for species) or biases in cultural transmission of artefact style.
It is natural to ask whether in cultural evolutionary models the analogous product of population size and rate of innovation emerges as a central parameter describing patterns of cultural diversity. This will be the case at least for a one-trait cultural model with random copying and no memory [12] as this is very close to the neutral model of population genetics. In this model, individuals carry a single cultural trait for which they may express one of several variants [5,6,13]. Alternatively, individuals may be regarded as either expressing or not expressing the trait. These two situations can be described in terms of a one-trait cultural model with many (the former case) or two (the latter case) variants segregating in the population, analogous to alleles in the one-gene population genetic setting. The main difference from classical population genetics is that, since the rules of cultural transmission are more flexible than Mendelian rules, the dynamics of one-trait cultural variation are expected to span a wider range [5].
But the fact that culture, particularly in humans, is acquired cumulatively during an individual's lifespan makes the issue of the interaction between population size and innovation rate more complicated. When individuals are subject to both individual and social learning (i.e. cultural innovation and transmission), each is likely to acquire and express a certain number of different cultural traits during its lifetime (e.g. lists of poisonous foods; techniques to build arrows and make a fire; methods of hunting, cultivation and domestication; modes of social organization; or mystical beliefs). The analogies between cultural evolution models and standard neutral models from population genetics may then fail. Here, the role of the cultural 'memory', or its opposite, cultural 'obsolescence', may be just as important as innovation in producing the distribution of cultural diversity [14,15]. Further, the rules of social learning themselves, such as whether a trait is copied at random from the population or with some particular preference [5,6,13], may critically affect the distribution of cultural diversity at both the individual and population levels.
Understanding why different individuals express different traits thus entails understanding the dynamics of the accumulation of cultural traits (each of which may vary), a process that may be affected by demographic factors as well as the processes of cultural innovation and transmission. In this paper, we study two aspects of the accumulation of multiple independent cultural traits in finite populations (stochastic models). First, we ask how many cultural traits are expressed at a steady state of the cultural dynamics at both the individual and population levels; that is, what is the form of the distribution of the number of traits? Second, we ask how the trait numbers and the level of cultural homogeneity across individuals within populations vary as functions of demographic factors (such as the size of the population or its degree of subdivision) and of the features of social learning rules, such as whether individuals learn from others by random copying, by conformist transmission, or by anti-conformist transmission.
2. Multi-trait cultural model
(a) Individual decision process
We consider a panmictic population of finite size N (see table 1 for a list of symbols). Each individual in this population may carry up to c distinct culturally transmitted traits. We assume that a focal individual in this population is characterized by the state vector 2.1where oi = 1 if this individual carries trait i, oi = 0 otherwise. We assume that each state, absence or presence (0 or 1), of each trait changes in a probabilistic way as a result of individual and/or social learning events (collectively referred to as updating events). Denote by pi the probability that an individual who carries trait i before updating also carries that trait after updating and by qi the probability that an individual who does not carry trait i before updating carries that trait after updating.
Whether the cultural traits are updated synchronously (all individuals in the population update their traits in the same time period), asynchronously (one individual updates per time period), or some mixture of the two, the set of transition probabilities {p1, q1, p2, q2, …, pc, qc} determines the change in the cultural state t = (o1,o2, …, oc) of an individual in the population to a new state t′ = (o′1,o′2, … , o′c) after updating. These transition probabilities can take different forms, ranging from the case where each trait is updated independently from any other to the case where the state of any trait depends on the cultural state of all the other traits of all individuals in the population (e.g. pi = pi(t1, … , tN), qi = qi(t1, … , tN), where tj = (o1j,o2j, … , ocj) is the cultural state of the jth individual). In the latter case, the state of the total population for each cultural trait might affect the dynamics of acquisition or loss of trait i in any individual j; this would produce very complicated cultural dynamics.
For simplicity, we assume that each cultural trait evolves independently of all others. With this assumption, the transition probabilities for a particular trait, say i, are independent of the distribution of the other traits in the population, but depend on the number of individuals in the population carrying trait i (e.g. pi = pi(h), qi = qi(h), where h represents the number of individuals in the population carrying trait i). It then follows that we can track the dynamics of trait i in a finite population independently of what is occurring at other traits in exactly the same way as the simplifying assumption of linkage-equilibrium in population genetics allows one to analyse the dynamics of multi-locus genotypes under different demographic assumptions (e.g. Wright's distribution [16]).
(b) Individual and population stationary trait-number distributions
We allow the distribution of the state of each cultural trait for each individual in the population to eventually converge to stationarity. The independence of the trait-wise distributions then allows us to obtain the individual and population level stationary trait-number distributions, which we define as the distributions of the number of different cultural traits, nf and np, carried at steady state by a focal individual randomly sampled from the population, and by all individuals in the population, respectively.
In order to obtain these two trait-number distributions, we note that the number (random) of cultural traits nf carried by a focal individual is given by 2.2which is the sum over all traits carried by an individual (recall that oi = 1 if an individual carries trait i; 0, otherwise). Similarly, the random number of different cultural traits carried by all individuals in the population is given by 2.3where ai = 1 if at least one individual in the population carries the trait at locus i, and ai = 0 otherwise.
Because the traits are independent, the stationary trait-number distributions (i.e. Pr(nf = j) and Pr(np = j), where 0 ≤ j ≤ c) can be expressed in terms of products of the expectations (means) of the indicator variables appearing in equations (2.2)–(2.3) after each trait has reached its stationary distribution (e.g. E[oi], E[ai], where the expectations are over the stationary frequency distributions of individuals carrying trait i). These expectations give the probabilities that a single, randomly sampled individual and at least one individual in the population, respectively, carry a focal trait.
If each cultural trait were to evolve under a different dynamic from every other trait (e.g. trait-specific updating rules), then the resulting trait-number distributions would not reduce to any simple form. But if one assumes that the parameters describing the dynamics of each cultural trait are the same (i.e. p = p1 = ⋯= pc and q = q1 = ⋯= qc), then at steady state all traits have the same probability of being carried by an individual and are identically and independently distributed. We then denote by ρf the stationary probability that an individual carries a focal trait and ρp the stationary probability that at least one individual in the population carries that trait (ρf = E[o1] = ⋯ = E[oc] and ρp = E[a1] = ⋯ = E[ac]).
If we further assume that the number of cultural traits c that may possibly be carried by an individual becomes very large and that both ρf and ρp become very small as c becomes large, standard results show that the stationary trait-number distributions are Poisson: Pr(nf = j) = 𝒫(j;λf) with parameter λf = cρf, which is the expected number of cultural traits carried by an individual, and Pr(np = j) = 𝒫(j;λp) with parameter λp = cρp, which is the expected number of different cultural traits in the population ([17] with c → ∞ in λf and λp, and 𝒫(j;λ) = exp(−λ)λj/j!). Hence, the distributions of cultural diversity at the individual and population levels are fully characterized by the two means, λf and λp, respectively, of the trait-number distributions.
The fact that both ρf and ρp become vanishingly small as c becomes large can be justified if the total innovation rate of cultural traits by an individual during a given time period is a constant. Then, it is natural to posit that the innovation rate per trait is inversely related to trait number and that both ρf and ρp will be proportional to this innovation rate (see examples below).
(c) Abundance distribution and measure of cultural homogeneity
In order to evaluate the means, λf and λp, of the trait-number distributions, we must find expressions for ρf and ρp. To obtain these, we need the stationary abundance distribution x(i), which gives the probability that i individuals in the population carry a focal trait and which ultimately depends on the transition kernels p and q. From the abundance distribution, one then has 2.4where i/N is the probability that a randomly sampled individual from the population carries the focal trait when i individuals in the population carry that trait and x(i) is the probability of the latter event. We also have 2.5which is the probability that at least one individual in the population carries the cultural trait.
Different individuals will carry different cultural traits and the population will be heterogeneous for the expression of these traits. In order to obtain some intuition about the level of cultural homogeneity in the population, we introduce the probability ρs that two individuals randomly sampled without replacement from the population both carry a focal trait. This is 2.6which is related to the standard population genetic measure of the probability of identity between pairs of distinct individuals (Wright's fixation index [18–21]) except that here we take into account only the probability that two individuals carry the same trait and not the probability that neither carry the trait. From ρs we can evaluate the average number of shared traits between two individuals as λs = cρs because each trait is independent of all others. Then the proportion of shared traits among two randomly sampled distinct individuals in the population is 2.7namely, the average number of shared traits between two individuals divided by the average number of traits per individual.
3. Invention, recollection and transmission of cultural traits
(a) Transition probabilities
Our aim now is to analyse the values that λf, λp and φ can take under various models of cultural evolution. To that end, we assume that both individual and social learning may affect the transition probabilities p(h) and q(h) of a focal trait, where h is the number of individuals in the population carrying that trait. Specifically, we assume that just before updating of a focal trait, a focal individual previously carrying that trait remembers it with probability r and if the trait is not remembered, the individual invents it de novo with probability μ. More generally, r can be interpreted as the probability that the individual retains a trait acquired previously.
If the individual neither remembers nor invents the focal trait, it may be acquired through social learning according to some social learning rule s(y), which gives the probability that an individual adopts the focal trait from another individual when the frequency of other individuals in the population carrying that trait is y. The social learning rule may include transmission schemes such as threshold responses, conformism, or anti-conformism [22]. If the individual had not carried the trait previously, it either invents it with probability μ or it copies it from the population with probability s(y).
From the above assumptions, we have for h ≥ 1 3.1and for N > h ≥ 0 3.2where the first term in both equations can be thought of as the probability of individually learning the focal trait, while the second term is the probability of learning the trait socially.
Because the transition probabilities, p(h) and q(h), apply to each individual in the population, they can be used to derive models of synchronous updating, asynchronous updating or a mixture of these updating processes. It is well established in the stochastic process literature that the simplest process that leads to an explicit expression for the probability x(i) that i individuals in the population carry a focal trait is asynchronous updating (e.g. [16, p. 9], [17, p. 269], [23]). We therefore assume asynchronous updating and the details of the calculation of x(i) are presented in appendix A (see equations (A 1)–(A 5)).
(b) Random copying
In order to investigate how cultural diversity depends on various social learning rules, we start by assuming the simplest frequency-dependent social learning rule; namely, random copying: 3.3Hence, when social learning occurs, an individual copies the trait from another individual randomly sampled from the population, with probability β.
Using equation (3.3) and U = cμ, which is the total innovation rate of cultural traits per individual, we find that the mean λf of the individual trait-number distribution is approximated by 3.4when the number of cultural traits, c, and the population size, N, are large (equations (A 8)–(A 13) of appendix A). This equation shows that λf tends to increase with increasing values of each parameter (U, β, r and N). The second term in equation (3.4) accounts for the effect of stochastic fluctuations in number of individuals carrying a focal trait (i.e. sampling effects). These stochastic effects are greater when there are fewer exemplar individuals in the population from whom to copy traits, which tends to decrease the number of traits carried by a focal individual. The exact expression for λf is graphed in figure 1, but numerical investigations suggest that λf is very well approximated by equation (3.4) for most parameter values.
The expected number λp of different cultural traits in the population when it becomes large is approximated by 3.5which increases with NU, the product of population size and the innovation rate per individual (equations (A 8)–(A 14)). When r = 0 and the third term is neglected, this equation reduces to a result established previously by Strimling et al. [24]. Hence, when individuals carry an infinite number of cultural traits (c → ∞), update their traits through social learning by random copying (e.g. according to equation (3.3)), and have no memory (r = 0), our model becomes similar to that of Strimling et al. [24]; see also equation (A 11) of appendix A. Note, however, that the model of Strimling et al. [24] is based on different biological assumptions than our model. An 'updating' event of cultural traits in their case actually involves a single individual dying and its replacement individual inventing new traits at rate U and adopting each trait of a randomly sampled cultural parent with probability β, which suggests that models with long-living forgetful individuals can be recast as models with short-living individuals with perfect memory. The exact expression for λp is graphed in figure 1, but as was the case for the individual mean, numerical investigations suggest that λp is generally well approximated by equation (3.5) even for population sizes as small as N = 10.
Figure 1 suggests that the average number of different traits carried by an individual can be low while at the same time the average number of different traits in the population may be very high, which suggests that the proportion of shared traits between two individuals, φ, is likely to be low. When the population size becomes large, this proportion is approximated by 3.6We see first that as population size increases, φ decreases and approaches zero and, second, that φ does not depend on the innovation rate U (equations (A 8)–(A 15)). Hence, it is mainly social learning that causes the homogenization of the population, and the higher the memory the higher the proportion of shared traits because individuals tend to remember invented traits, which can then be copied by others. The exact expression for φ is graphed in figure 2, and the approximation of φ given by equation (3.6) is good even for small population size when the parameters β and r are small; otherwise the approximation requires that population size is large (N > 50).
While there might be high cultural diversity in the population at steady-state under the random copying social learning rule, two individuals are unlikely to share the same cultural traits when the population size becomes large (figures 1 and 2). In order to investigate the extent to which this depends on the assumptions of the learning rule (equation (3.3)), we now analyse the values that λf, λp and φ can take under other social learning rules.
(c) Beyond random copying: sensitivity to minority and biased conformist transmission
In copying the cultural traits of others in the population, individuals may express various preferences resulting in different social learning rules [22]. Here, we consider preferences that result in sensitivity to minority or biased conformist transmission. These two cases can be analysed with the following social learning rule: 3.7When α = 1 we recover the random copying social learning rule (equation (3.3)), while for α < 1 the probability of adopting a focal cultural trait is increased at low prevalence of the trait in the population (e.g. sensitivity to minority). When α > 1 we have biased conformist transmission, and the social learning rule curves down at low prevalence (i.e. it is convex) and up at high prevalence.
How λf, λp and φ vary as functions of the parameters for these two social learning rules is graphed in figure 3. Sensitivity to minority (α < 1) increases both λf and λp relative to the random copying rule. Each individual is then likely to carry more traits. But for a given value of population size N, the difference between the mean number of traits carried by an individual (λf) and the mean number of traits expressed by all individuals in the population (λp) decreases. Hence, the population becomes more homogeneous in the expression of cultural traits. This can also be noted from figure 3, which shows that the proportion of shared traits between two individuals, φ, no longer goes to zero as population size increases (as occurred under random copying, figure 2) but reaches a steady-state value. This is because under sensitivity to minority if there is one individual carrying a focal trait, then it is very likely to be copied by another individual in the population, thereby increasing the proportion of shared traits.
Exactly opposite patterns to those of sensitivity to minority are observed under conformist transmission (equation (3.7) with α > 1), where both λf and λp decrease relative to the random copying rule and at the same time the population becomes more heterogeneous (figure 3). Hence, as α increases, the proportion of shared traits between two individual traits decreases rapidly as population size increases (compare figure 3c and 3f). This is because in the limit of a large number of traits, the frequency of appearances of each trait will be low (as innovation per trait is very low). Under conformist transmission individuals are unlikely to copy a trait that is at low frequency in the population (say a trait carried by a single individual); hence conformist transmission will inhibit the increase in the number of individuals carrying a focal trait, thus decreasing the proportion of shared traits in the population.
(d) Culturally structured population
So far we have assumed that individuals interact at random in the population, but in reality interactions may be localized as individuals copy cultural traits from neighbours rather than from strangers [25]. In order to take such cultural viscosity into account, we now assume that the population consists of an infinite number of groups, each of finite size N. When a focal individual in a given focal group updates a focal trait, we assume that it copies a random individual from its group with probability (1 − m) and copies another individual, randomly sampled from another group, with probability m, where the parameter m can be thought of as the probability of learning from outsiders. With these assumptions, the social learning rule is now given by 3.8where y is the frequency of individuals in the focal group (excluding the focal individual) that carry the focal trait and ρf = ∑i x(i)i/N is, as before, the probability that an individual randomly sampled from the total population carries a focal trait. Here x(i) is the stationary probability that a group in the population contains i individuals that carry the focal trait, in which case the focal individual copies one of these with probability i/N (see also appendix Ab).
How λf, λp and φ vary as functions of the probability m of learning from outsiders ('cultural migration') in the presence of random copying (equation (3.3)) is illustrated in figure 4. As the rate m of cultural migration increases, the number of cultural traits expressed by a single individual or by all members in a group increases. This is because, as cultural migration increases, individuals tend to copy traits from others in the population with a fixed probability (i.e. second term in equation (3.8)), instead of copying individuals locally where the prevalence of a focal trait may fluctuate as a result of sampling effects. When m = 0, the model becomes similar to the panmictic finite population size model investigated above (equation (3.3) in equation (A 1)), which can be interpreted as the situation where a focal group of size N is completely isolated from other groups in the population (no exchange of cultural traits between groups). By contrast, when m = 1, the model becomes similar to the situation of a panmictic population of infinite size (equations (A 16)–(A 20) of appendix A), in which case there are no longer fluctuations in abundance frequencies owing to finite population size.
It follows from these considerations that the proportion of shared traits between individuals decreases as the rate of 'cultural migration' m increases (figure 4), and, as was the case for the panmictic model, the proportion of traits shared between individuals decreases as population size increases, which also reduces the magnitude of the sampling effects. The effect of demographic factors (here N and m) on the level of cultural homogeneity φ within groups is, therefore, qualitatively similar to the effect of these factors on the probability that two individuals carry identical variants in standard neutral evolutionary models, whether the variants are genetic [1,26] or cultural [5].
(e) Norms
So far we have assumed that the cultural traits are expressed as a result of decisions taken by individuals alone. But some decisions are taken collectively; they are made not by individuals acting alone, but by groups of individuals. Suppose that the group of N individuals has to choose whether or not to adopt a cultural trait at the population level, which we call a norm. Thus a norm is interpreted as being a cultural trait that results from the aggregation of cultural traits expressed by single individuals. In reality, the aggregation process may be a function of the cultural profiles of all individuals in the population and is therefore likely to be a complicated function of the expression of several different traits by each individual.
For simplicity, suppose that a norm results from the aggregation of the expression pattern of a focal trait only. We can then define the aggregation function A(o1,o2, … , oN) ∈ {0,1}, which maps the cultural pattern of the focal trait into presence or absence of the norm, where oj is the cultural state at the focal position of the jth individual. In order to evaluate the likelihood that the norm is expressed for various transmission rules, we introduce an ε-majority rule Aε such that Aε = 1 if the number of individuals carrying the trait at the focal position in the population is equal to or greater than ε: that is, Aε = 1 if ∑i =1N, oi ≥ ε; Aε = 0 otherwise. Given an ε-majority rule, the probability ηε that a norm is chosen by the individuals in the population is 3.9from which we can evaluate the probability of occurrence of a norm for the ε-majority rule under the sensitivity to minority and biased conformist social learning rules (the choice of the ε-majority rule and the implementation of the norm itself are other problems, whose analysis would entail modelling the games individuals are playing in the population). This is graphed in figure 5. The probability of adopting the norm is greater under sensitivity to minority than under biased conformist transmission unless the threshold ε becomes very high. This is due to the fact, already encountered, that at low prevalence the sensitivity to minority social learning rule tends to increase the prevalence of a trait in the population because individuals not carrying that trait tend to adopt it.
4. Discussion
We have presented a model for the accumulation of independent cultural traits through individual and social learning in finite populations. This multi-trait cultural model allows us to characterize the cultural diversity at the individual and population levels at the steady state of the learning dynamics and as a function of various features of the demography and the rules of cultural transmission. Our model has features in common with multilocus population genetic models [16], and is directly related to previous models of stochastic cultural evolution. When individuals in the population carry only a single trait (c = 1), it is similar in essence to the model by Lumsden & Wilson [22]. In contrast, when individuals may carry an infinite number of cultural traits (c → ∞), social learning occurs through random copying (equation (3.3)), and individuals have no memory (r = 0), our model becomes similar to the multi-trait model of Strimling et al. [24].
Our results suggest that when individuals may invent infinitely many cultural traits, the stationary individual and population-wide distributions of the number of distinct traits are Poisson. The means of these two trait-number distributions (λf and λp) then fully characterize the cultural diversity at the individual and population levels because of our assumption of the independence of the cultural traits, which is probably the most stringent of our model. But this assumption allows us to establish a null model for the trait number distribution that is tractable and to which other results can be compared. For instance, the Poisson distribution plays a central role in population genetics as the null model of reproduction (e.g. the ideal Wright–Fisher population, [3,16,27]), and it is by reference to this model that the effects of relaxing demographic assumptions may be assessed. One could thus relax the assumption of the independence of traits, and investigate how this might affect the steady-state distribution of trait-number at both the individual and population levels. Further, memory (r) might be modelled as a decreasing function of the number of traits an individual carries, or the total innovation rate (U) might be modelled as an increasing function of this number.
The means of the trait-number distributions (λf and λp) and the proportion of traits shared between two randomly sampled individuals (φ) are critically affected by the demographic details and the social learning rules. In a panmictic population with random copying (equation (3.3)), there might be high cultural diversity in the population, while at the same time single individuals may carry only a few traits (figure 1). The population will then be culturally heterogeneous, as any two individuals are unlikely to share cultural traits in common (figure 2). While this pattern seems somewhat counterintuitive as we expect individuals within populations to share cultural traits, random copying is probably the social learning rule that makes the accumulation model presented here closest to standard neutral models of population genetics. Indeed, it was shown by Strimling et al. [24] that with a change of variable one can recover from the mean number of traits λp, the expected number of different variants segregating in a population in a one-trait model, a well-known result in population genetics [10,16].
When social learning does not occur by random copying, very different levels of cultural homogeneity are observed. With biased conformist transmission two randomly chosen individuals are very unlikely to share common cultural traits, even when population size is low (figure 3). In contrast, when individuals express sensitivity to a minority, single individuals carry more cultural traits, two randomly chosen individuals are very likely to share common cultural traits, and cultural homogeneity of the population is increased (figure 3). These opposite patterns follow from the fact that if there is only one individual carrying a focal trait, then it is very likely to be copied by another individual under sensitivity to minority. By contrast, that trait is very unlikely to be copied by another individual under biased conformist transmission, thus preventing an increase in number of the focal traits in the population. Although this inhibiting effect of biased conformist transmission for the accumulation of cultural traits has not been recognized in the literature, one expects it to be observed more generally as most traits are likely to appear initially as a single (or a few) copy(ies) in a population.
Introducing population subdivison by allowing individuals to learn from others outside a focal group reduces the local fluctuations in abundance frequencies owing to sampling effects in finite populations. The result is an increase in the number of different traits carried by individuals (figure 4). This, in turn, decreases the level of shared traits within groups, φ, which also decreases with group size in exactly the same way as in a panmictic population (compare figures 2 and 4). The effects of the two demographic factors, m and N, are qualitatively similar to the effect of spatial structure on the distribution of genotypes within and between groups (e.g. [1–3]). Hence, the effects of demographic factors on the trait-number distribution appear to be qualitatively equivalent to their effects on the distribution of variants of a single gene (e.g. [1–3]).
We have assumed that infinitely many cultural traits may be invented but the number of possible independent cultural traits may be finite. From a qualitative point of view, allowing for a finite number of traits should not affect the main results reported here, because the assumption that all c traits are independent of each other allowed us to derive our results from single-trait dynamics; the number of different traits carried by an individual (or by all individuals in the population) then varies directly with c, holding everything else constant.
We have not incorporated organismal birth and death into our model. Including such features should not affect the qualitative results reported here if the number of updating events occurring during the lifespan of an individual is sufficiently large that the updating process converges approximately to stationarity. It would be interesting, however, to study the accumulation of cultural traits in the presence of a few transmission rounds within the lifespan of an individual and with intergenerational effects, which would follow from including organismal birth and death.
Overall, our results suggest that the cultural diversity at both the individual and population levels (λf and λp) are increasing functions of the demographic factors, namely the population size (N) and the cultural migration rate (m), and of the organismal parameters, namely the number of cultural traits (c) an individual may possibly carry, the per trait innovation rate (μ), the memory (r), and the probability of adopting traits learned socially from others (β). Hence, in addition to the demographic parameters and the innovation rate, which are well known to play an important role in describing diversity in classical population genetic models, the memory, and the intensity of cultural transmission (as well as the mode of transmission) are also likely to affect patterns of cultural diversity at both the individual and the population levels. All of the organismal features encountered may be under partial genetic control and thus subject to genetic evolutionary change. We can speculate that such genetic control of these parameters may have implications for the evolution of modern humans from their less culturally capable predecessors, or for their success in overcoming less cultural contemporary groups.
We thank two reviewers for useful comments that improved this manuscript, in particular for suggesting use of the number of shared traits φ as a measure of cultural homogeneity. We are grateful to K. Laland and his laboratory members for many helpful comments on the paper. This work is supported by grant PP00P3-123344 from the Swiss NSF to L.L., by NIH grant GM28016 to M.W.F. and by Monbukagakusho grant 17102002 to K.A.
One contribution of 14 to a Theme Issue 'Evolution and human behavioural diversity'.
- Received September 13, 2010.
- Accepted September 13, 2010.
- This journal is © 2011 The Royal Society
Appendix A
(a) Stationary abundance distribution
(i) Asynchronous updating
In this appendix, we present an explicit expression for the stationary probability x(i) that i individuals in the population carry a focal trait under asynchronous updating. For this case, the updating process follows a so-called birth–death process (e.g. [16, p. 91], [17, p. 269], [23]), and the stationary distribution is given by A 1where x(0) is chosen so that ∑i=0Nx(i) = 1; b(h) is the probability that, conditional on an updating event taking place in a population with h individuals carrying a focal cultural trait, a new individual carries that trait after updating; and d(h) is the probability that, conditional on an updating event taking place in a population with h individuals carrying the cultural trait, one fewer individual carries the trait after updating ([16, eqn 2.162]).
The values of b(h) and d(h) can be obtained from equations (3.1)–(3.2) by noting that in a population with h individuals carrying the focal trait, an individual not carrying it is sampled to update its cultural loci with probability (N − h)/N, in which case it carries the focal trait after updating with probability q(h), while an individual carrying the focal trait is sampled to update its cultural loci with probability h/N, in which case it does not carry the trait after updating with probability 1 − p(h). Thus A 2and A 3and on insertion of equations (3.1)–(3.2), one has A 4and A 5Note that these equations imply that a single individual updates all its cultural traits simultaneously. Alternatively, one could assume that a single individual in the population updates one cultural trait per unit time, in which case the right-hand sides of equations (A 4)–(A 5) would be divided by c, which will not affect the stationary abundance distribution but only the rate of convergence to equilibrium.
(ii) Linear updating
Substituting equation (3.3) and equations (A 4)–(A 5) into equations (A 1), we find after rearrangement that the stationary distribution can be expressed as A 6which allows us to evaluate ρf and ρp by using equations (2.4)–(2.5). The resulting expressions are complicated and involve hypergeometric functions, but can be easily calculated numerically, for example with Mathematica [28]. In the absence of memory, i.e. r = 0, however, it can be shown that A 7which is the same probability as that found in a population of infinite size (see equation (A 20)). No such simple expression was found for ρp when r = 0. In order to obtain more tractable analytical expressions than equation (A 6), we will evaluate the trait-number distributions in the limit as the number of cultural traits and population size become large.
(b) Culturally structured population
In a culturally structured population with an infinite number of groups following the same updating process, groups affect each other in a deterministic way [29]. Then, x(i) gives both the probability that i individuals in a focal group carry a focal trait (and thus satisfies equation (A 6)) and the probability that a randomly sampled group in the population consists of i individuals carrying a focal trait, which may affect the transition probabilities of the state of a focal group. This is the case for the updating probabilities p(h) and q(h) given by equations (3.1)–(3.2) (with equation (3.8)) of the main text, which are now functions of the stationary distribution itself through their dependence on ρf. Thus we can no longer obtain an explicit expression for x(i), which is now implicitly determined (e.g. insert equation (3.8) into equations (3.1)–(3.2), then equations (3.1) and (3.2) into equations (A 4)–(A 5)). This distribution can, however, be evaluated numerically from ρf = ∑ix(i)i/N, which has a closed form once equations (3.1)–(3.2), equation (3.8) and equations (A 4)–(A 5) have been inserted into equation (A 1). From this, we can then compute λf, λp and φ, which are presented in figure 4.
(c) Large population size
(i) Large population size approximation
Our aim in this section is to obtain a large population size approximation for λf, λp and φ when the stationary abundance distribution is given by equation (A 6). To that end, we use the variable , which can be interpreted as the expected number of traits of popularity i in the population (a quantity introduced by [24]) in the limit of an infinitely large number of traits. With this, we have A 8 A 9and A 10where we used equations (2.4)–(2.6).
By using μ = U/c in equation (A 6), it can then be shown that the expected number of traits of popularity i in the limit of an infinitely large number of traits (c → ∞) is given by A 11which, when r = 0, is equation (2) of Strimling et al. [24]. The derivation of equation (A 11) from equation (A 6) by using and μ = U/c is a bit messy to check by hand but it can easily be done with a symbolic algebra system such as Mathematica [28].
A first order Taylor expansion of equation (A 11) near N = ∞ with Mathematica gives, for N > 2 and 0 < β < (N − 1)/N, A 12where csc(·) is the cosecant function. Substituting equation (A 12) without the O(1/N2) term into equations (A 8)–(A 10) and letting N → ∞ in the summation gives A 13 A 14and A 15Substituting equations (A 13) and (A 15) into equation (2.7) gives φ ≃ β /[N(1 − β − r)] + O(1/N2). Note that N ≃ N − 1 when N is large and that Strimling et al. [24] used a different approximation in order to derive their expression for λp (their proposition 1).
(ii) Infinite population size
In this section, we present an equation for the dynamics of ρf for a focal trait when the population size becomes infinitely large. In that case, we can neglect fluctuations in the number of individuals carrying the trait during updating because the probability that a randomly sampled individual carries the trait converges to its expectation. Then, the probability p(ρf) that a focal individual who carries the focal trait before updating also carries that trait after updating can be written as a function of the expectation ρf that a randomly sampled individual from the population carries the trait. Similarly, the probability q(ρf) that a focal individual who does not carry the focal trait before updating carries it after updating becomes a function of ρf. Hence, the probability ρ′f that a focal individual carries the trait at the focal locus just after it has updated that position can be expressed as A 16and given the forms of p(·) and q(·), equation (A 16) can be solved for ρf at equilibrium; that is when ρ′f = ρf.
For our model, with random copying, the transition probabilities are, from equations (3.1)–(3.2), given by A 17and A 18
Substituting equations (A 17)–(A 18) into equation (A 16) and solving for ρf, the equilibrium probability that an individual carries the focal trait becomes A 19and in the absence of memory, r = 0, this reduces to A 20
Substituting μ = U/c into equation (A 19) and taking λf = limc→∞ cρf, we find that the mean of the trait-number distribution is given by λf = U/(1 − β− r).


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The EF-S 10-18 mm f/4.5-5.6 IS STM lens combines optical excellence with cutting-edge performance, providing an ultra-wide angle of view in a compact, portable package, perfect for EOS cameras with an APS-C sensor. It has a 4 group optical zoom system and includes a large-diameter element, an aspherical lens element, a UD lens element and enhanced lens coatings for high-contrast, high-resolution images with minimal glare and aberration. A circular, 7-blade aperture helps ensure fine background blur and the Canon Optical Image Stabilizer system provides up to four equivalent stops of shake correction. The lens has a stepping motor (STM) and a refined focus mechanism for smooth and continuous AF during video recording. It also has a rear focusing system, plus a high speed CPU and improved AF algorithm for high-speed AF; and offers full-time manual focus for quick adjustments. The EF-S 10-18 mm f/4.5-5.6 IS STM delivers reliable, speedy and quiet wide-angle performance, making it an ideal lens for everyday photography, travel, stills and video recording.
8.50 oz
EF-S ultra wide zoom lens with an impressive starting focal length (16mm in 35mm equivalence).
Compact design made possible by a new 4 group zoom optical system.
A stepping motor (STM) and newly-designed focus mechanism support the Canon EOS Movie Servo AF function to provide smooth and quiet continuous AF during video recording, as well as when shooting photos.
A large diameter element and an aspherical lens element help correct aberration to achieve higher image quality
One UD lens element helps reduce chromatic aberration throughout the zoom range for excellent image quality with high resolution and contrast.
Optical Image Stabilizer for up to four stops of correction.
Enhanced lens coatings help ensure outstanding color balance while minimizing ghosting and flare.
Circular aperture (7 blades) creates beautiful, soft backgrounds.
Rear focusing system, high-speed CPU and improved AF algorithm allow high speed autofocus.
Full-time manual focus allows manual focus adjustment while in AF Mode.
lens, lens cap, dust cap, documentation
Focus Adjustment: Automatic, ManualImage Stabilizer: Optical
Color: Black
Focal Length (max): 18.00 mmFocal Length (min): 10.00 mmLens Aperture: F/4.5-5.6Lens Type: Wide angleMounting Type: Canon EF
Magnification: 0.15 X
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Community Activists Network
The recent Liam Stacey case where a member of the public was jailed for 56 days for use of abusive, racist and threatening language has raised many questions about the emergence of Twitter and other forms of social media in a stable and cohesive society. We clearly live in an information age unlike any previously experienced with rolling 24/7 news output across several media, the internet in the palm of ones hand and the ability to communicate with millions across any time zone and all hemispheres instantaneously. The main qualitative differences here are that social media and the internet allow us to 'engage' – as the contemporary parlance describes it – with each other, the State, organs of power, business and political leaders, our favourite (and least favourite) footballers and soap stars – the list is as long as there are people with access to such technology. This new 'White Heat' of E-technology is a far cry from Harold Wilson's post-War 1960s optimism of technology being the key that turns the lock to industrial and technological advancement of our society and subsequent economic growth and liberty. We are facing something far more powerful yet if we fail to harness its power correctly something potentially more damaging and uncontrollable. Far be it from me to present myself as a Luddite for the new Millennium but the acceleration of how much society has embraced Twitter for instance is as exponential in its pace as it is ubiquitous in its regard. Where will this accelerated shift in the very nature of the way we communicate with one another and the way in which the individual communicates with the State and the general hegemony is beyond my comprehension. Whilst a dystopian vision of the future through some hermetically generated existence where we are all conjoined to our media tools is far from a reality I believe that we need to start assessing the best way to reap the benefits of social media as well as identifying the key dangers vis-a-vis community engagement.
Whilst policing is learning to address the reconfiguration of its services in a very new socio-economic and political landscape than just three years ago, recent notions of 'community policing', 'community cohesion' and 'participatory policing' are having to be reshuffled, unpicked, and re-evaluated in different more innovative ways. I have always been a strong advocate of such seismic change (of any form) being the crucible of innovation and these current changes are almost forcing the police (amongst other services) to come up with new more resourceful yet high impacting methods of policing our communities. The embracing of social media and Twitter in particular is far more than the police engaging in a 'Bring Your I-Phone to Work Day'. I personally receive Twitter-feeds from dozens of Police Divisions daily and this is growing rapidly. Those at the top are clearly aware of this and have sanctioned it but are they completely aware of the potential hazards of their rank-and-file staff's unchecked Twitter output?
Back to the Liam Stacey case: the standard Red-Top induced knee-jerk reactions from many quarters have inevitably begun. Those who believe that this is a clear indication that we need to closely monitor and police the 'virtual streets' more and those who feel that any greater political powers are effectively an Orwellian 1984 Police-State by the back-door, and then those who simply see that we are simply lacking the manpower and resources to do this even if we wanted to. I tend to be a little more circumspect in my appraisal of what is clearly a test-case here with Liam Stacey. The great frontier is opening in front of us – like Vasco de Gama, Magellan and the Wagon Trains we know not what to expect apart from the fact that we are venturing into the great wide open searching for new ways – all permutations and developments are possible. Not so much a Brave New World but the same one with fundamentally changing methods of interaction, exchange of knowledge, expression of emotion, shifting language and a second wave of declining deference to the institutions that for so long dominated the crime and disorder discourse – what sociologists and Gramsci referred to as the 'hegemonic bloc'.
One cannot put the Genie back in the Bottle and yet there is something rather primal and natural about the ephemeral tweet; a scream into the ears of millions of people in less than 140 characters instantaneously is a concept that even 20 years ago would have appeared to be something from a Star Trek episode or an Asimov novel. Such untrammelled power certainly raises many questions about the suitability of current legislation such as the already considerably outdated Communications Act (2003) which was tabled before Twitter was even invented!
It has also effected considerable debate about traditional notions of the interface of the state with the individual and what constitutes 'privacy' anymore – is it the Tweeter or the person Tweeted (the Tweetee perhaps) about whose privacy and freedoms must take primacy? I fear that the Civil Liberties of the former cannot be so readily reconciled with the legal protection of the latter's and certainly not with the currently weak legislation. Perhaps we must accept that the pace of technology and the Twittersphere/Blogosphere/Web (even the jargon changes so rapidly – language cannot keep up with the rapidity) of this ubiquitous techno-soapbox. The advent of social media has eroded privacy as we know it and perhaps traditional notions of policing and engagement will be insufficient to keep up with such shifts. For example if local CDRPs (Crime and Disorder Reduction Partnerships) are to remain true to their statutory obligations under the Crime and Disorder Act (1998) to combat Hate Crime and, say, conspiracy to riot etc. then this will require almost constant monitoring (even on a local basis) in order to suggest a solid commitment to such a Zero-Tolerance attitude to such (mis-)use of social media. Of course there will be the inevitable prioritisations as there have hitherto been in policing the internet through the emergence of video, mobile-phone and internet advancements over the last 30 years where they have been used to facilitate paedophile rings, illegal pornography, serious organised-crime and terrorist activity. But such cases by definition are cases where those who are suspects are monitored within the law in order to collate evidence to submit to the CPS. To suggest that, even in more financially profligate times, there could ever be a practical way of resourcing the requisite number of staff and technology to monitor all social media output is mere fantasy and akin to Sisyphus pushing that rock up the mountain side - that is to say self-defeating use of energy at best and more evidently impossible as time goes on. The current austere climate of post-CSR cuts and the behemoth nature of the internet would preclude most this anyway. Instead of attempting to be Masters of the Oceans we need to respect it and be aware of its power – discipline, best practice and planning. Many people use social media ineffectively and with scant regard for who is reading. Those people will learn through their mistakes a la Liam Stacey. The police cannot afford to make such errors and should learn NOW. As one Police Senior recently said "If we can teach them to shoot guns properly then we can teach them Tweet properly".
Some positive usage of Twitter by GMP during the Manchester riots, despite there being solid evidence of conspiracy to riot and communication between the rioters through social media that in many cases effected some kind of military operation on their behalf – a game of virtual tag ensued according to some reports from Police Officers and community leaders I have spoken with. Of course many of us could have turned off the TV and radio and simply watch things unfold on Twitter etc. This being so much the case that because of the lack of information being fed to reporters on the ground the main news networks' broadcast was taken up with Twitter-based reports and discussion/conjecture/hearsay. This of course is a rather dangerous precedent for the media but offers the police and the CPS some real clues if not evidence of the actions and identities of many of the looters and rioters. Of course this is somewhat of a special case and everyday community policing is very different. Effective usage of social media by the police however has great potential – if harnessed and used thoughtfully and strategically. Crime prevention tactics and hints at particular times of year or in particular weather for instance have already proved to have an impact upon local crime and disorder. With community policing and 'marketing' the message and image of the police in communities then it can act as a really effective tool in communicating with dis-engaged youth, hard to reach groups, BME communities, repeat offenders et al. The very people that the police suffer the perennial problem of engaging with in anything other than an operational face-to-face. Twitter will not change the 'game' of many of these groups' attitudes towards them but it may create an extra new mode of communication between them.
Many police often tell me that the problem with many young people who drift into delinquency and criminal behaviour is the importance of peer pressure and 'street respect' – being seen 'talking to a Copper' or being stopped in a group and being seen to cooperate can be not only socially exclusive but also potentially dangerous for that individual. 'Most of them are OK when you get them on their own' is the standard mantra and surely Twitter is a potentially great way of getting messages over to many individuals as an early intervention away from the gang, street, classroom etc. I am focussing mainly up the young here not because I believe that they were wholly or even mainly responsible for the recent riots or even for most crime but in terms of community policing there are key strategies of early interventions working in partnership with other key agencies which can stem the drift of many young people into crime and delinquency. If used properly social media can be an excellent lever of such new modes of engagement.
However, there are certain risks and dangers with Twitter and the internet in general and it would be remiss of any of us to assume to the police would be immune to such backfires, be they conscious or unwittingly so. The seemingly ephemeral nature of conveying a message to the 'Twittersphere' of less than 140 characters with such immediacy actually belies the hugely harmful impact that a slightly ambiguous or misjudged Tweet can cause and if this comes from a member of the Police then the harm done to local community relations and community policing in general can be so acute that in mere seconds, years of community cohesion and community relations can be undone. Much common sense comes into play here and self-policing from all Tweeters is the order of the day. However if the trend of police forces embracing the social media continues then it will not be too long before every operational member of the police (and beyond) are all expected to Tweet on a daily basis.
There are too many pitfalls as well as positive outcomes of effective usage of social media in communities to explore here but we certainly welcome your experiences, comments and thoughts for the future on this topic.
If you wish to discuss how Grant Moar Communities can assists you in embracing Social Media effectively whether you are a member of a key agency like the Police or a community based group or if you are interested in any of our other support and training services in community safety then please feel free to get in touch with us for a chat:
Facebook: Grant Moar Communities
Twitter: @lolgrant7 or @Max Moar
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Our local police tweet and it's a great service as far as I'm concerned. I would know nothing about local crime or police activity otherwise. They also use email but for me twitter is better.
You mentioned the Liam Stacey incident.
Do you have a view on the points made in this article?


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Why MCA?
We have a broad and purposeful view of education. We do much more than teach the subject areas. We are preparing our students to be virtuous, intelligent citizens who lead in a constitutional democracy. We believe in pursuing truth, goodness, and beauty, so that we might gain a deeper understanding of the world and live life more authentically. We believe in the classical structure of liberal education.
Imagine: a nation that was conceived as a city on a hill to shine for all the world to see. Imagine: eleven score and three years ago, our forefathers brought forth on this continent a new nation, conceived in liberty and dedicated to the proposition that all men are created equal. Imagine: this nation one generation from now, who in turn passes on for generations to come, not only the ideals and principles, but also the wherewithal for a more perfect union, with truer justice, with widespread domestic tranquility, with a more invulnerable common defense, with a deeper sense of personal and national well-being, and with the blessings of liberty more securely intact.
We do not necessarily channel our students into the political arena nor into the military field nor any particular career. It does not matter whether our students are butchers or bakers or candlestick makers. What matters is that we help equip them in how to live… as intelligent and virtuous citizens who lead.


text: I've noticed that there's a lack of oval events in RD. I understand that stock cars and oval racing is an acquired taste. But would there be any interest in Indy that runs 45%/55% ovals to road courses? So would it be possible to get an Indy RD league running? Is the RD community interested in participating in Indy?


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Discussion in 'Adwords' started by MiodragM, Jan 27, 2010.
Or do I have to buy my own domain?
it's always better to have your own assets.
but, for starters, you should at least buy dot info for .99
just in case google decides to delete your blog. at least,
you're not losing traffic and can redirect the traffic to
temporary landing page.
forget about hosting first. when you've enough money
n solid plan, then invest your money to another
project. but, this time, you should buy dotcom domain and hosting.
that's how i'll do it. poor to rich style plan.
Of course you can, but as penaakul wrote it's better to atleast buy a domain or get a free one (I don't know where) just so that your traffic stays flowing. If your good at designing you can make pretty decent sales page in blogger.
Quick tip:
Put this code in your template (HTML) to remove navbar.
Before the line, add in the following line of code:
#navbar { display: none; }
(Put it after ]]>)
Dude, if you have money to play the adwords game then surely you can spare 10 bucks or so to buy a domain!!!
Separate names with a comma.


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It's pickling time!!! Homemade picked everything! Today is all about a super easy basic pickling liquid that's perfect for healthy and delicious pickled red onion, chard stem, and baby fennel recipes and so many more!
There just aren't many things that are better to have on hand than things that have been pickled fermented and cultured. (As I recently mentioned when discussing easy homemade kefir)! Simple, cheap, and so rewarding, these foods pack a healthy punch with an incredible flavor that make absolutely everything more fun and exciting to eat. Add them to soups, sandwiches, salads, and even pizzas and you'll be amazed by the complexity they add to every dish. (You should try these pickled chard and fennel recipes in everything! Even blended into salad dressings and spreads!) Plus, there are all of these health benefits to pickled foods that are even better when you make them yourself.
As with all foods, pickled things can be as simple or as complex as you want them to be. There is absolutely no end to the fun you can have with your pickling liquids. You can add chili flakes and garlic, pickling spices (your own or one of the many blends out there), you can try cumin, coriander, and, fennel seeds, star anise, cinnamon, or anything else your heart desires! Ginger, citrus, and peppercorns add an amazing layer to your homemade pickles.
However, for those just starting out, you can totally use one absolutely basic pickling liquid for many, many different types of ingredients and just let your produce shine through. That's what I'm going to show you today. One simple pickling liquid that will work incredibly well for just about all of your homemade pickles. Today's basic pickling liquid is great for a ton of different pickles, not just for chard and fennel recipes.
Want to get creative? After you bring your liquid to a boil, turn it off, add your fun extras and let them just sit for about thirty minutes. Then strain them out, bring your liquid back up to a boil, and pour the liquid over your produce. You can, of course, also just leave your spices right in the liquid if you want! Just make sure you like those flavors, because they will continue to get stronger for a little while.
In the garden, my fennel is going crazy, so I wanted to pull a bunch of it out so that the remaining fennel would have more room to grow big and fat. I was considering all kinds of fennel recipes! Pickled fennel has a wonderful licorice-y flavor and is absolutely delicious in salads, salad dressings, and on sandwiches, so making a jar of pickled fennel was a no-brainer. I pulled out the smaller baby fennel to make room for the others, so they are what's in the picture. You can definitely pickle mature fennel, just cut it into strips or wedges first. If you are using baby fennel, cut any large pieces in half or in quarters so that the liquid can do its thing. Don't be afraid to add the stems as well if you have them! They have great flavor and hold up really well to being pickled. Fennel is one of the many plants that you can use all of the parts of in your fennel recipes, so don't let all of that good flavor end up in the trash. Not just the bulbs, but the stems, fronds, and the seeds, and pollen are fantastic, which is one of the reasons they're so rewarding to grow. (Another reason is that here in California, fennel grows so easily it's sometimes considered an invasive species. You can find it growing wild along the roads and highways.) A year or two ago, while testing and tasting everything in the garden, I discovered that green (immature) fennel seeds are also absolutely delicious! They're fantastic on their own, plus they make seriously nice tea.
It's also time to clear out my chard now that the weather is warming up. The next round of backyard garden produce needs room! The chard in the garden is just starting to try to bolt, so it makes sense to cut it down and make room for some new plants. While many people have a ton of favorite recipes for chard leaves, the stems often get overlooked, which is a huge shame. Chard stems taste absolutely amazing raw (I worked for a very famous chef who just loves raw chard stems; they remind her of her childhood. She likes to reach out and grab a few stems when chard is on the menu and we're prepping mountains of it, snacking on them as she passes through the kitchen): they're light, delicate, and watery like celery, but with a fresh and bright flavor. There are way too many great ingredients out there that end up in the trash! I've said it before and I'll keep saying it. Keep tasting everything! You might find that you just love something that you would never have thought about otherwise.
A lot of pickles follow the same basic technique.
- Clean your ingredient (trim it if it's too big/thick) and put it in a nonreactive container (glass is great)
- Bring your pickling liquid to a boil
- Pour it over your ingredient, making sure that your ingredient is totally submerged. (You might need to cover it or weigh it down to keep it below the liquid.)
- Let it cool, and keep it in your refrigerator.
That's it! Super simple.
Now, there are plenty of recipes that don't follow these steps exactly, but so many of them do. If you have really strongly flavored ingredients like garlic and ginger, you frequently want to boil them before you pickle them. There are also recipes that call for salting your ingredient first to draw out the excess moisture and bitterness. However, for fresh produce like chard stems, baby fennel, onions, shallots, radishes, celery, carrots, beans, and so on, that's totally unnecessary. Just bring your liquid to a boil and pour it over!
Basic Pickling Liquid for Homemade Pickles
(Perfect for Red Onion, Chard, and Fennel Recipes, Plus Others!)
- 3 cups vinegar (rice wine, champagne, or any other vinegar or combination of vinegars you like)
- 3 cups water
- ¾ cup sugar
- ¼ cup salt (I prefer Kosher Diamond)
- Bring all of the ingredients to a boil, and make sure the sugar and salt are dissolved completely.
- Pour over your ingredients in a non-reactive container (glass is perfect), making sure your ingredients are completely submerged (weigh them down if necessary).
- Allow to cool. Keep in refrigerator.
Looking for more cool DIY ideas and homemade pantry staples? You might like
Unbelievably Easy Two-Ingredient No-Cook Preserved Lemons
Liquid Sunshine: Homemade Limoncello
Creamy and Decadent Homemade Ricotta
Seriously Simple Homemade Kefir Yogurt
Basil Oil (or Whatever Green Oil You Like!)
Crazy Easy Chili Oil (plus Szechuan Chili Oil and Fermented Kimchi Hot Sauce!)


text: Have you already read The Joy Formula? by Mary | Dec 3, 2015 | The Joy Formula | 0 comments Click the title of this post to leave a comment. I'd love to hear from you. XO Mary Submit a Comment Cancel reply Your email address will not be published. Required fields are marked *Comment Name * Email * Website Notify me of follow-up comments by email.