{'fraction_non_alphanumeric': 0.027062999112688554, 'fraction_numerical': 0.01774622892635315, 'mean_word_length': 5.370056497175141, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
ECOLOGICAL VERSUS EVOLUTIONARY HYPOTHESES: DEMOGRAPHIC STASIS AND THE MURRAY‐NOLAN CLUTCH SIZE EQUATION

In explaining patterns ofphenotypic variation in and among natural populations, it is important for evolutionary biologists to consider alternative hypotheses. In particular, basic ecological principles may often offer parsimonious explanations ofpatterns observed in nature and should always be considered when examining putative evidence for specific evolutionary hypotheses. As an example we will draw on Murray's (1979, 1985; Murray and Nolan, 1989; Murray et aI., 1989) hypothesis that natural selection "favors females that lay as few eggs as are necessary for replacement" (Murray and Nolan, 1989 p. 1699). Specifically, we will focus on an equation (most recently presented in Murray and Nolan, 1989 and Murray et al., 1989) which, given survivorship and the number ofsuccessful clutches laid per year, predicts clutch size in two quasi-stable avian populations. Murray and his colleagues conclude that the match between the predictions ofthis equation and the data supports the hypothesis that clutch size has evolved to be the minimum required to offset mortality. We demonstrate that the Murray-Nolan (M-N) equation predicting clutch size can be derived from the Lotka-Euler (L-E) equation for a population that is neithergrowing nor shrinking (Latka, 1925; Euler, 1970) without considering phenotypic evolution at all. We argue that an alternative hypothesis for the apparent success ofthe M-N equation is that it reflects the simple fact that in a static population, birth rate on average equals death rate. We argue that, regardless ofthe evolutionary factors that influence clutch size, the M-N equation will always correctly predict clutch size, given that demographic assumptions are met. We should point out that in this note we are not attempting to criticize or evaluate in any detail the many facets of Murray's theory ofclutch size evolution, but instead are developing an alternative rationale for why the M-N equation might be valid. Indeed we agree with Murray's view that considering detailed age-specific fecundity and survivorship schedules for different genotypes may be ofgreat importance in understanding the evolution