Mathematical Treatment of Evolutionary Ecology
{'Code': '03040100', 'Directorate': {'Abbreviation': 'MPS', 'LongName': 'Direct For Mathematical & Physical Scien'}, 'Division': {'Abbreviation': 'DMS', 'LongName': 'Division Of Mathematical Sciences'}}
{'SignBlockName': 'Michael Steuerwalt', 'PO_EMAI': None, 'PO_PHON': None}
This project is concerned with the study of the effects of                 natural selection and diffusion on a population consisting of a                 single evolving species with a genetic system of one locus with                 two alleles.  The  model is an example from evolutionary ecology,               which is a fusion of population ecology with population genetics.               The model is more realistic than those encountered in the                       classical theory of population genetics because it allows                       density dependent selection.  It is assumed that increase in                    population size decreases the fitness of the individuals in the                 population.  A future goal will be to study the case of several                 interacting species, or coevolutionary theory with diffusion.                   Mathematically, this is a system of reaction-diffusion equations.               It is necessary to prove the existence of travelling waves                      connecting two rest points lying on different invariant                         manifolds.  Each of these manifolds corresponds to the absence of               one allele.  The stability of these waves will be examined.  The                results will give a more complete picture of what has been shown                by the principal investigator on the asymptotic behavior of                     solutions to the reaction-diffusion system.  It will give insight               into the ways to handle systems where the maximum principle is                  hard to apply.
{'FirstName': 'Roger', 'LastName': 'Lui', 'PI_MID_INIT': 'Y', 'PI_SUFX_NAME': None, 'PI_FULL_NAME': 'Roger Y Lui', 'EmailAddress': 'rlui@wpi.edu', 'NSF_ID': '000387116', 'StartDate': '07/15/1988', 'EndDate': None, 'RoleCode': 'Principal Investigator'}
{'Name': 'Worcester Polytechnic Institute', 'CityName': 'WORCESTER', 'ZipCode': '016092247', 'PhoneNumber': '5088315000', 'StreetAddress': '100 INSTITUTE RD', 'StreetAddress2': None, 'CountryName': 'United States', 'StateName': 'Massachusetts', 'StateCode': 'MA', 'CONGRESSDISTRICT': '02', 'CONGRESS_DISTRICT_ORG': 'MA02', 'ORG_UEI_NUM': 'HJNQME41NBU4', 'ORG_LGL_BUS_NAME': 'WORCESTER POLYTECHNIC INSTITUTE', 'ORG_PRNT_UEI_NUM': None}
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{'Code': '1266', 'Text': 'APPLIED MATHEMATICS'}
{'url': 'https://www.nsf.gov/awardsearch/download?DownloadFileName=1988&All=true', 'xml': '8801968.xml'}