Effects of Releasing Maladapted Individuals: A Demographic‐Evolutionary Model

A model of the joint dynamics of change in population size N and evolution in a quantitative trait z, as a result of a general form of density dependence, local stabilizing selection, and immigration of individuals deviating from the local optimum, is analyzed. For weak selection and migration, a reduction in total equilibrium population size below the initial level without immigration, K, is shown to occur if the immigrants deviates more than \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$\sqrt{8}=2.83$$ \end{document} genetic standard deviations from the optimum and if the rate of migration m is sufficiently large relative to the strength of stabilizing selection s. For the Lotka‐Volterra form of density dependence, two additional equilibria are shown to exist below K, provided that the strength of selection is large relative to the strength of density dependence. Reintroduction of an initially extinct population is possible if the immigrants are not too maladapted and if the genetic variance is sufficiently large. For a simplified version of the model corresponding to competition between similar species or different haplotypes, the equilibrium population size is always exactly at K if \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage[OT2,OT1]{fontenc} \newcommand\cyr{ \renewcommand\rmdefault{wncyr} \renewcommand\sfdefault{wncyss} \renewcommand\encodingdefault{OT2} \normalfont \selectfont} \DeclareTextFontCommand{\textcyr}{\cyr} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \landscape $$m< Ksz^{2}_{1}/ 2$$ \end{document} and is above K otherwise, which shows the importance of including recombination in the model.