Abstract
We analyze mathematical models to examine how the genetic basis of fitness affects the persistence of a population suddenly encountering a harsh environment where it would go extinct without evolution. The results are relevant for novel introductions and for an established population whose existence is threatened by a sudden change in the environment. The models span a range of genetic assumptions, including identical loci that contribute to absolute fitness, a two-locus quantitative genetic model with nonidentical loci, and a model with major and minor genes affecting a quantitative trait. We find as a general (though not universal) pattern that prospects for persistence narrow as more loci contribute to fitness, in effect because selection per locus is increasingly weakened with more loci, which can even overwhelm any initial enhancement of fitness that adding loci might provide. When loci contribute unequally to fitness, genes of small effect can significantly reduce extinction risk. Indeed, major and minor genes can interact synergistically to reduce the time needed to evolve growth. Such interactions can also increase vulnerability to extinction, depending not just on how genes interact but also on the initial genetic structure of the introduced, or newly invaded, population.
Highlights
The ‘holy grail’ of invasion biology has been the identification of both suites of traits of introduced species, and characteristics of the environment of invasion, that permit a reasonably accurate prediction of the success or failure of invasive species
If the population mean fitness remains consistently less than unity, individuals are not being replaced across generations, on average, and the population will inexorably decline towards extinction in the absence of heritable genetic variation in fitness
We have used a series of mathematical models to examine the impact of genetics on a new population invading a Probability of extinction
Summary
We begin with the biologically most abstract, but mathematically most tractable, case where postinvasion fitness is determined by summing over a set of loci, each of which impacts fitness. We assume the parameterization mAA;i 1⁄4 rmax=n; mAa;i 1⁄4 rmax=n À si=2; and maa;i 1⁄4 rmax=n À si such that a population fixed for the A allele at all loci grows at intrinsic rate of increase rmax These Malthusian fitnesses are called ‘additive’ (Crow and Kimura 1970) since each copy of A at locus i adds si/2 to individual fitness compared with that of an aa homozygote at that locus. Consider how the number of loci affects T when assuming the total initial variance in fitness, V0 1⁄4 nq0ð1 À q0Þs2=2, along with m0 and rmax are held constant for different n We use this framework to relax the assumption that loci make identical contributions to individual fitness, and examine the consequences of demographic stochasticity
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