Evolutionary suicide and evolution of dispersal in structured metapopulations

Abstract

We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur.

Surprising evolutionary predictions from enhanced ecological realism

“…If the resultant densities fall below the threshold density of an allee effect, or if they imply a much elevated risk of accidental extinction, the population is doomed. The potential ubiquity of selection-driven extinctions is underscored by other examples of extinctions caused by adaptation in different traits, including anti-predator behavior (Matsuda and Abrams, 1994b), sexual traits (Kirkpatrick, 1996;Kokko and Brooks, 2003), dispersal rates (Gyllenberg et al, 2002), mutualism rates , cannibalistic traits , maturation reaction norms (Ernande et al, 2002), levels of altruism (Le Galliard et al, 2003), and selfing rates (Cheptou, 2004); see also the review by Parvinen (2006). Furthermore, Dieckmann and Ferrie`re (2004) showed, by examining ecologically explicit multilocus models featuring either diallelic loci or continua of alleles, that the incidence of evolutionary suicide is by no means restricted to phenotypic models of asexual evolution, but robustly occurs also when sexual inheritance is taken into account.…”

Spatial Dimensions of Population Viability

“…At equilibrium, this quantity should equal 1, hence R I . It can also be shown that the equilibrium value of R I given by Equation (5b) tends to R 0 as the immigration rate I tends to zero (Gyllenberg et al 2002).…”

“…To investigate this question we have to turn to more complicated models that explicitly prescribe local dynamics in terms of parameters that describe individual behavior. Such models are called structured metapopulation models and have been treated by, among others, Gyllenberg andHanski (1992, 1997), Hanski and Gyllenberg (1993), Gyllenberg et al ( , 2002, Gyllenberg and Metz (2001), Metz and Gyllenberg (2001), and Parvinen (2001a, 2001b. In Section 4 the persistence and viability of metapopulations is investigated within the context of structured models.…”

“…This was carried out by Gyllenberg et al (2002). However, to calculate R 0 there is a shortcut, which we shall follow.…”

“…At the metapopulation steady state the condition R I = 1 holds (see Box 2), and Figure 4 shows plots of the equilibrium fraction of occupied patches determined by this condition as a function of the emigration rate (from Gyllenberg et al 2002). It may be a surprise that, even for r(0) ≤ µ(0), in which case the metapopulation is not persistent, there might very well exist a range of emigration rates m(0) over which the metapopulation is viable.…”