Eco-evolutionary dynamics of dispersal in spatially heterogeneous environments

Abstract

Ecology Letters (2011) 14: 1025-1034 ABSTRACT: Evolutionary changes in natural populations are often so fast that the evolutionary dynamics may influence ecological population dynamics and vice versa. Here we construct an eco-evolutionary model for dispersal by combining a stochastic patch occupancy metapopulation model with a model for changes in the frequency of fast-dispersing individuals in local populations. We test the model using data on allelic variation in the gene phosphoglucose isomerase (Pgi), which is strongly associated with dispersal rate in the Glanville fritillary butterfly. Population-specific measures of immigration and extinction rates and the frequency of fast-dispersing individuals among the immigrants explained 40% of spatial variation in Pgi allele frequency among 97 local populations. The model clarifies the roles of founder events and gene flow in dispersal evolution and resolves a controversy in the literature about the consequences of habitat loss and fragmentation on the evolution of dispersal.

Figure 1

Comparison between patch-specific incidences of occupancy (p_i*; left panels) and mean dispersal phenotypes (q_i*; right panels) in the quasi-stationary state of the stochastic model (vertical axis) and its deterministic approximation (horizontal axis) in a heterogeneous network of 100 habitat patches. Patch areas are log-normally distributed, with mean of 2.0 and standard deviation of 0.5, and the patches have random spatial locations within a square area of 10 by 10 units (note that patch areas are not measured in the same unit). Parameter values: (a) α= 0.5, γ= 0.75, c=0.0065, ε= 0.001, ρ= 2.5, Δ = 5; (b) α= 2.0, γ= 0.75, c=0.0039, ε= 0.001, ρ= 2.5, Δ = 5; (c) α= 1.5, γ= 0.0, c=0.0009, ε= 0.05, ρ= 2.5, Δ = 5; and (d) α= 1.5, γ= 0.0, c=0.00085, ε= 0.05, ρ= 2.5, Δ = 2. In all panels, r₀ = 1 and v=1.

Figure 2

Relationships between the observed frequency of the C allele in Pgi_111 against (a) the frequency of the C allele in the sources of immigrants () and against (b) the surrogate measure of extinction rate, , where A_i is patch area. Black squares are for newly-established and open triangles for old populations. In (a) the continuous regression line is for new populations and the broken line is for old populations.

Figure 3

Spatially correlated variation in the frequency of fast-dispersing individuals (q_i). (a) A model-predicted quasi-stationary state in terms of the q_i values in the real patch network in the Åland Islands in Finland. The prediction was generated with the stochastic model, which was run for a network of 1037 habitat patches (parameter values α= 1, γ = 0, r₀ = 0.1, v=0.5, ρ = 0.1, Δ = 5, ε = 0.13 and c=0.017). Only those patches (n=671) that happened to be occupied in the snap-shot that was sampled from the simulation are shown in the figure. The size of the symbol is proportional to patch area, the shading indicates the value of q_i. (b) Test of spatial independence of the q_i values by envelopes of Besag's L-function. The continuous line gives the mean of the test function for the pattern in (a) with short-range dispersal, the broken line gives the mean for a species with long-range dispersal (α = 0.1, c=0.09, other parameters as in panel a; n=645 occupied patches). When the null line is outside the shaded area, the q_i values for pairs of populations within distance r from each other exhibit significant (P<0.01) spatial correlation. (c) Empirical result for the Glanville fritillary butterfly, using the frequency of the C allele in Pgi_111 as a measure of q_i (n=518 populations). (d) Test of spatial independence in the empirical data in (c).

Figure 4

The equilibrium metapopulation size and the average frequency of fast-dispersing individuals in 200 patch networks with a dissimilar degree of fragmentation. Each dot represents one network. Each network has 100 patches with log-normally distributed areas, but the distributions were generated with different means and variances (exp (X), where X is the underlying normal distribution with mean and variance drawn from the uniform distributions [1..3] and [0..0.3], respectively). The amount and fragmentation of habitat in each network was measured by metapopulation capacity, and metapopulation size was measured as the weighted average of the patch occupancy probabilities as prescribed by the theory (Hanski & Ovaskainen 2000). Panels (a) to (c) depict three situations with decreasing strength of immigration in relation to the colonisation rate (ρ= 1, 0.5 and 0.1 in (a), (b) and (c), respectively; other parameter values are r₀ = 1, v=1, α = 0.2, γ = 0, Δ = 5, ε = 0.01 and c=0.01). Panels (d) to (f) have the same parameter values as (a) except that there is less environmental stochasticity (v=0.5) in (d), there is local selection against fast-dispersing individuals (γ = 0.2) in (e), and dispersal rate is generally reduced (c=0.005) in (f).