Intense or spatially heterogeneous predation can select against prey dispersal

Abstract

Dispersal theory generally predicts kin competition, inbreeding, and temporal variation in habitat quality should select for dispersal, whereas spatial variation in habitat quality should select against dispersal. The effect of predation on the evolution of dispersal is currently not well-known: because predation can be variable in both space and time, it is not clear whether or when predation will promote dispersal within prey. Moreover, the evolution of prey dispersal affects strongly the encounter rate of predator and prey individuals, which greatly determines the ecological dynamics, and in turn changes the selection pressures for prey dispersal, in an eco-evolutionary feedback loop. When taken all together the effect of predation on prey dispersal is rather difficult to predict. We analyze a spatially explicit, individual-based predator-prey model and its mathematical approximation to investigate the evolution of prey dispersal. Competition and predation depend on local, rather than landscape-scale densities, and the spatial pattern of predation corresponds well to that of predators using restricted home ranges (e.g. central-place foragers). Analyses show the balance between the level of competition and predation pressure an individual is expected to experience determines whether prey should disperse or stay close to their parents and siblings, and more predation selects for less prey dispersal. Predators with smaller home ranges also select for less prey dispersal; more prey dispersal is favoured if predators have large home ranges, are very mobile, and/or are evenly distributed across the landscape.

Figure 1. Schematic depiction of predation in the individual-based model.

Predators are pictured as open circles while prey individuals are represented as black dots. Thick black lines represent the spatial distribution of foraging effort for each predator (i.e. the probability density of attack as described by kernel a in the model), while the dotted line, which is the sum of the black curves, represent the relative predation risk for the prey. , the spatial dispersion of the foraging effort distribution, is referred to in the main text as the predator home range size. On average, predators tend to kill more prey in the center of their home range so that prey progressively concentrate at predator home range boundaries; and this creates a negative spatial correlation between predator and prey distributions.

Figure 2. The effects of competition and predation intensity on the evolutionarily stable adult prey dispersal rate.

Pairwise invasibility plots (PIPs) computed from the moment equations, for a gradient of competition rate (upper row) and predation rate (lower row). White colouring indicates the mutant invades, and black that the mutant loses (does not invade). On the x-axis is represented the resident dispersal rate ( and on the y-axis the mutant dispersal rate (). The ESS dispersal rate is located at the intersection between black and white parts of the plane, along the diagonal. It is also convergence stable, in that it can be attained in a series of small ‘mutational’ steps. The first row shows that increases with prey competition strength, while the second row shows to decrease with predation rate. Parameters held constant are . First row , second row . Here there are no post-natal predator movements ().

Figure 3. The effect of predator spatial pattern on the evolution of adult prey dispersal rate.

These plots have been obtained by performing only two invasions for each parameter combination, corresponding to the opposite top left and bottom right corners of the PIP plots of Figure 2, for 3 predator spatial patterns (segregated, uniform, aggregated). The color represents the evolutionary outcome, white = selection for maximum dispersal, black = selection for no adult dispersal, gray = existence of an intermediate ES dispersal rate. The first row represents results obtained in one dimension, without predator demography. The second row presents the results with the predator demography. The third row depicts results obtained in two dimensions, without predator demography. Detailed parameters. General parameters are (a–b–c) No feedbacks, one dimension. . Uniform case, , Segregated , Aggregated . The values of the spatial autocorrelations are those that would have been obtained, if feedbacks were included (see below for the parameter values of predator demographic rates). (d–e–f) Demographic feedbacks, one dimension. Predator parameters . Specific parameters (d) (e) (f) (g–h–i) Two dimensions (no demography) .

Figure 4. Effect of predator space-use parameters (movement rate, home range size) on adult prey dispersal rate.

We present the invasion fitness of a dispersive mutant prey in a non-dispersive resident population (a convenient index of selection for dispersal that has been confirmed by more detailed PIPs) as a function of (a) predator home range size and predator movement rate ; and (b)as a function of average predator dispersal distance () and predator movement rate . White indicates selection for dispersal (, maximal value), and black against (), while gray values around zero fitness are an intermediate zone where there actually is a positive ES dispersal rate (as shown in Figure 2). Parameters held constant are . In (a) and in (b) . Invasion fitness was computed using the moment approximation.

Figure 5. The effect of the evolutionarily stable prey dispersal strategies (adult dispersal rate) on the prey population sizes, for various predator home range sizes.

In the upper panels (a) and (b) the equilibrium density of a resident () non-dispersive type (resp. dispersive) is represented with a filled line (resp. a dashed line), both when the predator numerical response is absent (a) and present (b). In the lower panels, we show an index of the selective pressure for dispersal, the invasion fitness of a dispersive mutant () in a non-dispersive population (filled lines). The zero fitness value is shown with a horizontal dashed line, and separates selection against dispersal (below) versus selection for dispersal (above). The thin dotted line separates in all panel parameter regions selecting for and against dispersal. The case without a predator numerical response is presented in (c), while the numerical response is added in (d). Parameters: . In the right column (b–d), additional predator parameters generating the demography take positive values; . The solid lines are computed using the moment approximations, and the open circles and crosses in (a) and (b) are the landscape densities of prey averaged over 50 realisations of the IBM on a 1D line of length .