Eco-evolutionary dynamics, density-dependent dispersal and collective behaviour: implications for salmon metapopulation robustness

Abstract

The spatial dispersal of individuals plays an important role in the dynamics of populations, and is central to metapopulation theory. Dispersal provides connections within metapopulations, promoting demographic and evolutionary rescue, but may also introduce maladapted individuals, potentially lowering the fitness of recipient populations through introgression of heritable traits. To explore this dual nature of dispersal, we modify a well-established eco-evolutionary model of two locally adapted populations and their associated mean trait values, to examine recruiting salmon populations that are connected by density-dependent dispersal, consistent with collective migratory behaviour that promotes navigation. When the strength of collective behaviour is weak such that straying is effectively constant, we show that a low level of straying is associated with the highest gains in metapopulation robustness and that high straying serves to erode robustness. Moreover, we find that as the strength of collective behaviour increases, metapopulation robustness is enhanced, but this relationship depends on the rate at which individuals stray. Specifically, strong collective behaviour increases the presence of hidden low-density basins of attraction, which may serve to trap disturbed populations, and this is exacerbated by increased habitat heterogeneity. Taken as a whole, our findings suggest that density-dependent straying and collective migratory behaviour may help metapopulations, such as in salmon, thrive in dynamic landscapes. Given the pervasive eco-evolutionary impacts of dispersal on metapopulations, these findings have important ramifications for the conservation of salmon metapopulations facing both natural and anthropogenic contemporary disturbances.This article is part of the theme issue 'Collective movement ecology'.

Keywords: alternative stable states; dispersal; eco-evolutionary dynamics; salmon metapopulations; straying.

Figure 1.

The steady-state densities of N_i and N_j versus straying m for the constant straying model. Alternative stable states exist for regimes I and II, labelled RI and RII, respectively. In regime I, the system can approach qualitatively different states: a symmetric, intermediate state (purple), and asymmetric dominant (red) and subordinate (blue) states. In regime II, only one type of attractor exists: an asymmetric dominant/subordinate state (red and blue points, respectively), and its mirror image where identities of dominant and subordinate are exchanged. Inset: a qualitative sketch of the bifurcation diagram, showing the stable (solid lines) and unstable (dashed lines) fixed points in regimes I (light grey area) and II (dark grey area). The symmetric condition (sym.) is the horizontal line at the base of the inset, whereas the asymmetric condition (asym.) is represented by the curved line. (Online version in colour.)

Figure 2.

Measures of metapopulation robustness for the constant straying model as a function of straying m. Alternative stable state regimes I and II corresponding to those in figure 1 are labelled RI and RII, respectively. (a) Portfolio effect as a function of m. (b) Recovery time as a function of m. Measures of metapopulation robustness are shown with respect to different induced disturbances: the near-collapse of both populations (black), and the lone extinction of either the dominant (dark grey) or subordinate (light grey) population. Portfolio effects are different for the near-collapse and single extinction scenarios due to different CVs for the populations and aggregate in alternative basins of attraction that exist in regimes I and II.

Figure 3.

Comparison of steady-state population densities for the constant straying model and density-dependent straying model. Inset: steady-state densities for the constant straying model (purple) and density-dependent straying model (green) for different strengths of collective behaviour. Low C corresponds to strong effects of collective behaviour. The top row shows steady-state densities as a function of individual straying m₀; the bottom row shows steady-state densities as a function of straying at the steady state m*. Vertical green lines link paired subordinate and dominant population densities. Main: The absolute difference in steady-state densities averaged across intervals of low straying (0 < m, m₀ < 0.25; blue) and high straying (0.25 < m, m₀ < 0.5; red). Horizontal dashed lines correspond to the mean absolute differences in steady-state densities for low (blue) and high (red) density-independent straying. As , mean absolute differences in steady-state densities become equivalent.

Figure 4.

Measures of metapopulation robustness for the density-dependent straying model as a function of individual straying m₀ and the strength of collective behaviour C (note the log₁₀ scale, including (a) the portfolio effect, (b) the time to recovery following near-collapse of both populations, (c) the time to recovery following the extinction of the subordinate population and (d) the time to recovery following the extinction of the dominant population. (Online version in colour.)

Figure 5.

Alternative stable state regimes I (grey) and II (black) as a function of individual straying m₀ and the strength of collective behaviour C (note the log₁₀ scale). Regime I signifies parameter space where there is either (1) an intermediate-density, symmetric steady state, or (2) an asymmetric dominant/subordinate density. Regime II signifies parameter space where there is an asymmetric dominant/subordinate steady-state density. The white space to the left (lower values of m₀) signifies high-density, symmetric steady states, and the white space to the right (higher values of m₀) signifies low-density, symmetric, steady states. Relationships are shown for (a) low habitat heterogeneity (Δθ), (b) intermediate habitat heterogeneity and (c) high heterogeneity. The horizontal cut-off of Region I at low values of C in (a) is due to numerical limitations.

Figure 6.

Alternative stable state regimes I (grey) and II (black) as a function of individual straying m₀ and the strength of collective behaviour C (note the log₁₀ scale), for the case where individual straying increases with lower habitat heterogeneity (inset). Regime I signifies parameter space where there is either (1) an intermediate-density, symmetric steady state, or (2) an asymmetric dominant/subordinate density. Regime II signifies parameter space where there is an asymmetric dominant/subordinate steady-state density.