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Evolution of Plastic Dispersal in Stable Environment: Local Information of Fitness Consequence

Wayne Liang, Rufus Johnstone

TL;DR

The paper tackles how dispersal fitness can be inferred when global landscape information is unavailable by linking local demographic processes to dispersal decisions, enabling plastic dispersal strategies in stable environments. It develops a patch-based modeling framework and shows that a patch's net migration flux dictates the direct fitness consequences of dispersal, while local growth rates provide the cue for dispersal decisions. The results establish that the evolutionary stable state tends to balance influx and efflux locally, with dispersal costs, accidental dispersal, and kin selection shaping the outcome. The framework reduces reliance on extensive landscape data and extends to continuous spaces, offering practical tools for predicting and testing plastic dispersal in complex habitats.

Abstract

Fitness consequence of dispersal depends on property of the entire landscape, which patches are available and what are the cost of moving. These are information that are not available locally when an organism make the decision to disperse. This poses a problem to the organism, where it is unclear how an adaptive decision can be made. This also poses a problem to the scientist, since in order to study the adaptiveness of dispersal, we need information of the entire landscape. For theorist, this is through making a series of assumption about either the landscape or the organism, and for empiricists, this means a large amount of measurements needs to be made across a large area. In this paper, we propose a link between local demographic process, which an organism can have access to, to the fitness consequence of dispersal. This meant local environmental cue can be used for the decision on dispersal, and hence allow the evolution of plastic dispersal strategy. We will then show that using this approach, evolution of dispersal on complex landscape can be modelled with relative ease, and to show that accidental dispersal in one patch can drive the evolution of adaptive dispersal in another.

Evolution of Plastic Dispersal in Stable Environment: Local Information of Fitness Consequence

TL;DR

The paper tackles how dispersal fitness can be inferred when global landscape information is unavailable by linking local demographic processes to dispersal decisions, enabling plastic dispersal strategies in stable environments. It develops a patch-based modeling framework and shows that a patch's net migration flux dictates the direct fitness consequences of dispersal, while local growth rates provide the cue for dispersal decisions. The results establish that the evolutionary stable state tends to balance influx and efflux locally, with dispersal costs, accidental dispersal, and kin selection shaping the outcome. The framework reduces reliance on extensive landscape data and extends to continuous spaces, offering practical tools for predicting and testing plastic dispersal in complex habitats.

Abstract

Fitness consequence of dispersal depends on property of the entire landscape, which patches are available and what are the cost of moving. These are information that are not available locally when an organism make the decision to disperse. This poses a problem to the organism, where it is unclear how an adaptive decision can be made. This also poses a problem to the scientist, since in order to study the adaptiveness of dispersal, we need information of the entire landscape. For theorist, this is through making a series of assumption about either the landscape or the organism, and for empiricists, this means a large amount of measurements needs to be made across a large area. In this paper, we propose a link between local demographic process, which an organism can have access to, to the fitness consequence of dispersal. This meant local environmental cue can be used for the decision on dispersal, and hence allow the evolution of plastic dispersal strategy. We will then show that using this approach, evolution of dispersal on complex landscape can be modelled with relative ease, and to show that accidental dispersal in one patch can drive the evolution of adaptive dispersal in another.
Paper Structure (23 sections, 16 theorems, 94 equations, 4 figures)

This paper contains 23 sections, 16 theorems, 94 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Models
  3. Taster Model
  4. General Model
  5. Model for Non-Linear Local Population Growth Rate
  6. Results
  7. Direct Fitness Benefit of Dispersing can be Deduced from the Net Flux into the Patch
  8. Population Growth Rate Equals Migration Flux in a Stable Population
  9. Evolutionary Stable State of Dispersal Matches the Influx to Efflux
  10. Adaptive Dispersal cannot Evolve with Homogeneous Environment without Kin Selection
  11. Adaptive Dispersal can be Driven by Accidental Dispersal
  12. Incoorporating Kin Selection
  13. Discussion
  14. So, Why does This Work?
  15. Plastic Dispersal Strategy
  16. ...and 8 more sections

Key Result

Theorem 1

Let $o_{\min}, o_{\max} \in \mathbb{R}^n$ with and let $T \in \mathbb{R}^{n \times n}$ be a square transition matrix satisfying: An ESS is defined as a vector $o \in \mathbb{R}^n$ such that $o_{\min,i} \leq o_i \leq o_{\max,i}$ for all $i$, and moreover

Figures (4)

  • Figure 1: Box plots of 15 realisations of two island dispersal scenario in simulated evolution. Red line is the prediction from the analytical result. the x axis is dispersal cost with y-axis being the A) dispersiveness of the smaller patch, B) the ratio between immigrant and emigrant in the small patch, and C) the dispersiveness in the large patch.
  • Figure 2: Migration structure with "paradoxical" fitness benefit. Arrow width and labels denote migration rates. Both small populations have positive net immigration, with $\mathbf{i}_1 - \mathbf{o}_1<\mathbf{i}_2 - \mathbf{o}_2$. The unit of migration being the small population size, which is assumed to be the same in the two small populations. For the ease of graphing dispersal cost is assumed to be 0. Even though staying in the focal population leads to less competition then leaving for small population 2, dispersal still brings fitness advantage according to the calculations.
  • Figure 3: Selection gradients on dispersal probabilities in a two-patch system. Arrows indicate the direction and strength of selection. Left: when dispersal can be reduced to zero in both patches, selection drives both toward minimal dispersal. Right: imposing a lower bound on dispersiveness (red boundary) generates a persistent migration flux and changes the ESS where the large patch evolve to have minimal dispersal which leads to adaptive dispersal being selected for in the large patch. This demonstrates how accidental dispersal in one patch can drive the evolution of adaptive dispersal in another. The selection gradient is drawn by setting the large patch to be 5 times more productive than the small patch with dispersal cost of 0.5, and minimal accidental dispersal to be 0.2.
  • Figure 4:

Theorems & Definitions (32)

  • Theorem 1
  • Definition 1
  • Lemma 1: Equivalent characterization of $\mathrm{FP}$
  • proof
  • Definition 2
  • Proposition 1
  • proof
  • Lemma 2
  • proof
  • Lemma 3: Isotonicity of the transition map
  • ...and 22 more