Pulsed Immigration Events Can Facilitate Adaptation to Harsh Sink Environments by Penniston, James; Barfield, Michael; Holt, Robert

Summary

In this article, we extent the literature on the evolutionary effects of variable migration and investigate how temporal variation in immigration rates influences adaption to environments outside a species’ niche (i.e., sink environments).

When immigration events are too frequent, gene flow can hamper local adaptation in sexual species, but sufficiently infrequent pulses of immigration allow for repeated opportunities for adaptation with temporary escapes from gene flow during which local selection is unleashed.

We address how the frequency of immigration pulses influences adaptation to sink environments…. we will also examine how density dependence and genetic architecture modulate the impact of pulsed immigration on local adaption. We conjecture that changing the frequency of immigration could alter the relative impacts of the opposing positive (e.g., increased genetic variant) and negative (e.g., maladaptive gene flow) effects of immigration sketched above.

“we observed an adaptive benefit of spacing out immigration events only when sink environments were sufficiently harsh (high v). For relatively mild sink environments, the probability of adaptation was high for all immigration frequencies (fig. 3B, asterisks), but for harsher sink environments the probability of adaptation was low for constant immigration but then increased as immigration events became less frequent (fig. 3B, circles and crosses).” (Peniston et al., 2019, p. 325)

More generally, immigration frequency has some impact as immigration adds diversity of genes to a sink, but if it is too frequent, local adaption cannot occur because the population of maladapted organisms is too high (this is similar to findings in Virulence on the Edge). However, if there is a balance between immigration rates and local adaptation, then evolution is more likely to occur. This varies between the harshness of the sink where with mild sinks, immigration cohorts could more readily adapt, while in more harsh sinks the less frequent pulses led to local adaptation.

Methods

Will use

1. Deterministic models
2. Stochastic individual-based simulations
   1. Deterministic models don’t allow for extinction
   2. Deterministic models assume that the population if fixed
   3. Similalrly ignores stochastic effects

• Without density dependence
• Genetic architectures
  • Single-locus haploid
  • Single-locus diploid
  • Multi-locus quantitative genetic variation
• One way sink (i.e., “black hole”) with discrete generations
• Fitness was the product of a phenotype-dependent probability of survival until adulthood and a phenotype independent fixed fecundity
• Immigrants arrive as adults

$$\begin{align} N = N_1 + N_2 \newline W_i(N) = \text{Density depdent abskyte fitness of genotype } A_i \newline V_i(N) B= \text{Absolute fitness} \end{align}$$ For a sink

$$\begin{align} W_2(N) \lt 1 \ \text{for all N} \newline W_1(N) \gt 1 \ \text{for some N} \end{align}$$

Haploid model

Then the mean fitness, $\bar W$ is:

$$\begin{align} p = \frac{N_1}{N_1+N_2} \newline \bar W(N) = pW_1(N) + (1-p) W_n(N) \newline W_i(N) = \frac{w_i}{1+CN} \end{align}$$ Where if c = 0, then there is no density dependence.

Diploid model

$$\begin{align} \bar W (N) = p^2W_{11} + 2p(1-p)W_{12}(N) + (1-p)^2W_{22}(N) \newline W_{ij}(N) = \frac{w_{ij}}{1+cN} \end{align}$$

Main Points

• Frequency of immigration events did not affect adaption to a sink environment

Introduction

Immigrations

• Increases genetic diversity
• Boosts the population size
• Increase adaption by counteracting Allee effects vocabulary/Allee

Questions

Code/ Supplemental Data

Lots of C++ data are available.

Implications for Infectious Diseases