Speciation by local adaptation and isolation by distance in extended environments

Abstract

Speciation is often associated with geographical barriers that limit gene flow. However, species can also emerge in continuous homogeneous environments through isolation by distance. When the environment is not homogeneous, natural selection contributes to differentiation by local adaptation and tends to facilitate speciation. To explore how isolation by distance and adaptation combine to determine species diversity, we implemented a model regulated by these two components. The first is implemented via mating restrictions on spatial proximity and genetic similarity. The second is realized by an ecological phenotype subjected to adaptation by natural selection. We consider scenarios where the environment is either homogeneous, with a single ecological optimum, or heterogeneous with two distinct optima. We show that the interplay between selection and isolation by distance affect not only species formation but also phenotypic distributions and speed of speciation. In homogeneous environment, speciation occurs only under restrictive mating, but it takes longer if selection is weak. In contrast, in heterogeneous environments with two local optima and strong selection, species well adapted to each of the optima emerge along the spatial structure, leading to the formation of groups with distinct phenotypes. Permissive mating leads to the formation of only two species, each occupying one of the optima; restrictive mating leads to several species per optimum, in a much faster speciation process. Interestingly, when selection is weak and mating is restrictive, several species form, but the process is slow. Moreover, species average phenotypes do not remain constant over generations, causing the phenotypic distribution to oscillate, never reaching a stationary pattern.

Figures (5)

• Figure 1: Representation of the model: the lattice with $M$ individuals is divided into two environments. An individual is selected and chooses a genetically compatible mating partner within a radius $S$, such that $D_{ij} < G$. The offspring inherits a random combination of reproductive loci from both parents. Each locus may mutate with a given probability, flipping the value of the binary allele. The phenotype is determined by the sum of the loci in the environmental chromosome, which determines the offspring's fitness. The new generation of individuals replaces the old one, and the process is repeated over time, allowing the population to evolve under the influence of mutation, selection, and reproductive constraints.
• Figure 2: Diversification dynamics in homogeneous environments. (a) Evolution of species richness, $N_{spp}(t)$, and (b) total population size, $M(t)$, averaged over 50 simulations. (c--f) Phenotypic density distributions $d(P)$ and corresponding spatial organization at selected times (shown in (a) by symbols) for a representative replica and different parameter values: (c) $\sigma_e = 0.05$, $G = 0.05B$ -- strong selection and restrictive mating; (d) $\sigma_e = 0.4$, $G = 0.05B$ -- weak selection and restrictive mating; (e) $\sigma_e = 0.05$, $G = 0.3B$ -- strong selection and permissive mating; (f) $\sigma_e = 0.4$, $G = 0.3B$ -- weak selection and permissive mating. Dots represent individuals and are proportional to the environmental trait. Different colors represent species.
• Figure 3: Diversification dynamics in heterogeneous environments. (a) Evolution of species richness, $N_{spp}(t)$, and (b) total population size, $M(t)$, averaged over 50 simulations . (c--f) One instance of phenotypic density distributions $d(P)$ and corresponding spatial organization at representative times (pointed in (a) by symbols) for different parameter values: (c) $\sigma_e = 0.05$, $G = 0.05B$ -- strong selection and restrictive mating; (d) $\sigma_e = 0.4$, $G = 0.05B$ -- weak selection and restrictive mating; (e) $\sigma_e = 0.05$, $G = 0.3B$ -- strong selection and permissive mating; (f) $\sigma_e = 0.4$, $G = 0.3B$ -- weak selection and permissive mating. Dots represent individuals and are proportional to the environmental trait. Different colors represent species.
• Figure 4: An instance of the phenotypic distribution over time for the case of weak selection ($\sigma_e = 0.40$) and restrictive mating ($G = 0.05B$). Phenotypic peaks oscillate between the local optima and 0.5, which is the expected value by random mutations and drift only -- instead of reaching a static equilibrium on local optima. Colored bars refer to different species.
• Figure 5: Individual-level genetic differentiation versus geographic distance at $t=5,000$ on a log-log scale. Pairwise Euclidean geographic distance is plotted against genetic distance $D_{ij}$ (Eq. \ref{['eq::Dij']}). In each panel, colored dots represent pairs of individuals belonging to the same species (intraspecific), while gray dots represent pairs from different species (interspecific). (a--b) Restrictive mating regime ($G=0.05B$) showing a gap between intra- and inter-specific genetic distances under strong (a) and weak (b) selection. (c--d) Permissive mating regime ($G=0.30B$) where diversification only occurs under strong selection (c). Solid black lines represent the intra-specific linear regression (slopes 0.14--0.33), while dashed black lines indicate the total population regression, which captures inter-specific genetic gaps (slopes up to 0.92). Data points represent all possible pairwise combinations from a single representative simulation.