An Elementary Microscopic Model of Sympatric Speciation

TL;DR

The paper investigates sympatric speciation arising from competition for resources within a shared niche by developing a spatially explicit, agent-based model. It contrasts simple phenotypic theory with a microscopic framework where beak-like phenotypes evolve on a two-dimensional grid via a genotype-phenotype mapping, a Gaussian seed-eating kernel, and asexual reproduction with mutation. The main finding is that increasing specialization (smaller $c$) relative to seed-size dispersion $b$ drives the population from a unimodal to a multimodal phenotypic distribution, i.e., evolutionary branching, while the dynamics remain robust to parameter changes; spatial diffusion is not essential in the present fast-mixing setup. The work provides a tractable, didactic platform for exploring speciation, with plans to incorporate sexual mating, recombination, and fluctuating resources to study their impacts on speciation and ecosystem resilience.

Abstract

Using as a narrative theme the example of Darwin's finches, a microscopic agent-based model is introduces to study sympatric speciation as a result of competition for resources in the same ecological niche. Varying competition among individuals and resource distribution, the model exhibits some of the main features of evolutionary branching processing. The model can be extended to include spatial effects, different genetic loci, sexual mating and recombination, etc.

Figures (5)

• Figure 1: Darwin's finches. (left) Four of the species observed by Darwin in the Galapagos island during its voyage on the Beagle. The drawings are due to the zoologist J. Gould who first recognized the birds as a new peculiar group of finches. (right) Galapagos islands location in the Pacific Ocean.
• Figure 2: Static fitness $H_0$ and dynamic fitness $H$, due to the presence of a three-peaked distribution $p$. Note that the peaks correspond to the maxima of the dynamic fitness. Image from Ref. Bagnoli1997.
• Figure 3: Scheme of the microscopic model. Seeds (yellow circle) of size $x$ (in the interval $(0,1)$) are distributed in each cell according to the distribution $H(x)$. Birds (red pacmen) moves on the grid searching for a seed of the right size, affecting the resulting seed abundance.
• Figure 4: Evolution of phenotypic distribution in time. Static fitness (top panel, blue line) is slightly asymmetric $a=0.4, b = 0.2$. The initial phenotype population (i.e. colonizing species, $x_0=0.6, N = 10$) evolves toward the fitness maximum and undergoes a series of evolutionary branching events (red trajectory) if the competition range is fixed to $c=0.1$. In this case, the steady-state phenotypic distribution (at $T = 10^5$) shows four well separated peaks (top panel, red dotted line). Otherwise, if $c \geq b$, the population stabilizes around the fitness maximum (green trajectory, $c=0.2$).
• Figure 5: Species Formation from competition for resources. Well defined phenotypic clusters (species) appears when the competition range $c$ exceeds the standard deviation of the distribution of seeds, $b$. (Left) Phenotypes distribution (at steady-state, $T=10^5$) as a function of the normalized competition range $c/b$, where $b=0.2$, is held fixed. Inset: mean number of species at steady-state vs normalized $c$. (Right) Asymptotic phenotypes distribution ($T=10^5$) varying $b$ keeping $c=0.1$ fixed.