Violaine Llaurens | Search arXiv

arXiv2026

Dynamics of Two Species with Density-Dependent Interactions and Application to Mutualism

Ecological interactions shape the dynamics of natural populations in the wild. Density-dependent processes are widespread and may change the respective effects of populations on one another, for instance by shifting interactions from mutualistic to parasitic relationships. Here, we develop a general deterministic model of two interacting populations, assuming density-dependent costs and benefits for the interacting individuals within and between species. This framework aims at generalizing pre-existing population dynamics models involving competition, predation, mutualism and parasitism, by allowing ecological interactions to transition when the respective densities of interacting species change. Through ordinary differential equations and phase portrait analysis, we derive general principles governing these systems, identifying constraints on the organization of equilibria and sufficient conditions for the emergence of certain dynamic behaviors. In particular, we show that equilibrium indices alternate along isoclines under broad geometric assumptions, and that limit cycles can arise when interactions include mutualistic and parasitic phases, while they cannot be generated locally in strictly mutualistic regions where the relevant interaction signs remain fixed. This framework provides a general approach for characterizing the population dynamics of interacting species and highlights the effect of the density-dependent transitions in ecological interactions.

q-bio.PE↗

arXiv2018

Looking for the right mate in diploid species: how dominance relationships affect population differentiation in sexual trait?

Divergence between populations for a given trait can be driven by natural or sexual selection, interacting with migration behaviour. Mating preference for different phenotypes can lead to the emergence and persistence of differentiated populations. Dominance between alleles encoding for divergent phenotypes can interfere in such processes. Using a diploid model of trait determining both mating success and migration rate, we explored differentiation between two connected populations, assuming either co-dominance or strict dominance between alleles. The model assumes that individuals prefer mating with partners displaying the same phenotype and therefore tend to move to the other population when their own phenotype is rare. We show that the emergence of differentiated populations in this diploid model is limited as compared to results obtained with the same model assuming haploidy. When assuming co-dominance, differentiation arises only when migration is limited as compared to preference. Such differentiation is less dependent on migration when assuming strict dominance between haplotypes. Dominant alleles frequently invade populations because their phenotype is more frequently expressed, resulting in higher mating success and rapid decrease in migration. However, depending on the initial distribution of alleles, this advantage associated with dominance (i.e. Haldane's sieve) may lead to fixation of the dominant allele throughout both populations. Depending on the initial distribution of heterozygotes, persistence of polymorphisms within populations can also occur because heterozygotes displaying the predominant phenotype benefit from mating preferences. Altogether, our results highlight that heterozygotes' behaviour has a strong impact on population differentiation and stress out the need of diploid models of differentiation and speciation driven by natural and sexual selection.

q-bio.PE↗