Coexistence of plant populations in a spatial continuum

In a recent paper of Etheridge et al. (Etheridge, et al. 2023), a new model for the dynamics of a plant population in a spatially heterogeneous environment is introduced. A particular feature of this model is that it separates juvenile and establishment phases of reproduction, leading to novel scaling limits. There are many potential applications of this model to the understanding of the evolution of populations. The particular focus of this project will be on plant populations in which distinct varieties produce seeds of different sizes, resulting in separate dispersal mechanisms. An obvious question, and the primary objective of this project, is whether these different varieties can coexist without any form of natural selection acting on the population.
As a first step, we will formulate a haploid model of reproduction in which total population size is regulated through a nonlocal logistic growth mechanism, and dispersal of seed is determined by seed size. We will then examine, for this toy model, whether or not coexistence is possible under neutrality. This stage will involve both numerical and analytical work. There is some preexisting code available for simulating the models of Etheridge et al. (Etheridge, et al. 2023), based on a powerful software called SLiM, but it requires modification for this scenario. In this part of the project, we shall seek input from Peter Ralph (University of Oregon). The analysis will draw on experience of models of competing species
in which heterogeneity is arises through interaction rather than migration (Blath, Etheridge and Meredith 2007). Natural questions we expect to follow from this initial analysis include
how many different seed sizes can coexist? What if there is a continuum of seed sizes?
Of course, this is not a realistic model and will require more complex modification. The next
step will be to introduce the dispersal of pollen, which one would expect to follow another type of mechanism (often long-range dispersal through either the wind or pollinators such as
bees). We will then add a model of heritability of seed size, which will be developed after discussion with biologists. After these adjustments to the model, one would then like to
understand the implications of seed size heterogeneity for patterns of genetic variation.
This work will be partly in collaboration. The motivating question of this project originally
arose through discussions with Magnus Nordborg (Gregor Mendel Institute of Molecular Plant Biology, Vienna). We additionally expect to draw on the expertise of Peter Ralph
(University of Oregon) for developing mathematical and numerical tools and techniques. This project falls within the EPSRC mathematicalsciences research area.
References
Blath, Jochen, Alison Etheridge, and Mark Meredith. 2007. "Coexistence in locally regulared
competing populations and survival of branching annihilating random walk." The Annals of
Applied Probability 17 (5-6): 1474-1507.
Etheridge, Alison, I Letter, Kurtz TG, Ralph PL, and Ho Lung TT. 2023. "Looking forwards and
backwards: dynamics and genealogies of locally regulated populations." ArXiv [Preprint]
arXiv:2305.14488v2.