Coexistence Through Life-History Variation Revisited in Tractable Models With Explicit Patch Aging And/or Size-Structure

Abstract

A persistent puzzle in ecology is understanding the mechanisms of competitive coexistence in nature. One of the major hypotheses of how competitive coexistence can arise, in a variety of systems, but especially among tree species in forests (which are important given their role in the global carbon cycle), is that species differ in their successional niches. However, much work remains to fully understand the differences in demographic strategy that could mediate this successional niche differentiation, and the degree to which it is at play in nature. Mathematical modeling has proven to be an important tool for quantifying the influence of differential demographic strategies. However, modeling successional niche differentiation requires consideration of both patch-age structure and size-structure within competing populations. In this thesis, we develop a suite of mathematical models that include these structures and systematically assess—using analytical and numerical approaches—their potential to give rise to opportunities for variation between species among demographic trade-offs to enable coexistence.

The first set of models (Ch. II) we consider incorporate patch-age structure which is defined as the subsequent progression of competitive dynamics, or the ‘aging’ of patches after disturbance events. Patch-age has been posited as creating opportunities for coexistence of species competing on a landscape if they differ in their life history (demographic) strategies. Mathematical models used to study this possibility are either too simple, not modelling patch aging explicitly, or far more complex and requiring extensive simulation.

We study four patch-age structured nonlinear partial differential equation (PDE) models that are still analytically tractable in most cases but allow explicit consideration of the progression of competitive dynamics as patches age after disturbance. We consider three possible types of density-dependence for their importance in coexistence under disturbance: 1) on reproduction, 2) on recruitment, or 3) on mortality. Although in nature all three types of density-dependence are likely acting in concert in many systems, here we consider each in turn on its own, both to help retain analytical tractability, and to identify which type of density-dependence is critical to set up conditions for coexistence.

Under density-dependence on recruitment alone, the model does not permit feasible coexistence. However, under density-dependent reproduction or under density-dependent mortality, variation between two species along a reproduction-survival and a sensitivity-to- competition/mortality trade-off both allow for feasible and stable coexistence.

The second set of models (Ch. III) we consider incorporate size-structure. Models capturing the size-structured nature of competition between trees are complex, and have faced barriers to complete analysis, leaving the specific demographic trade-offs that could allow for coexistence unclear.

Under only density-dependent mortality further numerical analysis is planned. While we find that coexistence is not possible under density-dependent recruitment alone, we are able to show that hierarchical size-structuring allows for stable coexistence under density-dependent reproduction when species trade-off between reproduction and max-height.

The third set of models (Ch. IV) we consider employ both size and patch-age structure simultaneously. We consider a size and patch-age structured model which has both a size hierarchy as well as an explicit patch-age structure. Under density-dependent recruitment the model does not permit feasible coexistence. However, under density-dependent reproduction—and when shading effects are felt from all individuals—we show coexistence can occur through a trade-off between growth and survival.