Doctor of Philosophy (PhD), Ohio University, 2024, Biological Sciences (Arts and Sciences)

Plant communities that occur on restrictive soils are characterized by stressful soil conditions and isolated patches of habitat, both of which have important consequences for the ecology and evolution of the species that occur on them. Despite their restrictive nature, edaphic communities contain high biodiversity, comprising a unique assemblage of plants, many of which are rare. Edaphic communities contain numerous, distantly related species that evolved under similar stressful conditions, but we still do not understand how the evolutionary process of edaphic specialization and speciation unfolds or the myriad of ecological and evolutionary consequences of occurring on restrictive soils. I examined species that occur on and off gypsum-edaphic communities to answer four questions, each as its own chapter: (Chapter 2) What fitness consequences do plants that occur on restrictive soils experience, (Chapter 3) how do diversification rates change for clades where gypsum endemism occur, (Chapter 4) how have dispersal syndromes and dispersion changed in edaphic communities because of their restrictive, fragmented substrate, and (Chapter 5) has selection favor limited dispersal in gypsum endemics? To answer those questions, I compared plant communities on gypsum outcrops (which contained both endemics and tolerators [= plants that grow on and off gypsum]) with surrounding, non-gypsum communities, and analysed selection and diversification rates of various gypsum associated clades. To determine the fitness consequences of inhabiting gypsum, I measured fitness for gypsum tolerating species across an edaphic gradient of gypsum to non-gypsum soils. I found negative and neutral fitness effects for species growing on gypsum soils. Various physical and chemical properties control fitness of tolerator species, but no common soil property was identified between the species that explained fitness changes on gypsum soil. To answer my second question, I gathered pre-constructed clado (open full item for complete abstract)

Committee: John Schenk (Advisor); James Dyer (Committee Member); Rebecca Snell (Committee Member); Jared DeForest (Committee Member) Subjects: Biology; Ecology; Plant Biology

Master of Mathematical Sciences, The Ohio State University, 2017, Mathematical Sciences

Two cases of species competition were considered. The first was the case of two-species-in-two-patches with both species being drifted from patch 1 to patch 2 at the same rate with the assumption that the organisms have an unconditional dispersal strategy (i.e. migrating from patch 1 to patch 2 at the same rate as from patch 2 to patch 1). In this case, ideal free distribution (IFD) only exists if the carrying capacity of patch 2, K2, is greater than K1, the carrying capacity of patch 1. If K2 is less or equal to K1, then, the resident species may have an evolutionarily stable strategy (ESS) only if it migrates from patch 1 to patch 2 at the rate d = infinity or d = 0, depending on the drift rate. The second case, was also two-species-in-two-patches; both species are assumed to migrate (drifted) from patch 1 to patch 2 at the same rate, but have a different rate of dispersal from patch 2 to patch 1. Furthermore, we assume that there is travel loss (i.e. species die during migration). In this case, although we showed that IFD does not exist, we analytically proved the existence of an ESS strategy. If the resident has such an ESS strategy, we proved that the equilibium point, at which the resident survives and the mutants vanish, is globally asymptotically stable.

Committee: Yuan Lou (Advisor); Adrian Lam (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2015, Mathematics

We investigate whether a dispersal strategy resulting in ideal free distribution (“IFD strategy”) is convergent stable. Species compete using fixed dispersal strategies in a patchy habitat with spatially varying but temporally constant carrying capacities. Population growth in each patch is governed by a function which is assumed only to be monotone decreasing and differentiable. For two-patch habitat, we give a complete description of outcomes when any two strategies compete. We show that there is selection toward IFD strategy, but such a strategy is not convergent stable because selection may be disrupted by emergence of a joint IFD between two species. We show also that IFD strategy is not convergent stable in an n-patch habitat. We derive some extensions of the model to allow for species-specific carrying capacities and analyze those extensions in the context of unconditional dispersal in a two-patch habitat. We present some numerical results for the case of time-periodic carrying capacities.

Committee: Yuan Lou (Advisor) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2011, Mathematics

We utilize reaction-diffusion-advection equations in an adaptive dynamic framework to study the evolution of dispersal of two competing species. The species are assumed to be identical except for their dispersal strategies which consist of random movement (diffusion) and biased movement (advection) upward along resource gradients. We focus on how spatial heterogeneity in the habitat influences selection. A key facet of this relationship is that diffusion creates a mismatch between a species population density at steady state and the resource function [9]. This led Cantrell et al. [9] to introduce a conditional strategy which can perfectly match the resource, resulting in the ideal free distribution of the species at equilibrium. This ideal free strategy (IFS) serves as a basis for our study. Not only do we show that it is a global evolutionarily stable strategy, but we find conditions under which it is convergent stable, varying random dispersal rates, advection rates, or both of these parameters at the same time. For two similar strategies on the "same side" of the IFS we show that when resource function is monotone, the strategy which is closer to the IFS is generally selected. For nonmonotone resource functions, we find that there may exist nonideal free strategies which are locally evolutionarily stable and/or convergent stable [21]. In addition, we find that for certain nonmonotone resource functions, two similarly competing species can coexist, which enables us to also show how three species coexistence is possible.

Committee: Yuan Lou PhD (Advisor); Chiu-Yen Kao PhD (Committee Member); Barbara Keyfitz PhD (Committee Member) Subjects: Mathematics

Doctor of Philosophy, The Ohio State University, 2007, Mathematics

We study the evolution of conditional dispersal using a Lotka-Volterra reaction-diffusion-advection model for two competing species in a nonhomogeneous, temporally constant environment. We assume that the two species are identical except for their dispersal strategies. Both species employ random diffusion combined with advection upward along resource gradients. We use a perturbation argument to understand the evolution of these rates. When the advection rates are small relative to the diffusion rates, we find that stronger advection is preferred. However, when the advection rates are large relative to the diffusion rates, we find that weaker advection is preferred. We also studied the case where the two species have differing strategies, one with a very strong biased movement relative to diffusion, and the other with a more balanced approach. If the advection rate of the latter is small, the two species can coexist. But if its advection rate increases sufficiently, the second species drives the first to extinction. So we see in these results a preference against overly strong advection and in favor of a more balanced strategy, suggesting the existence of an optimal intermediate rate.

Committee: Yuan Lou (Advisor) Subjects: Biology, Ecology; Mathematics