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Dynamics of interacting populations: Single-species models and evolutionary outcomes for cannibalistic spiders

Sara A Reynolds, University of Nebraska - Lincoln

Abstract

This thesis discusses several different models of interacting populations, each of which provide insights on the effects of energy acquisition. The first two models focus on evolutionary outcomes for cannibalistic spiders. The later models explore the significance of consumer-resource interactions and resource type for modeling consumer dynamics.^ The existence of high levels of precopulatory sexual cannibalism in some female fishing spider species is particularly perplexing, as it poses no benefit to the male and leaves the female at risk of remaining unmated. One proposed explanation for this behavior is the aggressive spillover hypothesis (ASH), where a female's propensity to cannibalize a mate is linked to her aggression towards prey. Higher levels of aggression lead to higher food consumption rates, larger adult size, and lower mating rates, a trade-off in fitness. From these assumptions, I construct a discrete-time, stochastic model of the ASH, perform optimization and invasion analyses, and predict the evolutionarily stable state of female aggression towards courting males. Additionally, I explore an alternate approach to the ASH where higher levels of juvenile energy acquisition lead to an earlier maturation age rather than a larger maturation size. A second discrete-time, stochastic model is constructed based on these modified assumptions. Importantly, the interactions of adult male and adult female spiders directly effect mate availability over time, playing a key role in model results.^ Single-species population models often include density-dependence phenomenologically in order to approximate higher order mechanisms. In a separate look at interacting populations and energy acquisition, we consider the common scenario in which density-dependence acts via depletion of a renewed resource. When the response of the resource is very quick relative to that of the consumer, the consumer dynamics can be captured by a single-species, density-dependent model. Time scale separation is used to show analytically how the shape of the density-dependent relationship depends on the type of resource and the form of the functional response. Resource types of abiotic, biotic, and biotic with migration are considered in combination with linear and saturating functional responses. In some cases, we derive familiar forms of single-species models, adding to the justification for their use. In other scenarios novel forms of density-dependence are derived, for example an abiotic resource and a saturating functional response can result in a nonlinear density-dependent relationship in the associated single-species model of the consumer. In this case, the per capita growth rate curve has both concave-up and concave-down sections.^

Subject Area

Applied mathematics

Recommended Citation

Reynolds, Sara A, "Dynamics of interacting populations: Single-species models and evolutionary outcomes for cannibalistic spiders" (2015). ETD collection for University of Nebraska - Lincoln. AAI3738971.
http://digitalcommons.unl.edu/dissertations/AAI3738971

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