| Date: | October 18, 2021 |
| Time: | 4:00pm |
| Location: | BLOC 302 |
| Speaker: | Jay Walton, Texas A&M University |
| Title: | A Hybrid Nonlinear Reaction-Diffusion, First-Order-Hyperbolic System Arising from a New Approach to Structured Population Dynamics |
| Abstract: | This talk considers population dynamics taking account of: (i) population structure such as age, stage, size and biomass; (ii) structure modulated population spatial mobility; (iii) structure modulated population growth including both hyperplasia (population number change) and hypertrophy (individual biomass change). Population structural features are modeled via space/time field variables rather than the traditional approach of introducing structure parameters as additional independent variables. In the special case of diffusive transport and mass or size structure, conservation postulates for these new structure field variables along with standard conservation postulates for population number lead to a hybrid nonlinear reaction-diffusion, first-order-hyperbolic system of PDEs. Results on various qualitative properties of this novel system are presented along with application to an aquatic species subject to harvesting. In particular, the model is used to study optimal configurations for marine protective areas designed to prevent catastrophic population collapse from over harvesting. |
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| Date: | November 8, 2021 |
| Time: | 4:00pm |
| Location: | BLOC 302 |
| Speaker: | Alexandru Hening, Texas A&M University |
| Title: | Harvesting in discrete-time stochastic population models |
| Abstract: | We analyze the long-term behavior of interacting populations which can be controlled through harvesting. The dynamics is assumed to be discrete in time and stochastic due to the effect of environmental fluctuations. We present powerful extinction and coexistence criteria when there are one or two interacting species. We then use these tools in order to see when harvesting leads to extinction or persistence of species, as well as what the optimal harvesting strategies, which maximize the expected long-term yield, look like. For single species systems, we show under certain conditions that the optimal harvesting strategy is of bang-bang type: there is a threshold under which there is no harvesting, while everything above this threshold gets harvested. |
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| Date: | November 22, 2021 |
| Time: | 3:00pm |
| Location: | BLOC 302 |
| Speaker: | Colton Watts, Texas A&M University |
| Title: | The evolution of sexual signaling in female animals |
| Abstract: | Sexual selection theory predicts that costly sexual signals can evolve if they provide an advantage in competing for limited mating opportunities. However, this framework struggles to explain empirical systems in which sexual signals have evolved in the limiting sex, such as in females of polygynous species. We explore whether a sexual signal can evolve in females of polygynous species if it increases the likelihood of associating with "high-quality" males that provide social benefits (e.g., increased survival) to their partners. Using a population genetic approach, we show that such a signal can spread in the population if there is variation in male quality and the marginal social benefit of mating with high-quality males is much larger than the costs to females of signaling. However, the ultimate fate of the signal depends on the costs to males of providing social benefits to their partners. If these costs are low enough that the high-quality male genotype can approach fixation, then the benefit of female signaling becomes negligible because even non-signalers are likely to associate with benefit-providing males. In this case, any costs of the signal will lead to its extinction following an initial increase in frequency. If, however, the costs to high-quality males are large enough to prevent fixation, the quality and signal loci can undergo damped oscillations to a coevolutionary equilibrium characterized by a low frequency of signaling genotypes and a high frequency of high-quality genotypes. Thus, our model demonstrates that sexual signals may evolve in the limiting sex by increasing access to high-quality partners, though the conditions under which this occurs are somewhat restrictive. |
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