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My work is focused on models of biological populations in which ecological and evolutionary processes interact to determine a population's dynamic behavior. These processes may occur on very different spatial or temporal scales or they may unfold simultaneously. When ecology and evolution occur on similar timescales, which they often do, coupled models of these processes have implications for real-world applications like the control of invasive species spread, infectious disease suppression, and the deployment and containment of genetically-modified organisms.
Models for these processes are complicated by numerous nonlinearities, multiple dimensions, and a number of interacting variables, thereby evading the grasp of most analytical tools. My primary approach involves formulating deterministic models of natural systems and analyzing their properties over biologically relevant swaths of parameter space. Because these interactions often occur between small numbers of individual organisms, I also employ stochastic equivalents of these models -- often agent-based -- to determine if, when, and how the stochastic nature of these processes is relevant. Determinstic models I employ are often based on systems of ordinary differential, partial differential, or integro-difference equations.
Perkins T.A. Evolutionarily labile species interactions and spatial spread dynamics of invasions. [in preparation]
Perkins T.A., Jager H.I., Chandler J.A., & Groves P.A. A conditional strategy model accounts for spatiotemporal life-history variation in Snake River fall Chinook salmon. [in preparation]
Perkins T.A., Valentovich T., Staaterman E., Rittger K., Dozier J. & Harte J. Reconciling local adaptation and climate envelopes: an in situ evaluation of seedling response to early snowmelt. [in revision]
Perkins T.A., Holmes W.R. & Weltzin J.F. (2007) Multi-species interactions in competitive hierarchies: new methods and empirical test. Journal of Vegetation Science 18:685-692. [chosen by the editors as one of the top five papers published in JVS in 2007 (JB Wilson, et al. 2008. JVS 19:1-2)]
Perkins T.A., Riechert S.E. & Jones T.C. (2007) Interactions between the social spider Anelosimus studiosus (Araneae, Theridiidae) and foreign spiders that frequent its nests. Journal of Arachnology 35:143-152.
Perkins, T.A. 2006. An individual-based model of the social spider Anelosimus studiosus. College Scholars Senior Project. University of Tennessee.
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