Rebecca C. Tyson

Bio: Rebecca C. Tyson is an academic researcher from University of British Columbia. The author has contributed to research in topics: Population & Population cycle. The author has an hindex of 14, co-authored 46 publications receiving 491 citations.

Moving forward in circles: challenges and opportunities in modelling population cycles.

Abstract: Population cycling is a widespread phenomenon, observed across a multitude of taxa in both laboratory and natural conditions. Historically, the theory associated with population cycles was tightly linked to pairwise consumer–resource interactions and studied via deterministic models, but current empirical and theoretical research reveals a much richer basis for ecological cycles. Stochasticity and seasonality can modulate or create cyclic behaviour in non-intuitive ways, the high-dimensionality in ecological systems can profoundly influence cycling, and so can demographic structure and eco-evolutionary dynamics. An inclusive theory for population cycles, ranging from ecosystem-level to demographic modelling, grounded in observational or experimental data, is therefore necessary to better understand observed cyclical patterns. In turn, by gaining better insight into the drivers of population cycles, we can begin to understand the causes of cycle gain and loss, how biodiversity interacts with population cycling, and how to effectively manage wildly fluctuating populations, all of which are growing domains of ecological research.

Seasonally Varying Predation Behavior and Climate Shifts Are Predicted to Affect Predator-Prey Cycles.

Abstract: The functional response of some predator species changes from a pattern characteristic for a generalist to that for a specialist according to seasonally varying prey availability. Current theory does not address the dynamic consequences of this phenomenon. Since season length correlates strongly with altitude and latitude and is predicted to change under future climate scenarios, including this phenomenon in theoretical models seems essential for correct prediction of future ecosystem dynamics. We develop and analyze a two-season model for the great horned owl (Bubo virginialis) and snowshoe hare (Lepus americanus). These species form a predator-prey system in which the generalist to specialist shift in predation pattern has been documented empirically. We study the qualitative behavior of this predator-prey model community as summer season length changes. We find that relatively small changes in summer season length can have a profound impact on the system. In particular, when the predator has sufficient alternative resources available during the summer season, it can drive the prey to extinction, there can be coexisting stable states, and there can be stable large-amplitude limit cycles coexisting with a stable steady state. Our results illustrate that the impacts of global change on local ecosystems can be driven by internal system dynamics and can potentially have catastrophic consequences.

Modelling the Canada lynx and snowshoe hare population cycle: the role of specialist predators

Abstract: Mathematical models of the snowshoe hare (Lepus americanus) and Canada lynx (Lynx canadensis) population cycles in the boreal forest have largely focused on the interaction between a single specialist predator and its prey. Here, we consider the role that other hare predators play in shaping the cycles, using a predator–prey model for up to three separate specialist predators. We consider the Canada lynx, coyote (Canis latrans) and great horned owl (Bubo virginianus). Our model improves on past modelling efforts in two ways: (1) our model solutions more closely represent the boreal hare and predator cycles with respect to the cycle period, maximum and minimum hare densities and maximum and minimum predator densities for each predator, and (2) our model sheds light on the role each specialist plays in regulation of the hare cycle, in particular, the dynamics of the raptor appear to be crucial for characterising the low hare densities correctly.

Stochastic Processes in Physics and Chemistry

Abstract: N G van Kampen 1981 Amsterdam: North-Holland xiv + 419 pp price Dfl 180 This is a book which, at a lower price, could be expected to become an essential part of the library of every physical scientist concerned with problems involving fluctuations and stochastic processes, as well as those who just enjoy a beautifully written book. It provides an extensive graduate-level introduction which is clear, cautious, interesting and readable.

Stochastic Differential Equations

Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

Complex Population Dynamics: A Theoretical/Empirical Synthesis

Abstract: In what case do you like reading so much? What about the type of the complex population dynamics a theoretical empirical synthesis book? The needs to read? Well, everybody has their own reason why should read some books. Mostly, it will relate to their necessity to get knowledge from the book and want to read just to get entertainment. Novels, story book, and other entertaining books become so popular this day. Besides, the scientific books will also be the best reason to choose, especially for the students, teachers, doctors, businessman, and other professions who are fond of reading.