### Friday, February 26, 2016 (12:30 p.m. in Rockefeller 309)

**Title: **Frontiers in Animal Movement Modeling and Encounter Theory in Ecology

**Speaker: **Eliezer Gurarie (Quantitative Ecologist, University of Maryland)

*Hosted by David Gurarie*

**Abstract: **Movements of animals (or – for that matter – most microscopic organisms and sub-organism structures) are fundamental to many ecological (or biological) processes. Historically, models of animal movement have been dominated by discrete step-based models, which are difficult to re-scale and depend on strong, often invalid assumptions. I will present a family of continuous time movement models, variations of integrated Ornstein-Uhlenbeck stochastic processes, which are scale invariant and can be described with biologically meaningful parameters (random and advective speeds, time scales of autocorrelation, angular rotations), and can be estimated with likelihoods – which allow for model comparison, selection, and estimates of precision. I will illustrate several non-trivial examples of their application. Next, I will apply some of the scaling principles of movement to consider the surprisingly complex problem of relating movements to encounter rates, upon which most ecological processes depend (e.g. predator-prey interactions, mate encounter, dispersers finding habitat patches, disease transmissions). I present a general framework for examining both deterministic and probabilistic encounters between searchers and targets in continuous space and continuous time, considering both mean encounter rates and first encounter rates. These rates depend on: movement behaviors, spatial scales and shapes of encounter kernels, birth and death dynamics of targets, the spatial distribution of the targets, and the nature (destructive or non-destructive) of the encounter. I derive analytical approximations for encounter rates in several special cases and use these results to infer general patterns. There will be cameo appearances by: roe deer, polar bears, kestrels, motile algae, and at least one whale.