In nature, animals routinely move about in landscapes that are dynamic in space and time.  These dynamics may be the product of seasonality, succession, human activities, or many other processes that involve a range of time and space scales. Our primary goal with this project was to bring together empirical and theoretical advances pertaining to animal dispersal to gain a deeper understanding of how animals move in such dynamic landscapes. This synthesis involved connecting the movement behaviors observed to occur in real animals to movements that appear, or are proven to be, ideal in a variety of mathematical models.  This integration focuses on aspects of real animal movement that are little-studied by mathematicians, including switching among different movement modes and using nonlocal information. 

We used a variety of mathematical modeling approaches to explore these issues, including analytical studies, numerical solution of especially complex equations, and agent-based simulation modeling.  Animal movement and decision-making may be informed by perception of conditions at some distance from an animal’s current location or by memory gained through experiences in previously visited areas.  We sought to understand how these factors, acting individually or jointly, influenced animals’ distributions in space and over time. Compared to models without features like memory and perception (which have traditionally dominated the field of mathematical biology), models featuring these biologically realistic components were found to yield improved matching between consumers and their resources in dynamic landscapes.  These results suggest that new discoveries concerning the mathematical optimality of different movement strategies are possible, and that benefits from memory and perception may strong enough to outweigh the costs associated with such features. Accordingly, these results suggest that great care should be taken when inferring generality from mathematical models that lack such modest touches of biological realism.

Additional work focused on models that allowed for exploration of the conditions that favor the evolution of non-local perception (i.e., the ability to detect resources beyond an animal’s current location) even when such perception is costly from a metabolic standpoint. Among other things, we found that the evolution of non-local perception is favored in resource-rich landscapes. This is because in resource-poor landscapes the costs of developing and maintaining the ability to secure resources at distance is not sustainability. These findings suggest pathways by which the evolution of perception may have happened early in evolution and support biological interpretations from scenarios in which perceptual ability has been lost (e.g., ‘blind’ animals in resource-poor cave systems.)

We also explored a relatively little studied area of mathematics involving so-called ‘reinforced diffusion.’  In our reinforced diffusion models, mathematical functions were designed that act as surrogates for how real animals might remember the specific path they have walked or the general area in which they have been.  We found that these types of models allow for qualitatively different kinds of movement pattern, including bounded wandering, attraction to a small region of space, and—most interestingly—repeated following of the same track even when the landscape is completely free of detail.

This project had broader impacts through the training and experience that project participants received, including 3 undergraduate students, 4 graduate students, and a (postdoctoral-level) research scientist.  All of these participants were coauthors on at least one of our research products (which helps them build their resumes as scientists) and the graduate and postdoctoral scholars were frequently first-authors (thereby giving them experience in project leadership). Plans for other outreach activities were greatly disrupted by the constraints that Covid-19 placed on all non-computational activities for 2.5 years out of the 3 year award.

Last Modified: 09/05/2022
Modified by: William F Fagan