Ecology and evolutionary biology have historically been two of the areas of biology which have most benefited from, and made use of, mathematical methods. Many distinguished mathematical biologists have contributed to these areas, and their efforts have illuminated much of ecological and evolutionary theory over the past century. An objective of this special year is to focus on specialized areas that offer particularly challenging mathematical problems, which are relatively unexplored and are of potentially great interest to observational biologists. Thus, an underlying goal of the proposed activities is to maintain direct connections to observable biology.
One thread of connection between the various proposed activities concerns spatial aspects of natural systems. Central questions about the history and structure of biological systems are affected by spatial variation. Additionally, numerous problems, which have great public impact, necessarily involve the spatial heterogeneity of biological systems, both those occurring through natural processes and those deriving from human actions. Conservation biology, biodiversity, harvest planning, invasive species control, and wildlife management are just a few of the applications that utilize mathematical methods to address major public policy issues. These applied areas rely greatly upon general ecological and evolutionary genetics theory. Determining how natural systems are affected by interactions of space and time leads to problems that require mathematical approaches. Although a large body of mathematical literature has developed over the past several decades dealing with spatio-temporal interactions, there are still many biologically important questions that require new mathematical approaches and would benefit from close collaborations between ecologists, evolutionary biologists, and mathematicians.
Beyond emphasizing the spatio-temporal nature of natural systems and the mathematical approaches that are used to address them, the special year is intended to foster interactions between individuals working on problems at different spatial/temporal scales. While the underlying biological questions may operate on quite different scales, the necessary mathematical approaches may be similar. Another theme for the year is linking between scales, for example, how might evolutionary models that account for the dynamics of spatial structure relate to ecological models, which operate on shorter time periods? How might genomic information that is rapidly becoming available assist in developing a theory for whole organism interactions with environment and the functioning of populations, communities, and ecosystems? What new mathematical approaches might contribute to better models for natural system response across the genome/organism/population interfaces? The proposed set of activities will enhance our ability to address these questions and hopefully lead to new collaborations between mathematicians and biologists that are beneficial to both fields.