Mathematical Challenges in Spatial Ecology, Volume 48, Number 11

T he word ecology comes from the Greek oikos, which means " house " , and was coined by the German zoologist Ernst Haeckel in 1870. It is, according to the Oxford English Dictionary, the " branch of biology that deals with organisms' relations to one another and to the physical environment in which they live. " Examples of such relations are predator prey interactions and plants competing for resources. Such interactions may be influenced by demographic and environmental fluctuations and occur over a wide range of spatial and temporal scales. Scientific curiosity by itself would be a sufficient impetus for studying ecology, but understanding species relations and interactions is not just an academic exercise: Humans rely on ecological services for purification of water and air, soil maintenance , pest control, waste management, nutrient recycling, and much more; these processes are controlled by complex interactions of species with each other and with the environment. We are altering the environment at an unprecedented rate: foremost are land-use changes and invasions of nonnative species. These human-caused alterations of the environment disrupt the functioning of ecosystems, often with devastating consequences. For instance, land-use changes, such as the conversion of forests into agricultural land, are often accompanied by soil erosion that affects water flow and nutrient recycling. There are numerous examples where species invasions drastically alter ecosystems: for instance, the water hyacinth , a plant native to the Amazon and considered one of the world's worst invaders, now covers many lakes and rivers in the tropics. Land-use changes and species invasions are the two major causes of species extinctions: it is estimated that human activities have increased extinction rates by a factor of 100 to 1,000. Both empirical work and theoretical work contribute to our understanding of how ecosystems function and to our ability to successfully manage and preserve them. Mathematicians can contribute to this understanding by collaborating with biologists on developing models, analyzing models, and relating theory to empirical work. I will focus on one factor that has become increasingly prominent in theoretical and empirical ecological studies: namely, space (see Tilman and Kareiva, 1997). We live in a spatial world, and the spatial component of ecological interactions has been identified as an important factor in how ecological communities are shaped. Understanding the role of space is challenging both theoretically and empirically. Since it is impossible to cover all aspects of this area in …