Population Ecology - Spatial structure Some History Basics of spatial effects on populations Types of models Metapopulation Approaches Survey of recent paper topics Papers to Read: Hanski, I., M. Kuussaari, M. Nieminen. 1994. Metapopulation Structure and Migration in the Butterfly Militaea Cinxia. Ecology 75:747-762. Tilman, D. 1994. Competition and Biodiversity in Spatially Structured Habitats. Ecology 75:2-16. References: Gilpin, M. and I. Hanski. 1991. Metapopulation Dynamics: Empirical and Theoretical Ionvestigations. Academic Press, London. Levin, S. A. 1976. Population dynamics models in heterogeneous environments. Ann. Rev. Ecol. System. 7:287-310. History: Up until very recently there has been very little investigation of spatial effects in ecological models. Skellam and Kierstad and Slobodkin in the early 1950's dealt with models for animal dispersal patterns and planktonic patchiness, using simple partial differential equation approaches. The population genetics literature has had an extensive discussion of spatial effects since the papers of Wright, Haldane and Fisher, but it was only in the 1970's that a literature dealing with the effects of spatial heterogeneity in environment became an very active area of ecological research. The theory of island biogeography was one factor which guided study here, and became the progenitor of a "patch" view of the world, in which we think of the world as made up of a patchwork quilt of varying types of habitats, with intervening areas of different types. The "metapopulation" approach, due to Richard Levins, was initiated in 1970 and considers a metapopulation to be a population of populations. Although this arose initially in a model to investigate the possibility of group selection being a significant factor in evolution, it has led to major new theoretical approaches to population structure. In the early 1970's, Simon Levin greatly elaborated the reaction-diffusion modeling approach to particularly investigate the effects of spatial disturbances on community structure and population dynamics, and relate this to discrete-patch dynamic models. Spatial effects on populations: There is a very large literature dealing with methods to characterize spatial patterning, and to tease apart the relationship between local abundances and underlying environmental or habitat factors. These mainly fall within the area of multivariate statistics although there is an active area called spatial statistics. Very simple methods here (such as the mean/variance ratio) aid in analyzing whether a particular measured population tends to be more clumped than random (where random refers to a Spatial Posson process, such that the number of individuals within a particular subregion has a distribution with is Poisson with parameter being linear in the area of the region), or more uniform (evenly dispersed) than random. Another aproach involves analyzing poipulation clines, meaning changes in population along some environmental gradient. Spatial effects may be grouped into effects external to the population of interest and internal effects. Internal effects would include spatial patterning due to intraspecific competitive interactions, leading to territory formation and well as shading and nutrient limitation effects in plants, allelopathy, pheromone release, and any type of behavioral interactions which lead to differential spatial use by certain individuials within a population relative to others (e.g. dominant individuals excluding sub-dominants from prime feeding locations). There is a large literature on territory formation and size, with little of this dealing in any explicit way with space - much of the objective is to determine when territoriality might most readily arise. Much of the literature on spatial patterning deals with how underlying environmental factors affect population structure. These include patch views of the world (the island case is one example of this, as well as the case of a refuge from predation), and cases in which there is an underlying continuous change in environmental factoirs with some spatial dimension (e.g. elevation). Some of the motivation in the latter dealt with understanding how spatial pattern may arise in circumstances which appear to be spatially uniform. The classic example of this is the formation of planktonic patches in the open ocean (discussed by Kierstad and Slobodkin). More recently, much of landscape ecology analyzes spatial variation and how it relates to population structuring. There are also many approaches to analysis of dispersal patterns and the pattern of spread of a population from an initial focus (such as release of an alien species, a small founder population, or spread of a pathogen). Types of models: 1. No explicit spatial representation - a population model with an immigration/emmigration term. 2. Patch occupancy models - a metapopulation approach in which the state variables represent the fraction of patches occupied and unoccupied - sort of a statistical mechanics of patches, in which no explicit concern is taken with exactly where one patch is relative to another. 3. Explicit patch models - metapopulatiuon models in which the population is characterized by some state variables (such as population size, age structure, etc.) within each of a collection of patches, there is movement between patches, and the dynamics of the state variables are followed for each patch explicitly. Here, the spatial relationship between patches may be considered explicitly (e.g. patch 1 is 2 km from patch 2 and 3 km from patch 3, etc.), or may be implicit, so that there is someexchange between patches sending propagules into a "bath" with which all patches exchange individuals. 4. Continuous space models - the environment is viewed as continuous with population density varying across it - typically leading to partila differential equation models framed as reaction-diffusion (reaction refering to local growth and diffusion refering to dispersal between nearby locations) along with advection terms (e.g. wind driven movement). 5. Individual-based approaches - population is viewed as made up of individuals moding around on a spatially-explicit landscape with rules dependent upon local conditions. Much of the historic interest in metapopulation models arose due to the idea of "spreading the risk", in which the overall population size may be more "stable" when split into several sub-populations with differing environmental conditions relative to the situation in which a single large population is exposed to variation in conditions at a single site. This is closely tied in to the SLOSS debate in conservation biology (Single-Large or Several Small) relating to reserve design. It is also closely related to arguments relating to dispersal/ dormancy characteristics, which is affected by the local stochasticity in environmental conditions relative to that at more regional extents at which dispersal may occur, and how this may be affected by spatial and temporal correlations in environmental; factors affecting individual growth and survival. The current interest in metapopulation approaches is driven by the acknowledgement that human-dominated landscapes are often highly fragmented, leading to analysis of such factors as corriders in maintaining long-term persistence of a population. Results from search on 1990's of ecological journals on topic of spatial dynamics: Community patterns 6 Animal dispersal 4 Metapopulation approaches 5 Fragmented landscape 3 Habitat selection 1 Spatial foraging 4 Statistical methods 2 Pathogen dispersal 3 Models and theory 5 Pollen dispersal 1 Patch dynamics 1 Population regulation 2 Competition and space 2 Ecotones 1 Refuges 1 Islands 1 Total: 42