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