Within-patch variability

Within-patch variability refers to those temporally varying properties of a physical location in space that it does not share with other localities (Chesson 1978, 1981, 1985, 1991).  The properties we think of are the organisms present, their properties, and the physical environment that they experience. We speak of a location in space as a "patch." Sometimes, the environment will have a natural discrete structure, with numerous areas of habitat separated from another, and we naturally call these "habitat patches" for the organisms of our focus, and are therefore the "patches" referred to here.  More generally, patches can be arbitrary subdivisions of space.  Properties of a patch invariably change over time.  But different patches experience different changes.  This is within-patch variability.  Its causes are many and varied.  Some of it is due to within-individual variability from the organisms on a patch. Provided the number of organisms on a patch is small, variation due to within-individual variability will be significant at the level of the patch.  Also, the phenotypic composition of the individuals on a patch will change over time, and this may happen in different ways on different patches due again to within-individual variability, causing chance fluctuations in phenotypic composition.  Such effects are contributions to temporal variation on a patch that are interactions between within-individual variability and between-individual variation. These sources of variation then can interact with local population dynamics and dispersal.  If local population dynamics are unstable, such interactions will enhance the uniqueness of population fluctuations and compositional changes on individual patches, and so will enhance within-patch variability.  Turning to the physical environment, there are numerous physical processes that have large elements of chance and so lead to different trajectories of change in the physical environment on different patches. This is pure spatio-temporal environmental variation and contributes directly to within-patch variability.  Note that spatio-temporal environmental variation inevitably interacts also with population dynamics, and so affects local population changes, enhancing within-patch variability.  Note that different patches will experience common elements of temporal fluctuations too.  The idea is that these common elements should be partitioned out from the total variation in the environment over time to leave that which is unique to the individual patch, within-patch variability.  Note that within-patch variation must lead to differences between patches in their population densities, phenotypic composition, and physical environment.  But these differences will change over time contributing to an ever changing spatial pattern.  Note also that patches will differ from one another at any one time due to permanent differences in their physical properties ("between-patch variation").  Such differences could be partitioned out from the total variation from patch to patch to obtain a residual amount due to within-patch variation.  Note, however, that between-patch variation may combine nonadditively ("interactively") with between-patch variation and thereby contribute to an ever changing spatial pattern in that way.  That interactive component of variation would be left over after between-patch and common temporal variation were partitioned out in an analysis of variance.  This interactive component might therefore might be thought of as part of within-patch variation if only because of the difficulty of distinguishing it from other sorts of within-patch variation. Because this interactively generated variation is likely to have similar effects on population and community dynamics to within-patch varation from other sources, there seems to be no good reason to classify it differently.

Within-patch variation is of great interest in scale transition theory (Chesson 1978, 1981, 1991; Chesson et al 2005).  It generates variation in space that interacts with nonlinearities in population dynamics, with profound effects on population dynamics on scales of many patches. 


Chesson, P.L. 1978. Predator-prey theory and variability. Ann. Rev. Ecol. Syst. 9, 323-347.


Chesson, P.L. 1984. Variable predators and switching behavior. Theor. Pop. Biol. 26, 1-26.


Chesson, P.L. 1985. Coexistence of competitors in spatially and temporally varying environments: a look at the combined effects of different sorts of variability. Theor. Pop. Biol. 28, 263-287.


Chesson, P. 1991. Stochastic population models. In "Ecological Heterogeneity," J. Kolasa and S.T.A. Pickett (eds), Ecological Studies: analysis and synthesis 86, 123-143. Springer-Verlag, New York.

 Chesson, P., Donahue, M., Melbourne, B., Sears, A. 2005. Scale transition theory for understanding mechanisms in metacommunities.  In Holyoak, M, Leibold, M.A., Holt, R.D., eds, Metacommunities: spatial dynamics and ecological communities, pp 279-306