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r
e s e a r c h.. f o c u s :
Fractal
geometry of nature and biodiversity
Ecologists
have long known that the number of species found in a particular
area is determined in part by the structural complexity or "heterogeneity"
of the habitat and resources used by organisms. Ho wever,
their poor understanding of why left them with no ability to predict
how much heterogeneity would lead to how many species. In addition,
theories predicting species richness largely ignored the important
role of spatial scale, that is the scale of the observer and scale
at which organisms perceive the environment. There is increasing
evidence that many, if not most, spatial patterns in nature are
fractal, that is, they exhibit similar statistical patterns across
several orders of  magnitude
in scale of observation. This allows heterogeneity to be described
with very simple mathematical relationships that explicitly account
for the scale of organisms and observers.
I
use fractal geometry in just this way to develop a theory of species
richness that accounts for competitive coexistence for resources
and habitats that exhibit statistical spatial similarity across
scales of observation. This approach has yielded models of optimal
foraging for non-randomly distributed resources, species richness
for "guilds" of species that use the same resources, models
of the growth of populations using fragmented habitats (metapopulations),
the use of space by individual animals of different body size (home
ranges), and the effects of habitat fragmentation on species richness.
A wide variety of new problems await to be solved including:
- How
competition for similar resources interacts with limits to the
ability of
 individual
organisms to colonize particular clusters of habitat,
- How
species richness changes with the area sampled by an observer,
- How
the mechanisms controlling species richness (competition, disturbance,
colonization and extinction) change with the scale of observation,
and
- How
the relative abundance of species, and their associated species
richness, change with the body size of organisms.
In
addition to this theoretical work, I plan to explore the community
ecology of dung beetles in South Africa. Communities of these beetles
utilize a range of different size and quality "patches"
of dung of different ungulate species, and are comprised of many
species that vary 4 orders of magnitude in body mass. Because their
resource, dung, is unambiguous and easily presented in patches of
different size and quality, dung beetles and dung represent an ideal
system for testing the predictions of the theoretical models.
Selected
Related Publications:
Ritchie,
M.E. 2002. Competition and coexistence in mobile animals. Pages
127-141 In: Sommer, U. and B. Worm (editors), Competition and
coexistence. Springer, Berlin.
Haskell,
J.H., M.E. Ritchie, and H.Olff. 2002. Fractal geometry predicts
varying body size scaling relationships for mammal and bird home
ranges. Nature 418: 527-530. [PDF]
Pitt,
W.C. and M.E. Ritchie. 2002. Influence of prey distribution
on the functional response of lizards. Oikos 96:157-163.
Olff,
H. and M.E. Ritchie. 2002. Fragmented nature: consequences
for biodiversity. Landscape and Urban Planning 58: 83-92.
Ritchie,
M.E. and H. Olff. 1999. Spatial scaling laws yield a synthetic
theory of biodiversity. Nature 400: 557-560. [PDF]
Ritchie,
M.E. 1998. Scale-dependent foraging and patch choice in fractal
environments. Evolutionary Ecology 12: 309-330.
Ritchie,
M.E. 1997. Population dynamics in a landscape context: sources,
sinks, and metapopulations. Pages 160-184 In Bissonette, J.A. (ed.).
Wildlife and Landscape Ecology, Springer, New York.
For
more details about my other research and related publications, please
select from the following:
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