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Abstract

A fundamental goal in ecology is to identify the appropriate scales at which to
observe trends in ecosystem behavior. Researchers often rely on intuition to
choose a sampling scale, which if too large or too small potentially obscures the
real system trends. A characteristic length scale (CLS) is a natural scale of a
system at which the underlying deterministic dynamics are most clearly observed
over stochasticity. The overarching aim of this research was to develop, examine
and apply a robust technique to detect CLSs of real ecological systems.
In this thesis, I first compared the robustness of two CLS methods, both of which
account for complex oscillatory dynamics of ecological systems using attractor
reconstruction from long time series of data. I applied these techniques to estimate
CLSs of spatial multispecies systems of varying complexity, showing that for
more complex models, the prediction r2 metric of Pascual and Levin (1999) is a
robust method. I then used an alternative method of CLS estimation, based on
prediction r2 but where repetition in space is largely substituted for repetition in
time in attractor reconstruction, to determine the CLS of a natural marine fouling
system. The new technique, requiring only a short temporal sequence of as few as
three highly resolved spatial maps, enabled unambiguous length scales to be
estimated for this system. Importantly, the estimated CLS was similarly based on
analysis of several species representing a spectrum of phyla and life history
patterns, indicating the adequacy of this method for objectively determining
optimal scales of observation for real systems. Moreover, the CLS estimates of
this system remained surprisingly consistent despite changes in time intervals
between the spatial maps, changes in the number of maps used in the temporal
sequence, and varying start dates of map sequences.
When the field results were compared to those derived from a spatially explicit
individual-based model of a similar marine community nearby, the average CLSs
of the two communities were strikingly similar (~ 0.35 m), suggesting that
dynamical trends of like systems may be best observed on similar scales.
I also considered whether the approach could be extended to identify trends based
on the dynamics of interactions among habitat types as opposed to interactions
among species groups. Analysis of maps produced from remote sensing data at
the habitat level successfully revealed unambiguous characteristic length scales of
a coral reef. Habitats distinct in their species assemblages, abundances and
morphologies provided similar length scales (~ 300 m), suggesting that the
system-level CLS detected is independent of the habitat type used for its
estimation.
Different species within the same system indicated dissimilar CLSs in some
spatial model communities where species were only weakly connected, either due
to the topology of network interactions or through spatial isolation as a result of
spatial self-organization and patchiness. I finally evaluated the sensitivity of CLS
estimates to varying levels of species connectivity and found that when species
were weakly connected in terms of their network topology, the estimates of scale
were likely to be dissimilar.
The results contained within this thesis illustrate that the new method developed
to detect natural scales of complex systems (1) can be applied to natural
dynamical systems with a reasonable quantity of data, (2) is robust to changes in
parameters that should not affect the scale of observation (e.g. initial
configuration of the landscape), but (3) is sensitive to variations that would likely
affect the spatial scale at which trends can be observed (e.g. connectivity).
Species or habitat level data can be used to estimate CLSs, which will be critical
for choosing the scale at which to sample real ecosystems to distinguish trends
from random variation. Characteristic length scales can now be implemented to
objectively guide the choice of observation scale, and I expect that in the future,
they will become a part of every assiduous ecologist's toolbox.

Item Type:	Thesis - PhD
Authors/Creators:	Habeeb, RL
Keywords:	Ecology
Copyright Holders:	The Author
Copyright Information:	Copyright 2005 the author
Additional Information:	Chapter 2 appears to be the equivalent of a pre-print article published as: Habeeb, R.L., Trebilco, J., Wotherspoon, S., Johnson, C.R. (2005), Determining natural scales of ecological systems, Ecological monographs, 75(4), 467–487, Copyright 2005 by the Ecological Society of America. Appendix C is the final published article.
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