Spatial Statistics and Digital Image Analysis (1991) / Chapter Skim
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7. Spatial Statistics in Ecology
7. Spatial Statistics in Ecology
Pages 129-146
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From page 129... ...
Perhaps the most important data for quantitatively oriented plant ecologists are complete maps of the vegetation in an area at different times. While the construction of such maps used to be an incredibly time-consuming fieldwork task, modern digitization techniques enable an increased use of aerial photographs and satellite images.
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From page 130... ...
Section 7.3 contains an outline of a point process approach to modeling single species forest growth. It must be emphasized here that the efforts to date of using stochastic models (in particular point process models)
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From page 131... ...
This is suggested on biological grounds, since Cataglyphis ants eat dead insects, mainly Messor ants, whereas the latter collect seeds for food. An example of a trivariate point process is the data collected by Gerrard (1969)
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From page 132... ...
discussed biological and statistical aspects of foraging paths for a single species. The study area consisted of about half scrub anti half field, and the Cataglyphas nests were located mostly in the field region.
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/;r) : for the Messor nests, calculated at 5-ft intervals, together with the envelope of 19 curves from simulated Poisson data.
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The solid dots correspond to Cataglyphas nests, and the open dots denote Messor nests. The field is between 330 and 340 ft wide.
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From page 135... ...
7.2.2 Cluster Processes as more complex The concepts of clustering and regularity are important ecological concepts, describing deviations from the completely random process. On an intuitive level, clustering describes the phenomenon of an ecological niche, or local regions with higher than average density, separated by regions of Tow density, while regularity indicates a tendency towards spacing between individuals.
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From page 136... ...
than a Poisson process. The most common Poisson cluster process is the Neyman-Scott process, in which a random number of points are laid out in an i.i.~.
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. Comparing this to the Poisson cluster process pgfl given above, we see that it is of the same form.
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From page 138... ...
On the whole, this analysis, while providing a nice description of the observed spatial pattern, fails to produce an ecological explanation of it. 7.2.4 Markovian Point Processes Markovian models, which are defined through a local dependence structure, have found much use in biology.
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From page 139... ...
The two most common approaches are to use approximations developed in statistical physics for the normalizing constant (Ogata and Tanemura, 1984, discuss some of these approximations; see also Ripley, 198S, ch. 4, and recent work using stochastic approximation techniques by ..
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From page 140... ...
7.3 A Spatio-Temporal Point Process Model for Tree Growth Most situations where spatial point process models can be useful include a temporal aspect. In this section, we discuss a possible approach to modeling tree growth in a pristine forest, with a view toward use for regenerative policies in national parks following major natural disasters.
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From page 141... ...
is to assess effects of changes in the driving forces of the ecological process, and evaluate various possible reseeding policies. It is straightforward to include modest amounts of harvesting in the model, which can then be used to assess various recruitment policies.
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There is a substantial need for more theoretical research into statistical inference based on interacting components of complex systems, and into the comparison of mode] data (be it the result of simulation, mathematical, or stochastic anaylsis)
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J Diggle, Simple Monte Carlo tests for spatial pattern, Appl.
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·e [24] Hertz, P., Uber die gegenseitligen durchschnittlichen Abstand von Punkten, die mit bekanuter mittlerer Dichte im Raum angeordnet sind, Math.
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C Cressie, A model for a spatial birth process, paper presented at the 1989 Joint Statistical Meetings, Washington, D.C., Department of Statistics, Iowa State University, 1989.
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B Davies, A statistical survey of earthquakes in the main seismic region of New Zealand, Part 2 Time series analyses, N.Z.
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