Ecological Indicators for the Nation (2000) / Chapter Skim
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Appendix B: Markov Matrices of Landscape Change
Appendix B: Markov Matrices of Landscape Change
Pages 159-164
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From page 159... ...
In contrast, policy must be based on predictive analyses of landscape trajectories given the current rates of changes from one land type to the others. The theory of Markov chains provides the mathematical basis for at least a first approximation of the consequences of current trends in land cover distributions.
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From page 160... ...
is something other than the desired time interval of the two maps (as frequently happens when using a historic set of air photos) , then the probabilities of change can be normalized to the desired time step (Pastor et al.
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From page 161... ...
, then the dominant eigenvector is still the steady state distribution of land cover classes if the dominant eigenvalue of the entire matrix equals that of the largest irreducible submatrix (i.e., a submatrix of non-zero transitions probabilities among a subset of land cover classes)
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From page 162... ...
Markov chains lend themselves to hierarchical classification systems. Suppose at the highest level of a classification system there are four land cover classes (say, forests, wetlands, agricultural lands, and urban lands)
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From page 163... ...
but with Subclasses Added From: la lb la 1B 1C 2a To: 2b 3a 3b 3c 4a 4b lc 2a ~ X I ~ X ~ 2b 1 3b 3c 4a 4b x Ixl xl xl 1 11 I X X X X X x IXT .
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From page 164... ...
They are first order because the changes involve no time delays longer than a single time step, and they are linear because the amount of land transferred from one class to another during a time step is simply a portion of the area of each land cover type. However, landscape dynamics are almost certainly nonlinear and often involve time delays.
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