Continuous-space models for (ecological) population dynamics - ICMS

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Overview Moment equations, with choices More general challenges References Assume spatial homogeneity Assume second-order spatial homogeneity and isotropy: i.e., that any 〈f (x, y)〉 depends only on |x − y| Alternatives Gradients Distance from edge of wave (pair-edge approximation: Habitat boundaries (Finite spatial patches) Ben Bolker Spatial <strong>models</strong> in ecology
Expand covariances Overview Moment equations, with choices More general challenges References Convert expectations of products (second central moments) to covariances (noncentral moments): 〈 (N(x) − ¯N)(N(y) − ¯N) 〉 ≡ CNN (|x − y|) Also have C µN , C µµ (assumed static); also higher central moments M 3 N,N,N (etc.) Alternatives: work with central moments instead scaled covariances (C/N), correlations (C/N 2 ) multiplicative correlations (Keeling) Ben Bolker Spatial <strong>models</strong> in ecology
Page 1 and 2: Overview Moment equations, with cho
Page 3 and 4: Model classes Overview Moment equat
Page 5 and 6: Outline Overview Moment equations,
Page 7 and 8: Master equation Overview Moment equ
Page 11: Overview Moment equations, with cho
Page 17 and 18: Continuum limits Overview Moment eq
Page 23 and 24: Analysis Overview Moment equations,
Page 25 and 26: Exploiting linearity Overview Momen
Page 29 and 30: Species coexistence Overview Moment
Page 33 and 34: More . . . Overview Moment equation

Continuous-space models for (ecological) population dynamics - ICMS

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