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

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Overview Moment equations, with choices More general challenges References 1 Dene the system (write master equation) 2 Write expectations of change in mean and pair densities 3 Assume spatial homogeneity 4 Expand products as covariances 5 Close moments 6 Take continuum limits 7 Analyze Solve numerically Ben Bolker Spatial <strong>models</strong> in ecology
Master equation Overview Moment equations, with choices More general challenges References Dene rates of a continuous-time stochastic process: patch size ω (small), positions x, y, time ∆t (small): e.g. the spatial logistic (with environmental heterogeneity in mortality rate): Event δN(x) Rate ∑ birth +1 y∈Ω fN(y)D(y, x)ω death (dens-independent) -1 µ(x)N(x) death (crowding) -1 N(x) ∑ y∈Ω αN(y)U(y, x) All kernels are symmetric (relax) and normalized: ∑ y∈Ω K(y)ω = 1 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: Outline Overview Moment equations,
Page 13 and 14: Expand covariances Overview Moment
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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