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Demographic and environmental stochasticity in population processes 1) Population dynamics

Demographic and environmental stochasticity in population processes 1) Population dynamics 2) Community dynamics 3) Selection in fluctuating environments Steinar Engen, Centre for Biodiversity Dynamics, Dept. of Mathematical Science , NTNU, Trondheim, Norway.

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Demographic and environmental stochasticity in population processes 1) Population dynamics

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  1. Demographic and environmentalstochasticity in populationprocesses • 1) Populationdynamics • 2) Communitydynamics • 3) Selection in fluctuatingenvironments • Steinar Engen, Centre for Biodiversity Dynamics, Dept. of Mathematical Science, NTNU, Trondheim, Norway

  2. For more detailed lectures on diffusion, extinction, dynamics ,age-structure and abundance models see www.math.ntnu.no/~steinaen/lovund_2012 and more on age-structure www.math.ntnu.no/~steinaen/ISEC_2012 and/or Lande, Engen and Sæther 2003, Stochastic Population Dynamics in Ecology and Conservation, Oxford University Press. These lectures are based on co-authored papers with Russell Lande and Bernt-Erik Sæther during the last 20 years. For a list see my home page www.math.ntnu.no/~steinaen

  3. Single species population dynamics Environmental and demographicstochasticity Diffusiontheory Extinction Some harvesting statistics Age structure Steinar Engen, Centre for Biodiversity Dynamics, Department of Mathematical Sciences

  4. Population fluctuations for some species

  5. Distribution of individual fitness w for two bird species

  6. The Green function

  7. Expected time to extinction

  8. The expected time to extinction is often very large

  9. The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time

  10. The rate of increase in fitness of any organism at any time is equal to its genetic variance in fitness at that time The rigour of its demonstration requires that the terms employed should be used stricktly as defined; the ease of its interpretation may be increased by appropriate conventions of measurement. For example, the ratio p:q should stricktly be evaluated at any instant by enumeration, not necessarily of the census population, but of all individuals having reproductive value, weighted according to the reproductive value of each.

  11. The total reproductive value V of the population growth exactly exponential, and lnV has exactly linear growth. R. A. Fisher The age distribution approaches the stable age distribution

  12. Age-structured population, no density regulation. (The total reproductive value serves as a filter) Population size Total reproductive value

  13. Community dynamics History The infinite allele model – neutral models Independent species dynamics Comparison of two dynamic models giving Fisher’s log series model

  14. The discovery of abundance patterns by Corbet and Williams in 1942:

  15. Poisson Gamma negative binomial

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