1 / 12

Integral projection models

Integral projection models. Continuous variable determines Survival Growth Reproduction. Easterling, Ellner and Dixon, 2000. Size-specific elasticity: applying a new structured population model. Ecology 81:694-708. The state of the population. Integral Projection Model.

clovis
Télécharger la présentation

Integral projection models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Integral projection models Continuous variable determines • Survival • Growth • Reproduction Easterling, Ellner and Dixon, 2000. Size-specific elasticity: applying a new structured population model. Ecology 81:694-708.

  2. The state of the population

  3. Integral Projection Model Integrate over all possible sizes Number of size x individuals at time t Number of size y individuals at time t+1 = Babies of size y made by size x individuals Probability size x individuals Will survive and become size y individuals

  4. Integral Projection Model Integrate over all possible sizes Number of size x individuals at time t Number of size y individuals at time t+1 = The kernel (a non-negative surface representing All possible transitions from size x to size y)

  5. survival and growth functions s(x) is the probability that size x individual survives g(x,y) is the probability that size x individuals who survive grow to size y

  6. survival s(x) is the probability that size x individual survives logistic regression check for nonlinearity

  7. growth function g(x,y) is the probability that size x individuals who survive grow to size y mean regression check for nonlinearity variance

  8. growth function

  9. Comparison to Matrix Projection Model Matrix Projection ModelIntegral Projection Model • Populations are structured • Discrete time model • Population divided into discrete stages • Parameters are estimated for each cell of the matrix: many parameters needed • Parameters estimated by counts of transitions • Populations are structured • Discrete time model • Population characterized by a continuous distribution • Parameters are estimated statistically for relationships: few parameters are needed • Parameters estimated by regression analysis

  10. Comparison to Matrix Projection Model Matrix Projection ModelIntegral Projection Model • Recruitment usually to a single stage • Construction from observed counts • Asymptotic growth rate and structure • Recruitment usually to more than one stage • Construction from combining • survival, growth and fertility functions into one integral kernel • Asymptotic growth rate and structure

  11. Comparison to Matrix Projection Model Matrix Projection ModelIntegral Projection Model • Analysis by matrix methods • Analysis by numerical integration of the kernel • In practice: make a big matrix with small category ranges • Analysis then by matrix methods

  12. Steps • read in the data • statistically fit the model components • combine the components to compute the kernel • construct the "big matrix“ • analyze the matrix • draw the surfaces

More Related