StageStructured Population Growth

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Stage-Structured Population Growth
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Assumptions

• Closed Population (No immigration or emigration)
• Vital rates are constant (no demographic or
  environmental stochasticity)
• No density-dependence
• However, Ramas Ecolab can relax these assumptions
  making models more realistic

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Stage-Structured Models

• Similar to Age-structured
• Use stages, not ages, for nodes
• Has fertility probabilities in top row
• Has the following growth probabilities
• Stasis in the diagonal (stay in the same stage)
• Growth in the subdiagonal (either to next stage
  or skipping a stage)
• Getting smaller in the area above the diagonal

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Stage-Structured Matrices

• Residence Time

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Residence Time

• Is the average time individuals spend in a stage
• Otherwise, finite rate of increase (?), stable
  age distribution, and reproductive value are
  exactly the same as in age-structured models

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Constraints

• In Ecolab, can specify that column sums
  (excluding the first row) must equal 1
• If your model includes vegetative reproduction
  (where elements in rows other than the first one
  contribute to reproduction), you need to specify
  to ignore constraints in the GENERAL INFORMATION
  section

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Adding Density Dependence

• Can specify either ceiling, scramble, or contest
  type
• Ramas Ecolab uses total abundance to modify all
  of the elements of the stage matrix proportionally

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Sensitivity Analysis

• What is the contribution of each element to the
  dynamics of the population?
• How sensitive is the future of the population to
  the elements in the stage matrix?
• Can calculate both sensitivities and elasticities
• Both measure the effect of each vital rate
  (transition element) on the eigenvalue of the
  stage matrix (the finite rate of increase or ?)

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Sensitivity

• Of lambda to changes in aij is proportional to
  the product of the ith element of the
  reproductive value vector and the jth element of
  the stable age distribution

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Elasticity

• Of lambda with respect to aij are the
  proportional contributions of each aij to
  lambda
• The sum of elasticities is 1