StageStructured Population Growth - PowerPoint PPT Presentation
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StageStructured Population Growth
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... Population Growth. Assumptions. Closed Population (No immigration or emigration) ... However, Ramas Ecolab can relax these assumptions making models more realistic ... – PowerPoint PPT presentation
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Title: 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
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