Dynamics - Matrix models
14 important questions on Dynamics - Matrix models
What are transient dynamics?
- Matrix projection
- Population development
- For years or decades
- Starting pop structure important
What are asymptotic dynamics?
- Lambda
- Elasticity
- After many decades/centuries
- Assumes stable stage distribution was reached
How is exploitation implemented in the matrix?
- Individuals removed => increase mortality
- Seed harvested => reduce reproduction rate
- Leaf harvest affects growth => reduce growth rate
- Indirect effect on other stages => change transitions
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How is exploitation implemented in the vector?
- Seed harvested => remove seeds
- Whole individuals harvested => remove individuals
- Plant part harvested => NOT!
How can matrix models be made sustainable?
- Population continues to grow: λ ≥ 1 (asymptotic)
- Exploitation does not strongly affect population growth: elasticity (asymptotic)
- Absolute population size stays the same: population projection (transient)
- Availability of resource remains the same: population projection (transient)
What are the pros of using lambda=1 as a sustainability criterion?
- Makes intuitive sense
- Easy to test
What are the cons of using lambda=1 as a sustainability criterion?
- Considers whole population, not resource
- Considers population growth, not its size
- Unaffected by starting conditions or disturbances
- Estimate of λ can be uncertain
What are the characteristics of the Maximum Sustained Yield concept?
- Departs from logistic growth model
- All growth is sustainably harvested
- Max at intermediate population size
- Parameters hard to obtain
- Is used in hunting & fisheries
What are differences between transient and asymptotic population growth?
Asymptotic: independent from starting population; transient: dependent on starting distribution
What information is used to calcluate the transition to the next class in *size*-based models?
In size-based models the transition to the next size classe is a function of:
- Individual growth rate
- survival rate
- 1/(category width)
Brazil nut tree: why does it take long to reach the stable size distribution?
- This is a long-lived species
- The matrix has many categories
Brazil nut tree: why can lambda be considered as an indicator for sustainable extraction?
Brazil nut tree: Why would a low elasticity for reproduction indicate scope for sustainable nut collection?
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