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Published on: July 30, 2019
Dynamic energy budget models with size-dependent hazard rates
Glenn Ledder1, J David Logan, Anthony Joern
1Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588-0323, USA. gledder@math.unl.edu
Journal of Mathematical Biology
|May 28, 2004
Summary
This study explores energy budget models to find optimal growth strategies for maximizing lifetime reproductive energy. It reveals that size-dependent death rates can favor growing large even with low survival probabilities.
Area of Science:
- Ecology
- Theoretical Biology
- Mathematical Biology
Background:
- Organismal energy budgets are crucial for understanding life history strategies.
- Size-dependent mortality, such as predation, significantly influences survival probabilities.
- Dynamic energy budget models provide a framework for analyzing growth and reproduction.
Purpose of the Study:
- To formulate and analyze dynamic energy budget models to determine optimal strategies for maximizing lifetime reproductive energy.
- To investigate the interplay between size-dependent death rates and optimal growth strategies.
- To calculate size at maturity and survival probability within a net production model.
Main Methods:
- Formulation of two dynamic energy budget models: a net assimilation model (constant allocation) and a net production model (2-stage allocation).
- Analysis of size-dependent per capita death rates.
- Calculation of size at maturity and probability of reaching it.
- Numerical simulations to explore parameter dependencies.
Main Results:
- A small probability of survival to maturity is incompatible with an exponential survival probability assumption.
- When the hazard rate is higher for smaller individuals, optimal strategy can be to grow large despite low survival probability.
- Optimal allocation strategies are shown to be dependent on parameter values.
Conclusions:
- Dynamic energy budget models, incorporating size-dependent mortality, can reveal complex optimal life history strategies.
- The relationship between survival probability and growth strategy is non-trivial and depends on mortality patterns.
- Understanding these strategies is key for predicting organismal responses to environmental factors.
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