### Abstract

1. Elasticity and sensitivity analyses are used widely in evolutionary biology, ecology and population management. However, almost all applications ignore density dependence, despite the widespread assumption that density dependence is ubiquitous. We assess whether this matters by comparing density-dependent and density-independent elasticity analyses for the LPA model of Tribolium.

2. Density-independent elasticities of lambda are a poor indicator of the effects of changes in demographic parameters on population size, even for populations at stable equilibrium. With non-equilibrium dynamics, the divergence can be particularly large. In the extreme, a change in a demographic parameter with a positive effect on individual fitness can reduce mean population size, so even the sign of a density-independent elasticity may be wrong. Elasticities of larval, pupal and adult numbers are not proportional to each other, neither are they proportional to elasticities of total population size.

3. A full density-dependent analysis is therefore vital when concerned with effects on population numbers, as in population management, pest control and prediction of population effects of toxins.

4. When examining the consequences for individual fitness of changes in demographic parameters, density-independent elasticities provide a more useful approximation to the density-dependent values. However, they fail to detect cases where non-equilibrium dynamics means that particular life histories gain an advantage by exploiting predictable periods when density dependence is relaxed.

5. This phenomenon can produce a marked change in the pattern of elasticities as a bifurcation is crossed. The corresponding changes in selection pressures may act to stabilize dynamics in some circumstances and destabilize them in others. There is no single answer to the question of whether selection should favour equilibrium or non-equilibrium dynamics.

Original language | English |
---|---|

Pages (from-to) | 94-105 |

Number of pages | 11 |

Journal | Journal of Animal Ecology |

Volume | 72 |

DOIs | |

Publication status | Published - 2003 |

### Keywords

- chaos
- life histories
- matrix models
- population dynamics
- sensitivity analysis
- STRUCTURED POPULATIONS
- SELECTION PRESSURES
- NATURAL-SELECTION
- GENETIC-ANALYSIS
- GROWTH RATE
- DYNAMICS
- EVOLUTION
- ENVIRONMENTS
- PARAMETERS
- CASTANEUM

### Cite this

**Density-dependent populations require density-dependent elasticity analysis: an illustration using the LPA model of Tribolium.** / Benton, Timothy Guy.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Density-dependent populations require density-dependent elasticity analysis: an illustration using the LPA model of Tribolium.

AU - Benton, Timothy Guy

PY - 2003

Y1 - 2003

N2 - 1. Elasticity and sensitivity analyses are used widely in evolutionary biology, ecology and population management. However, almost all applications ignore density dependence, despite the widespread assumption that density dependence is ubiquitous. We assess whether this matters by comparing density-dependent and density-independent elasticity analyses for the LPA model of Tribolium.2. Density-independent elasticities of lambda are a poor indicator of the effects of changes in demographic parameters on population size, even for populations at stable equilibrium. With non-equilibrium dynamics, the divergence can be particularly large. In the extreme, a change in a demographic parameter with a positive effect on individual fitness can reduce mean population size, so even the sign of a density-independent elasticity may be wrong. Elasticities of larval, pupal and adult numbers are not proportional to each other, neither are they proportional to elasticities of total population size.3. A full density-dependent analysis is therefore vital when concerned with effects on population numbers, as in population management, pest control and prediction of population effects of toxins.4. When examining the consequences for individual fitness of changes in demographic parameters, density-independent elasticities provide a more useful approximation to the density-dependent values. However, they fail to detect cases where non-equilibrium dynamics means that particular life histories gain an advantage by exploiting predictable periods when density dependence is relaxed.5. This phenomenon can produce a marked change in the pattern of elasticities as a bifurcation is crossed. The corresponding changes in selection pressures may act to stabilize dynamics in some circumstances and destabilize them in others. There is no single answer to the question of whether selection should favour equilibrium or non-equilibrium dynamics.

AB - 1. Elasticity and sensitivity analyses are used widely in evolutionary biology, ecology and population management. However, almost all applications ignore density dependence, despite the widespread assumption that density dependence is ubiquitous. We assess whether this matters by comparing density-dependent and density-independent elasticity analyses for the LPA model of Tribolium.2. Density-independent elasticities of lambda are a poor indicator of the effects of changes in demographic parameters on population size, even for populations at stable equilibrium. With non-equilibrium dynamics, the divergence can be particularly large. In the extreme, a change in a demographic parameter with a positive effect on individual fitness can reduce mean population size, so even the sign of a density-independent elasticity may be wrong. Elasticities of larval, pupal and adult numbers are not proportional to each other, neither are they proportional to elasticities of total population size.3. A full density-dependent analysis is therefore vital when concerned with effects on population numbers, as in population management, pest control and prediction of population effects of toxins.4. When examining the consequences for individual fitness of changes in demographic parameters, density-independent elasticities provide a more useful approximation to the density-dependent values. However, they fail to detect cases where non-equilibrium dynamics means that particular life histories gain an advantage by exploiting predictable periods when density dependence is relaxed.5. This phenomenon can produce a marked change in the pattern of elasticities as a bifurcation is crossed. The corresponding changes in selection pressures may act to stabilize dynamics in some circumstances and destabilize them in others. There is no single answer to the question of whether selection should favour equilibrium or non-equilibrium dynamics.

KW - chaos

KW - life histories

KW - matrix models

KW - population dynamics

KW - sensitivity analysis

KW - STRUCTURED POPULATIONS

KW - SELECTION PRESSURES

KW - NATURAL-SELECTION

KW - GENETIC-ANALYSIS

KW - GROWTH RATE

KW - DYNAMICS

KW - EVOLUTION

KW - ENVIRONMENTS

KW - PARAMETERS

KW - CASTANEUM

U2 - 10.1046/j.1365-2656.2003.00684.x

DO - 10.1046/j.1365-2656.2003.00684.x

M3 - Article

VL - 72

SP - 94

EP - 105

JO - Journal of Animal Ecology

JF - Journal of Animal Ecology

SN - 0021-8790

ER -