### Abstract

Most population viability analyses (PVA) assume that the effects of species interactions are subsumed by population-level parameters. We examine how robust five commonly used PVA models are to violations of this assumption. We develop a stochastic, stage-structured predator-prey model and simulate prey population vital rates and abundance. We then use simulated data to parameterize and estimate risk for three demographic models (static projection matrix, stochastic projection matrix, stochastic vital rate matrix) and two time series models (diffusion approximation [DA], corrupted diffusion approximation [CDA]). Model bias is measured as the absolute deviation between estimated and observed quasi-extinction risk. Our results highlight three generalities about the application of single-species models to multi-species conservation problems. First, our collective model results suggest that most single-species PVA models overestimate extinction risk when species interactions cause periodic variation in abundance. Second, the DA model produces the most (conservatively) biased risk forecasts. Finally, the CDA model is the most robust PVA to population cycles caused by species interactions. CDA models produce virtually unbiased and relatively precise risk estimates even when populations cycle strongly. High performance of simple time series models like the CDA owes to their ability to effectively partition stochastic and deterministic sources of variation in population abundance.

Original language | English (US) |
---|---|

Pages (from-to) | 1543-1554 |

Number of pages | 12 |

Journal | Ecological Applications |

Volume | 17 |

Issue number | 5 |

DOIs | |

State | Published - Jul 2007 |

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### Keywords

- Corrupted diffusion approximation
- Extinction
- Parameter estimation
- Population cycles
- Population viability analysis
- Predator-prey
- Projection matrix
- Species interactions
- Stage structure
- Stochasticity
- Time series
- Vital rate

### ASJC Scopus subject areas

- Ecology

### Cite this

**Predicting extinction risk in spite of predator-prey oscillations.** / Sabo, John; Gerber, Leah.

Research output: Contribution to journal › Article

*Ecological Applications*, vol. 17, no. 5, pp. 1543-1554. https://doi.org/10.1890/06-0630.1

}

TY - JOUR

T1 - Predicting extinction risk in spite of predator-prey oscillations

AU - Sabo, John

AU - Gerber, Leah

PY - 2007/7

Y1 - 2007/7

N2 - Most population viability analyses (PVA) assume that the effects of species interactions are subsumed by population-level parameters. We examine how robust five commonly used PVA models are to violations of this assumption. We develop a stochastic, stage-structured predator-prey model and simulate prey population vital rates and abundance. We then use simulated data to parameterize and estimate risk for three demographic models (static projection matrix, stochastic projection matrix, stochastic vital rate matrix) and two time series models (diffusion approximation [DA], corrupted diffusion approximation [CDA]). Model bias is measured as the absolute deviation between estimated and observed quasi-extinction risk. Our results highlight three generalities about the application of single-species models to multi-species conservation problems. First, our collective model results suggest that most single-species PVA models overestimate extinction risk when species interactions cause periodic variation in abundance. Second, the DA model produces the most (conservatively) biased risk forecasts. Finally, the CDA model is the most robust PVA to population cycles caused by species interactions. CDA models produce virtually unbiased and relatively precise risk estimates even when populations cycle strongly. High performance of simple time series models like the CDA owes to their ability to effectively partition stochastic and deterministic sources of variation in population abundance.

AB - Most population viability analyses (PVA) assume that the effects of species interactions are subsumed by population-level parameters. We examine how robust five commonly used PVA models are to violations of this assumption. We develop a stochastic, stage-structured predator-prey model and simulate prey population vital rates and abundance. We then use simulated data to parameterize and estimate risk for three demographic models (static projection matrix, stochastic projection matrix, stochastic vital rate matrix) and two time series models (diffusion approximation [DA], corrupted diffusion approximation [CDA]). Model bias is measured as the absolute deviation between estimated and observed quasi-extinction risk. Our results highlight three generalities about the application of single-species models to multi-species conservation problems. First, our collective model results suggest that most single-species PVA models overestimate extinction risk when species interactions cause periodic variation in abundance. Second, the DA model produces the most (conservatively) biased risk forecasts. Finally, the CDA model is the most robust PVA to population cycles caused by species interactions. CDA models produce virtually unbiased and relatively precise risk estimates even when populations cycle strongly. High performance of simple time series models like the CDA owes to their ability to effectively partition stochastic and deterministic sources of variation in population abundance.

KW - Corrupted diffusion approximation

KW - Extinction

KW - Parameter estimation

KW - Population cycles

KW - Population viability analysis

KW - Predator-prey

KW - Projection matrix

KW - Species interactions

KW - Stage structure

KW - Stochasticity

KW - Time series

KW - Vital rate

UR - http://www.scopus.com/inward/record.url?scp=34848909387&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34848909387&partnerID=8YFLogxK

U2 - 10.1890/06-0630.1

DO - 10.1890/06-0630.1

M3 - Article

C2 - 17708227

AN - SCOPUS:34848909387

VL - 17

SP - 1543

EP - 1554

JO - Ecological Appplications

JF - Ecological Appplications

SN - 1051-0761

IS - 5

ER -