Location of Repository

Patterns and rules for sensitivity and elasticity in population projection matrices

By David Carslake, Stuart Townley and David J. Hodgson


Sensitivity and elasticity analysis of population projection matrices (PPMs) are established tools in the analysis of structured populations, allowing comparison of the contributions made by different demographic rates to population growth. In some commonly used structures of PPM, however, there are mathematically inevitable patterns in the relative sensitivity and elasticity of certain demographic rates. We take a simulation approach to investigate these mathematical constraints for a range of PPM models. Our results challenge some previously proposed constraints on sensitivity and elasticity. We also identify constraints beyond those which have already been proven mathematically, and promote them as candidates for future mathematical proof. A general theme among these rules is that changes to the demographic rates of older or larger individuals have less impact on population growth than do equivalent changes among younger or smaller individuals. However, the validity of these rules in each case depends on the choice between sensitivity and elasticity, the growth rate of the population and the PPM structure used. If the structured population conforms perfectly to the assumptions of the PPM used to model it, the rules we describe represent biological reality, allowing us to prioritise management strategies in the absence of detailed demographic data. Conversely, if the model is a poor fit to the population (specifically; if demographic rates within stages are heterogeneous) such analyses could lead to inappropriate management prescriptions. Our results emphasise the importance of choosing a structured population model which fits the demographics of the population

Topics: QA, QH301
Publisher: Ecological Society of America
Year: 2009
OAI identifier: oai:wrap.warwick.ac.uk:3104

Suggested articles



  1. (1992). A demographic interpretation of Grime's triangle. doi
  2. (1987). A stage-based population model for loggerhead sea turtles and implications for conservation. doi
  3. (1995). Comparing plant life histories using elasticity analysis: the importance of life span and the number of life-cycle stages. doi
  4. (2007). Darwinian fitness and the intensity of natural selection: studies in sensitivity analysis. doi
  5. (1991). Demographic models for Leptogorgia virgulata, a shallow water doi
  6. (2000). Elasticities: A review of methods and model limitations. doi
  7. (1986). Elasticity: The relative contribution of demographic parameters to population growth rate. doi
  8. (1998). Estimating biocontrol agent impact with matrix models: Carduus nutans in New Zealand. doi
  9. (1996). How to keep fit in the real world: Elasticity analyses and selection pressures on life histories ln a variable environment. doi
  10. (2007). Invasion dynamics of the varnish clam (Nuttallia obscurata): A matrix demographic modeling approach. doi
  11. (2000). Life histories and elasticity patterns: perturbation analysis for species with minimal demographic data. doi
  12. (2004). Linking management changes to population dynamic responses: the transfer function of a projection matrix perturbation. doi
  13. (1994). Loop analysis: evaluating life history pathways in population projection matrices. doi
  14. (1998). Mathematical constraints on transition matrix elasticity analysis. doi
  15. (2001). Matrix population models: construction, analysis, and interpretation. Second edition. Sinauer Associates, doi
  16. (1994). Modeling population viability for the desert tortoise in the western Mojave desert. doi
  17. (1996). Models to evaluate headstarting as a management tool for long-lived turtles. doi
  18. (1966). Moulding of senescence by natural selection. doi
  19. (2008). Nonlinearity in eigenvalue-perturbation curves of simulated population projection matrices. doi
  20. (2008). On second order sensitivity for stage-based population projection matrix models. Theoretical Population Biology, doi
  21. (1945). On the use of matrices in certain population mathematics. doi
  22. (1998). Patterns of variance in stage-structured populations: evolutionary predictions and ecological implications. doi
  23. (1993). Pod-specific demography of killer whales (Orcinus orca). doi
  24. (1994). Predicting the impact of turtle excluder devices on loggerhead sea-turtle populations. doi
  25. (2000). Prospective and retrospective perturbation analyses: their roles in conservation biology. doi
  26. (2007). Rapid population growth of a critically endangered carnivore. doi
  27. (1965). Study of population growth in organisms grouped by stages. doi
  28. (1995). Sustainable harvesting of tropical trees: demography and matrix models of two palm species in Mexico. doi
  29. (1969). The sensitivity of population growth rate to perturbations in the life cycle components. doi

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.