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Open Access Highly Accessed Research article

Predation and fragmentation portrayed in the statistical structure of prey time series

Ditte K Hendrichsen12, Chris J Topping3 and Mads C Forchhammer1*

  • * Corresponding author: Mads C Forchhammer

Author Affiliations

1 Department of Arctic Environment, National Environmental Research Institute, Aarhus University, Frederiksborgvej 399, DK-4000 Roskilde, Denmark

2 Department of Population Biology, Institute of Biology, University of Copenhagen, Universitetsparken 15, DK-2100 Copenhagen, Denmark

3 Department of Wildlife Ecology and Biodiversity, National Environmental Research Institute, Aarhus University, Grenåvej 12, DK-8410 Rønde, Denmark

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BMC Ecology 2009, 9:10  doi:10.1186/1472-6785-9-10

Published: 6 May 2009



Statistical autoregressive analyses of direct and delayed density dependence are widespread in ecological research. The models suggest that changes in ecological factors affecting density dependence, like predation and landscape heterogeneity are directly portrayed in the first and second order autoregressive parameters, and the models are therefore used to decipher complex biological patterns. However, independent tests of model predictions are complicated by the inherent variability of natural populations, where differences in landscape structure, climate or species composition prevent controlled repeated analyses. To circumvent this problem, we applied second-order autoregressive time series analyses to data generated by a realistic agent-based computer model. The model simulated life history decisions of individual field voles under controlled variations in predator pressure and landscape fragmentation. Analyses were made on three levels: comparisons between predated and non-predated populations, between populations exposed to different types of predators and between populations experiencing different degrees of habitat fragmentation.


The results are unambiguous: Changes in landscape fragmentation and the numerical response of predators are clearly portrayed in the statistical time series structure as predicted by the autoregressive model. Populations without predators displayed significantly stronger negative direct density dependence than did those exposed to predators, where direct density dependence was only moderately negative. The effects of predation versus no predation had an even stronger effect on the delayed density dependence of the simulated prey populations. In non-predated prey populations, the coefficients of delayed density dependence were distinctly positive, whereas they were negative in predated populations. Similarly, increasing the degree of fragmentation of optimal habitat available to the prey was accompanied with a shift in the delayed density dependence, from strongly negative to gradually becoming less negative.


We conclude that statistical second-order autoregressive time series analyses are capable of deciphering interactions within and across trophic levels and their effect on direct and delayed density dependence.