Ecology, 87(6), 2006, pp. 1445–1451Ó 2006 by the Ecological Society of AmericaSTRENGTH OF EVIDENCE FOR DENSITY DEPENDENCEIN ABUNDANCE TIME SERIES OF 1198 SPECIESBARRY W. BROOK1AND COREY J. A. BRADSHAWSchool for Environmental Research, Institute of Advanced Studies, Charles Darwin University,Darwin, Northern Territory 0909 AustraliaAbstract. Population limitation is a fundamental tenet of ecology, but the relative roles ofexogenous and endogenous mechanisms remain unquantified for most species. Here we usedmulti-model inference (MMI), a form of model averaging, based on information theory(Akaike’s Information Criterion) to evaluate the relative strength of evidence for density-dependent and density-independent population dynamical models in long-term abundancetime series of 1198 species. We also compared the MMI results to more classic methods fordetecting density dependence: Neyman-Pearson hypothesis-testing and best-model selectionusing the Bayesian Information Criterion or cross-validation. Using MMI on our largedatabase, we show that density dependence is a pervasive feature of population dynamics(median MMI support for density dependence ¼ 74.7–92.2% ), and that this holds acrosswidely different taxa. The weight of evidence for density dependence varied among species butincreased consistently with the number of generations monitored. Best-model selectionmethods yielded similar results to MMI (a density-dependent model was favored in 66.2–93.9% of species time series), while the hypothesis-testing methods detected densitydependence less frequently (32.6–49.8%). There were no obvious differences in the prevalenceof density dependence across major taxonomic groups under any of the statistical methodsused. These results underscore the value of using multiple modes of analysis to quantify therelative empirical support for a set of working hypotheses that encompass a range of realisticpopulation dynamical behaviors.Key words: Akaike information criterion; density dependence; endogenous population dynamics; multi-model inference; negative feedback; population regulation; strength of evidence; time series.INTRODUCTIONIf density dependence is to be a cornerstone of ecologicaltheory, a certain burden of proof needs to be satisfied.—den Boer (1991)Most biologists accept that density-dependent demo-graphic processes (or more generally, negative feedbackmechanisms; Berryman 2002) work to regulate naturalpopulations (Turchin 1999, Lande et al. 2002), at leastunder some circumstances (Hixon and Carr 1997). Thatsaid, statistical detection of regulation using populationabundance indices (as opposed to demographic data)can be problematic. For instance, exogenous (density-independent) factors may overwhelm endogenous (den-sity-dependent) processes (Andrewartha and Birch1954), small s ample sizes (i.e., few time steps ofobservation relative to the generation length of theorganism being studied) reduce statistical power (Solowand Steele 1990), and sampling error can affect bothType I and Type II error rates (Shenk et al. 1998). Themost biologically intuitive means of quantifying regu-lation (and determining critical mechanistic detail) is bydirect examination of the relationship between density,realized demographic rates, and environmental covar-iates (Osenberg et al. 2002). However, a broad-scaleevaluation of the nature and prevalence of populationregulation across many species requires a differentapproach, such as meta-analysis of abundance timeseries.Although considerable effort has been given todeveloping statistical approaches to detect densitydependence in time series data, no single, superior testhas emerged (Fox and Ridsdillsmith 1995). Classic teststhat fall under the Neyman-Pearson hypothesis testing(NPHT) framework (e.g., Bulmer 1974, Pollard et al.1987, Dennis and Taper 1994) determine the probabilitythat a null (density-independent) model generated theobserved or more extreme data (Johnson 1999), withdensity independence rejected if this probability is small(typically ,5%). Alternative approaches have typicallyinvolved selecting a best model from an a priori set ofcandidate density-independent and density-dependentmodels, using either the Bayesian Information Criterion(BIC; e.g., Zeng et al. 1998, Dennis and Otten 2000) orjackknifed cross-validation (C-V; e.g., Turchin 2003).In recent years, statistical approaches that attempt toprovide strengths of evidence for multiple workinghypotheses have found favor (Hilborn and Mangel1997, Burnham and Anderson 2002), based on ideasManuscript received 27 June 2005; revised 31 October 2005;accepted 8 November 2005; final version received 10 January2006. Corresponding Editor: J. T. Cronin.1E-mail: [email protected] well over a century ago (Chamberlin 1890).The most-widely adopted method for this multi-modelinference uses information theory based on the AkaikeInformation Criterion (AIC; Burnham and Anderson2002), which employs Kullback-Leibler information as afundamental, conceptual measure of the relative dis-tance of a given model from full reality. Despite itsobvious advantages for examining complex ecologicalprocesses, AIC has rarely been used in studies of densitydependence in time series, except in a few individual casestudies (e.g., Morris and Doak 2002). Bayesian methodsare commonly used for model averaging (Wintle et al.2003), but are yet to be applied in this way for thedetection of density dependence.The relative importance of endogenous vs. exogenousprocesses on the dynamics of real populations can bemost convincingly settled by empirical means ratherthan a priori arguments of logic (Cooper 2001). Here webuild on the work of Turchin and Taylor (1992),Woiwod and Hanski (1992), Zeng et al. (1998), andothers by undertaking a diverse portfolio of analyses(AIC, BIC, C-V, NPHT) to evaluate the relativestrength of evidence for density-dependent and density-independent population dynamics in long-term timeseries abundance data from a substantial dataset of 1198species spanning a broad range of taxa. We demonstratethat density dependence is a pervasive feature of thepopulation dynamics of these species, bu t find noimportant differences between the taxonomic groups(e.g., invertebrates vs. vertebrates).METHODSWe used a set of high-quality, long-term populationdynamics time series data for 1198 species (one timeseries per species) comprising 639 invertebrate, 529vertebrate, and 30 plant species, and