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Ecologically realistic estimates of maximum population growth using informed B ayesian priors
Author(s) -
Delean Steven,
Brook Barry W.,
Bradshaw Corey J. A.
Publication year - 2013
Publication title -
methods in ecology and evolution
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.425
H-Index - 105
ISSN - 2041-210X
DOI - 10.1111/j.2041-210x.2012.00252.x
Subject(s) - prior probability , statistics , population , mathematics , population model , posterior probability , deviance (statistics) , deviance information criterion , bayesian probability , econometrics , markov chain monte carlo , demography , sociology
Summary Phenomenological density‐feedback models estimate parameters such as carrying capacity ( K ) and maximum population growth rate ( r m ) from time series of abundances. However, most series represent fluctuations around K without extending to low abundances and are thus uninformative about r m . We used informative prior distributions of maximum population growth rate, p ( r m ), to estimate B ayesian posterior distributions in R icker and θ ‐logistic models fitted to abundance series for 36 mammal species. We also used state‐space models to account for observation errors. We used two data sets of population growth rates from different mammal species with associated allometry (body mass) and demography (age at first reproduction) data to predict r m prior distributions. We assessed patterns of differences in posterior means (r ¯m) from models fitted with and without informative priors and used the deviance information criterion ( DIC ) to rank models for each species. Differences in posteriorr ¯mfrom models with informative vs. vague priors co‐varied with the prior mean (r ^m) for R icker models, but only posteriorθ ¯co‐varied with priorr ^min θ‐ logistic models. Informative‐prior R icker models ranked higher than (81% of species), or equivalent to (all species), those with vague priors, which decreased to 70% ranking higher for state‐space models. Prior information also improved the precision ofr ¯mby 13–45% depending on model and prior. Posteriorr ¯mwere highly sensitive tor ^mpriors for θ‐ logistic models (halving and doubling prior mean gave −56% and 95% changes inr ¯m, respectively) and less sensitive for R icker models (−25% and 35% changes inr ¯m). Our results show that fitting density‐feedback models without prior information gives biologically unrealisticr ¯mestimates in most cases, even from simple R icker models. However, sensitivity analysis shows that high r m − θ correlation in θ‐ logistic models means the fit is largely determined by the prior, precluding the use of this model for most census data. Our findings are supported by applying models to simulated time series of abundance. Prior knowledge of species' life history can provide more ecologically realistic estimates (matching theoretical predictions) of regulatory dynamics even in the absence of detailed demographic data, thereby potentially improving predictions of extinction risk.