Ecologically realistic estimates of maximum population growth using informed Bayesian priors

Phenomenological density-feedback models estimate parameters such as carrying capacity (K) and maximum population growth rate (rm) from time series of abundances. However, most series represent fluctuations around K without extending to low abundances and are thus uninformative about rm. We used informative prior distributions of maximum population growth rate, p(rm), to estimate Bayesian posterior distributions in Ricker and theta-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 rm prior distributions. We assessed patterns of differences in posterior means (rm) from models fitted with and without informative priors and used the deviance information criterion (DIC) to rank models for each species. Differences in posterior rm from models with informative vs. vague priors co-varied with the prior mean (rm) for Ricker models, but only posterior theta co-varied with prior rm in theta-logistic models. Informative-prior Ricker 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 of rm by 13-45% depending on model and prior. Posterior rm were highly sensitive to rm priors for theta-logistic models (halving and doubling prior mean gave -56% and 95% changes in rm, respectively) and less sensitive for Ricker models (-25% and 35% changes in rm). Our results show that fitting density-feedback models without prior information gives biologically unrealistic rm estimates in most cases, even from simple Ricker models. However, sensitivity analysis shows that high rm - theta correlation in theta-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.