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 (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 Bayesian posterior distributions in Ricker 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 posterior r-m from models with informative vs. vague priors co-varied with the prior mean (r̂_m) for Ricker models, but only posterior θ- co-varied with prior r̂_m in θ-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 r-m by 13-45% depending on model and prior. Posterior r-m were highly sensitive to r̂_m priors for θ-logistic models (halving and doubling prior mean gave -56% and 95% changes in r̄m, respectively) and less sensitive for Ricker models (-25% and 35% changes in r̄m). Our results show that fitting density-feedback models without prior information gives biologically unrealistic r̄m estimates in most cases, even from simple Ricker 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.