• bryophyte;
  • climate;
  • environmental stochasticity;
  • hierarchical Bayesian model;
  • plant population and community dynamics;
  • plant–climate interactions;
  • population viability;
  • stochastic growth rate;
  • uncertainty


1. Understanding the variation in population abundances requires accounting for the environmental variability and uncertainty on different scales. We developed and evaluated a Bayesian hierarchical model for the inter-annual variation in population abundance of the epixylic bryophyte Buxbaumia viridis. The model accounts for spatio-temporal variability on two spatial scales. We used data on population abundance and on the weather variables at regional level collected between 1996 and 2003, and data on dead wood amount collected between 1996 and 2008. We also provide a Bayesian estimate of the population viability, specifically the population stochastic growth rate (log λS), which accounts for natural variability and uncertainty.

2. Previous estimates of population viability did not account for uncertainties in a satisfactory way. First, point estimates of log λS cannot, by definition, express variation. Second, the commonly used approach to estimate log λS and its confidence interval underestimates uncertainties. The approach aims to estimate the mean of log λS, with the confidence interval representing the uncertainty in the estimate of this mean. The interval does not reflect the natural variation and uncertainty.

3. We estimated a probability distribution of log λS, where the probability distributions of the year-specific growth rates (log λy) are accounted for. The species is likely to decline under current environmental conditions. Based on the probability distribution of log λS, we estimated this risk to be 81%.

4. We found support for the hypotheses that the population dynamics are driven by autumn frosts, by spring precipitation and temperature (regional variables), and by the preceding year’s population abundance (local variable).

5.Synthesis. Statements about the viability of populations should not be based on point estimates of log λS. Instead, the full probability distribution of log λS should be used, which explicitly accounts for the hierarchically structured natural variability and uncertainty. This distribution allows estimating the risk for a population decline, or providing an estimate of the confidence in a statement about a decline. This quantitative information can be weighed against other interests. We expect this Bayesian approach to be especially useful in the viability analysis of natural populations experiencing environmental variability.