Search

We describe the application of Bayesian hierarchical models to the analysis of data from long-term, environmental monitoring programs. The goal of these ongoing programs is to understand status and trend in natural resources. Data are usually collected using complex sampling designs including stratification, revisit schedules, finite populations, unequal probabilities of inclusion of sample units, and censored observations. Complex designs intentionally create data that are missing from the complete data that could theoretically be obtained. This “missingness” cannot be ignored in analysis. Data collected by monitoring programs have traditionally been analyzed using the design-based Horvitz–Thompson estimator to obtain point estimates of means and variances over time. However, Horvitz–Thompson point estimates are not capable of supporting inference on temporal trend or the predictor variables that might explain trend, which instead requires model-based inference. The key to applying model-based inference to data arising from complex designs is to include information about the sampling design in the analysis. The statistical concept of ignorability provides a theoretical foundation for meeting this requirement. We show how Bayesian hierarchical models provide a general framework supporting inference on status and trend using data from the National Park Service Inventory and Monitoring Program as examples. Supplemental Materials Code and data for implementing the analyses described here can be accessed here: https://doi.org/10.36967/code-2287025.

Active management is needed to sustain healthy limber pine (Pinus flexilis E. James) forests in the Southern Rocky Mountains (henceforth, Southern Rockies), as they are threatened by the interaction of the mountain pine beetle (Dendroctonus ponderosae Hopkins) epidemic, climate change, and the spread of the non-native pathogen that causes white pine blister rust disease (Cronartium ribicola A. Dietr.). Appropriate source material for restoration and proactive introduction needs to be selected, taking into account potential genetic differentiation that would hamper management success. We conducted a common garden study in a greenhouse to determine the degree of genetic differentiation among limber pine populations in the Southern Rockies. We evaluated the differential responses of populations from northern and southern portions of the Southern Rockies to different moisture regimes during early seedling growth by measuring primary needle length, stem diameter, water potential, biomass allocation between root and shoot, and carbon isotope ratios (δ13C; a proxy for water-use efficiency). There were significant (p < 0.05) effects of source region for root length, stem diameter, needle length, and total dry mass, with seedlings from southern sources bigger than seedlings from northern sources. Furthermore, there was a marginally significant interaction between soil moisture regime and source region for carbon isotope ratio (p = 0.0778), suggesting possible local adaptation. These data indicate that genetic differentiation exists among populations in the Southern Rockies, potentially increasing the risk of maladaptation when moving seed far from its source for active management.

Maternal effects, the effect of the maternal environment during development on offspring growth, can complicate the interpretation of common garden studies. Growing one or more generations in a common environment can help minimize maternal effects, but is often not practical with long-lived species. In Pinus aristata Engelm. and Pinus flexilis James, we assessed maternal effects by growing offspring sourced over multiple years from the same mother trees, comparing growth traits between source years. Additionally, we explored the effect of maternal environment on seed characteristics by collecting five twig clippings from each mother tree and measuring characteristics indicative of the relative vigor of the tree during each seed source year. The effect of year was significant for twig growth characteristics, seed size, and seedling performance. For both species, there were significant relationships between the relative inter-annual (RIA) variation in seed mass and the RIA variation in numerous seedling traits including cotyledon length, seedling total dry mass, and needle length. Variation in seed mass was not predicted by yearly variation in the maternal plant’s phenotypic traits. These results support the hypothesis that maternal effects translate into variation in early seedling growth and suggest possibilities to statistically account for them in common garden studies involving long-lived species.