Stochastic population dynamic models as probability networks

The dynamics of a population and its response to environmental change depend on the balance of birth, death and age-at-maturity, and there have been many attempts to mathematically model populations based on these characteristics. Historically, most of these models were deterministic, meaning that the results were strictly determined by the equations of the model and random variability was ignored. More recently, population modelers have moved away from deterministic models toward stochastic models that explicitly incorporate random variation and uncertainty [1, 2]. Stochastic models have the advantage of both characterizing the central tendencies of a population (similar to deterministic models) and addressing at least three sources of variability and uncertainty: (1) temporal or spatial variation in population structure and environmental conditions, (2) intrapopulation variation among individuals and (3) uncertainty in parameter estimates. Representations of uncertainty and variability are especially critical for populations at risk of becoming extinct or losing signifi cant genetic resources through declines. Chance occurrences can be catastrophic for species already on the brink of extinction. Conversely, some nuisance species may be of little concern on average, but can become major pests when population numbers periodically explode. Central tendencies or expected values resulting from deterministic models are insuffi cient for assessing these risks. The probabilities of catastrophic outcomes or population explosions can be considered using stochastic models that simulate temporal or spatial variation.