The distribution of birth and death in Daphnia magna: Implications for stochastic models
Populations are characterized by discrete demographic events (e.g. births, deaths) which occur at rates determined by genes and the environment. In theory, each type of demographic event is stochastic (i.e. probabilistic), meaning that even among clones in identical conditions, specific outcomes may differ. The probability distribution of such events is expected to be either Poisson or binomial, but it is rare to test whether this holds for all relevant demographic events within a species. Crucially, if the distribution of one or more demographic events in a population is not Poisson or binomial, this has important implications for constructing accurate stochastic models of population growth.
To test this, we grew clones of Daphnia magna under common conditions and quantified the distribution of demographic events in the population; specifically: juvenile maturation rate, juvenile death rate, adult birth rate, adult offspring number, and adult death rate. We characterized the distribution of each demographic parameter and then constructed stochastic models based on our findings. Finally, we examined how different assumptions about demographic events and their probability distributions affected the outcomes of these stochastic models.
We found that the distribution of demographic events was generally Poisson and binomial among D. magna clones. This is in line with theoretical expectations and emphasizes the importance of considering demographic events as occurring not as fixed, deterministic rates but as fixed probabilities.
The results of our stochastic models of D. magna population growth depended strongly on assumptions about the number and distribution of demographic events. For example, when juvenile demographic events were not considered separately from adult demographic events, model outcomes differed substantially from the fully explicit model. These results suggest that the creation of accurate stochastic models requires a detailed understanding of the demographic events occurring within a population.