Population projection modeling assumes that the histories of individuals do not matter to population dynamics. This assumption is operationalized by forcing estimates of state at time t+1 to rely only on state at time t. However, studies investigating the impacts of past events in the lives of individuals suggest that individual history should impact population dynamics.
We developed an R package to develop projection models using an extra year of individual history. In this package, the state of an individual in time t+1 relies on state at both times t and t-1, and the impacts of these two time steps on core vital rates can be assessed. This package develops both raw and function-based matrices, in which the former matrices are determined via counts of actual individuals in each state across time, while the latter involves the estimation of key demographic parameters as linear models. It also estimates both standard "ahistorical" matrices, in which time t-1 is not assumed to matter, as well as "historical" matrices, in which it does, and even estimates integral projection models (IPMs) using a standardized and fairly simple protocol.
We used this package to analyze two case studies. The first is a population of Lathyrus vernus (Fabaceae) from Sweden, and the second is a population of Cypripedium candidum (Orchidaceae) from the United States.
Results/Conclusions
Comparisons of population projections resulting from ahistorical and historical matrices showed a lower population growth rate associated with historical matrices in both cases. This meets expectation because historical matrices are subject to trade-offs operating across multiple years, while ahistorical matrices assume that such trade-offs are not sufficiently strong to influence population dynamics. Matrix sensitivities also differed between the two classes of models, with particular sorts of transitions differing in their impact on population growth rate. Integrating longer periods of monitoring data also tended to show more significant impact of history, particularly via negative temporal autocorrelation in vital rates. The speed of estimation of all matrices with this package was exceedingly fast, with historical matrices of dimensionality 2916 x 2916 estimated within approx. 1-2 sec on a contemporary MacBook Pro, and the equivalent ahistorical matrix estimated within 0.1 sec.
We show the promise of integrating individual history into population projection matrices, and offer an open-source method that makes it easy. We encourage more population ecologists to try these methods and the impacts of history, particularly long-term trade-offs, on their study populations.