Graphical Modeling of Ecological Time Series Data
Graphical models offer a powerful tool for studying ecosystem function. Changes in relationships among extrinsic and intrinsic biological and environmental variables can be explored. We discuss the application of graphical modeling to ecological data and illustrate this with an example case study. Ecological datasets are characteristically small with few data points, covering only a short period of time, and with high seasonal variation. This high variation, along with the fact that the data sets are small, can present problems for graphical modeling. Despite this, in general, considerable insight into ecosystem function can be gained from the use of graphical modeling. In our case study we modelled the ecosystem relationship between mice and food abundance. In New Zealand cyclical waves in the mice population size within beech forest roughly correspond to periods after a heavy beech tree seeding year. One explanation for this cycle is that years of heavy beech seeding causes an increase in mouse population. Understanding the ecosystem relationship will help understand possible causal links. In this study we used data collected by the Orongorongo valley near Wellington between August 1971 and November 1996. We used three ecosystem measures: mouse population size, mouse breeding and seed fall and compared graphical models among seasons. Mice population size was estimated from counts in mice traps adjusted for trapping-effort. Beech seed fall was measured using seed traps under mature trees. Mouse breeding was measured by the proportion of mice caught in traps that were pregnant females and the proportion of adult males in the population. Direct assessment of seasonal effects on micebeech forest ecosystem relationships was by comparison among seasonal-models. Separate graphical models were produced, one for each leading season: a model with spring as the most recent time, a model with autumn as the most recent time, and so on. The seasonal-graphical models were helpful in understanding the relationship among variables. The winter observed mouse numbers are dependent on the numbers in the previous season, autumn, and on levels of seed fall. Similarly summer mouse numbers are dependent on the size of the population in the previous season, spring. There was no direct link with seed fall as there was with the size of the previous winter’s mouse population. The number of mice in spring was related to mice numbers in the winter before. All these relationships are positive, i.e., with an increase in mouse numbers in winter, mouse numbers in spring will increase. Graphical models for time series can be used for a wide range of environmental studies. The complexity of ecosystem interactions can be described by modelling the multivariate system with graphical links for the changing interactions through time. Comparison among models for different seasons, or for periods pre- and postperturbation can be used for quantifying temporal change.