What determines population size?
Population size of acorn woodpeckers is a function of the number of social groups and mean group size. Restricting analysis to areas monitored throughout the study, the number of groups varied between 17 and 50, increasing considerably over the 51-year period (Figure 1a). Figure 2a presents the same data for mean group size, illustrating how it also increased during the study, albeit less dramatically than the number of groups. Overall, about two-thirds of the increase in population size is attributable to increased density of groups, while about one-third is due to increased group size.
What if we altered the length or the start date of the study? Mean values of the correlation coefficient (r -value) between the dependent variable (N groups or mean group size) and the length of the study is illustrated in Figures 1b (for N groups) and 2b (for mean group size) and for start date in Figures 1c (for Ngroups) and 2c (for mean group size). In these analyses, all “runs” of data were averaged. For example, in Figure 1b, the first value considers all consecutive runs of 6 years regardless of what year they were started, while in Figure 1c, the first value considers all studies starting in 1973 regardless of their length. (Here and below we ignore temporal autocorrelation for simplicity and illustrative purposes.)
In both cases, the length of the study (Figures 1b and 2b) has a relatively small effect on the apparent outcomes as determined by the mean r -values compared to the year the study was (hypothetically) initiated. Based on the adjusted R 2 values of linear regressions, the proportion of variance explained by start year is twice that explained by N years for N groups and over 10 times that of N years for mean group size (Table 1). Even both independent variables together add only a modest amount of explanatory power compared to start year alone.
Comparing these results to Polya’s urn scheme is clearly an oversimplification; some of the differences are due to changing environmental conditions during the study. Nonetheless, in these examples, the differences due to variable, stochastic forces are much greater among hypothetical studies started in different years than among studies of different length. Long-term studies are not immune from being strongly influenced by idiosyncratic, random factors defining the years it is conducted. This is as true of a 50-year study as it is for a 6-year study.