Limiting factors and population regulation

The great debate over the meaning and relevance of population regulation lingers on under the perceived difference between limitation and regulation of animal numbers / what Murray (1999) calls the ‘‘population limitation hypothesis’’ versus the ‘‘density dependent regulation hypothesis’’. Berryman et al. (2002) attempt to solve this dilemma by (1) arguing that the problem is partly caused by ambiguity and inconsistency in the use of the term density dependence, (2) deducing the necessary and sufficient conditions for population regulation from first principles, and (3) concluding that there is no real distinction between the concepts of population limitation and regulation. Apparently we were unconvincing. White (2004) criticizes our argument on empirical grounds -‘‘the evidence from nature is that populations are not regulated; they are limited by the capacity of the environment to support them’’and insists that limitation and regulation ‘‘are fundamentally different processes’’. In spite of the rhetoric, it seems to me that the latter issue is the crux of the problem because, if I can show that limitation and regulation are in fact part and parcel of the same phenomenon, it should put the other matters to rest as well. In addition, the empirical evidence for population regulation has been addressed at length previously (Sinclair 1989, Harrison and Cappuccino 1995, Huffaker et al. 1999). Since our appeal to logic seems to have failed, I now try a more empirical approach. Figure 1 shows the dynamics of six Tribolium confusum populations growing in the laboratory on constant but different food supplies (Chapman 1928). Notice that the six populations grow at first but eventually stabilize at, or more correctly fluctuate to varying degrees around, an average density (I note that the population with the largest food supply may not have reached its steady-state). Since the level at which the populations stabilize is directly related to the quantity of food, White would probably say that these Tribolium populations were being limited by food, and few ecologists (including this one) would disagree with him (Berryman 1999). Stated another way, we could say that food acts as the limiting factor, an old idea in ecology (Liebig 1840, Blackman 1905, Allee et al. 1949, Odum 1971). However, some of us would add that the Tribolium populations were also being regulated by density-induced negative feedback (Huffaker et al. 1999, Berryman et al. 2002). On this point, however, White would undoubtedly disagree, claiming that ‘‘there is no need to evoke regulation by negative feedback loops.’’ I now try to clarify this difference of opinion by reference to Chapman’s experimental populations. It seems pretty obvious that the per-capita birth (B) and death (D) rates of a population at or near steadystate must, on the average, be equal. Defining the realized per-capita rate of change of a population over a given interval of time as R ln(1 B D); then we can say that, on the average, R /0 during the latter part of the Tribolium experiments, when the populations were at their highest. (See Berryman 1999, 2003 for the reasons why R is expressed as a natural logarithm.) In contrast, births must have exceeded deaths, and consequently R /0, at the beginning of the experiment when the populations were small. From this it seems logical to propose that R must be inversely related to population size, N. Actually, since the Tribolium populations can only change through births and deaths, the value of R over a sampling interval can be estimated by subtracting the logarithmic count at the first sampling date from that at the second; i.e. R lnNt lnNt 1; where Nt is the size of the population sampled at time t. Plotting R against the initial size of the population, Nt 1, gives us the Rfunctions for the populations growing on different food supplies (Fig. 2). Notice that all the functions have a negative slope over the complete range of the data, which satisfies both the necessary and sufficient conditions for population regulation (Berryman et al. 2002). As White (2004) finds no fault with the formal derivaO N P O I I N I I P O O N Opinion is intended to facilitate communication between reader and author and reader and reader. Comments, viewpoints or suggestions arising from published papers are welcome. Discussion and debate about important issues in ecology, e.g. theory or terminology, may also be included. Contributions should be as precise as possible and references should be kept to a minimum. A summary is not required.