I have been thinking a lot recently about how people view population dynamics. Most have worked on a single population of animals (e.g., Soay sheep) or a particular group of animals (e.g., birds), but we have been talking about populations in general. I have worked for most of my life on bark beetles (a group of forest insects), but in my waning years have been trying to apply general theories to real data. I have worked with hundreds of species of animals. However, I have not delved very deeply into the world of plants. Many of the animals I have worked with I know very little about and I can be criticized on this basis. However, I think that knowing very little about the details of the biology of a species and may be an advantage. Let me try to explain this with possibly the best data set I know of, the larch bud moth Zeiraphera diniana (you can get the literature on this insect by searching Google Scholar for “larch bud moth”, or “Werner Baltensweiler”, the man who did most of the work on this insect).

The bud moth is a cyclic insect, going through large increases in density (10,000 fold increase in 4-5 years) and then crashing to very sparse densities (10,000 fold decrease in 4-5 years). Thus it takes 8-10 years to complete the cycle (mean 8.47 ). The increasing phase is exponential or linear on the logarithmic scale. The insect has one generation per year. Thirteen population cycles have been monitored quantitatively (about 100 years) and have been deduced from tree rings for a much longer period of time (about 300 years). It is a remarkable series of data much of it taken over a large area of forest for a long period of time. No other data set comes near to it in terms of the length of the series.

The first thing to note is that this cyclic dynamics can only be produced by a cyclic exogenous (external) factor or by an endogenous (internal) delayed feedback process. No external factor has been demonstrated to have such a constant cyclical pattern so that an endogenous process must cause the dynamics. Now a delayed feedback process can only be created by a factor which increases its impact on the population in the year after a population increase occurs (and vice versa). The most usual cause in populations of insects is an increase in univoltine insect parasitoids, which survive in large numbers when there are lots of host insects present and then multiply in the next year to attack more hosts. The major impact is on next years hosts, not the current year, which leads to a one-year time delay in the action of the mortality factor. It can be shown that this time delay can cause fairly regular cycles of abundance of the host and parasitoid populations (see the Fourth Principle, and Mathematics of the Fourth Principle on this web page). But this is not the whole story. During the population increases the parasitoid just follows the bud moth without causing additional percentage mortality. This is seen by plotting population growth of the host on the logarithmic scale, which shows a linear increase; i.e., a constant reproductive rate. Thus, the parasitoids are just causing the same percentage mortality to the bud moth population as it grows and, therefore, they cannot be controlling it (control is only created by an increase in percentage mortality). However, at its peak the bud moth population runs out of food and can go no further (Baltensweiler and colleagues also say that the foliage changes quality at this time and this causes increased mortality). Whatever, the bud moth runs out of good quality food and the parasitoids catch up and increase their percentage control of the population. Parasitism during the collapse of the population reaches over 90% and causes the bud moth to undershoot its carrying capacity by a large margin (the actual carrying capacity, where a stable population can be sustained is somewhere near the middle of the logarithmic trend). Thus, the conditions are set up for the next cycle. By the way, this analysis was done on larch bud moth populations in the high Alps (1850 meters). Samples taken at low altitudes (500 m) show bud moth populations cycling with much lower amplitude and to be much more stable (see Fig. 3 in Berryman et al. 1987).

The thing is, can we gather any information from this about human populations? That is, will humans go through a cycle so that we crash precipitously, or will we reach a stable population that is in equilibrium with its environment? The major question is, is the feedback from the environment rapidly induced or is it time delayed, the cause of the high amplitude cycles in the bud moth! The data do not seem to be encouraging. We can identify numerous factors that are being changed and that can act with a time delay; e.g., climate warming, global carbon dioxide, depletion of fossil fuels, destruction of ocean fisheries, running out of fresh water, etc. These are warnings that we have exceeded the carrying capacity of this planet. At least this should be taken seriously and moves made to reduce the impact of the human population. Unfortunately I see no attempt from politicians to seriously address this problem.

Berryman, A. A., Stenseth, N. C. and Isaev, A. s. 1987. Natural regulation of herbiverous forest insect populations. Oecologia 71: 174-184.