New World Pleistocene Extinctions, System Dynamics and Carrying Capacity: A Critique of Whittington and Dyke (1989)

Elin Whitney-Smith

elin@quaternary.net

Abstract

In previous computer simulation models of Pleistocene/Holocene megafaunal extinctions carrying capacities of both herbivores and humans are fixed values. For the animals in question, herbivores and humans, carrying capacity is largely determined by food. A simulation using the values of the previous models and a dynamic definition of carrying capacity is presented. This suggests that overkill, as presented in previous simulation models, is not possible.

Overkill model proposed by Mossiman and Martin

Mossiman and Martin (1975) created a simulation model to estimate how many Homo sapiens might be sufficient to cause megafaunal extinctions without leaving much in the way of archaeological evidence. They based their simulation model on mathematical equations from Budyko's (1967, 1974) work on mammoth extinction in Europe. According to their simulation extinction could be caused rapidly, within 3 years of filling the continent, if H. sapiens colonized the continent in a "front". A "front" is a colonizing mechanism where a dense narrow band of population enters a virgin area and moves radially away from its point of entry as population grows. The population kills or eats all its prey species as the front passes through leaving the area behind the front denuded of the prey species. This has been observed in the spread of snails, fish and large herbivores into previously uninhabited but habitable regions. Thus, H. sapiens was assumed to have entered the new world around 11500 BP and to have swept across the continent in a front killing megafauna as they went.

The criticisms of their model fall into three major categories:

  1. that their input values are to high (Human population density Albini 1975, Hallum 1977) (Prey destruction rate Stauffer 1975, Webster 1981)(Human population growth rate Hassan 1978, Webster 1981)
  2. that their date of entry is too late (Rouse 1976, MacNeish 1976, Bryan et al. 1978), and
  3. that the notion of a front is too simplistic (Webster 1981).

Overkill model proposed by Whittington and Dyke

To correct and deal with these objections Whittington and Dyke (1989) built their own simulation model. They did not propose a front nor did they specify that extinction had to occur within three years of filling the continent. Their model is, therefore, less restrictive.

They changed their baseline and input and values to answer the objections raised by Mossiman and Martin's model. Whittington and Dyke's input and baseline values are based on:

Model 1 - System dynamics simulation based on Whittington and Dyke (1989)

The results of a system dynamics simulation using the values in table 1 is shown in graph 1.

Problems with Whittington and Dyke

Whittington and Dyke, like Mossiman and Martin before them used a fixed notion of carrying capacity. Whittington and Dyke based their carrying capacity on Budyko (1967) which reflects the carrying capacity in Europe at the end of the Upper Paleolithic. Neither Whittington and Dyke nor Mossiman and Martin have thought through what the notion of carrying capacity stands for. It is a shorthand value assigned to represent the things an animal need from its environment in order to live and reproduce. It is used for simulations of ecosystems that are in equilibrium. This makes it imperative that the notion of carrying capacity be carefully examined.

Model 2 - System dynamics simulation with interactive carrying capacity

For Homo sapiens food is an important part of what constitutes carrying capacity. This means that it is impossible for Homo sapiens to over hunt its food supply and continue to increase population. Carrying capacity must, of necessity, change as the food supply diminishes.

The difficulty in the modeling exercise was determining how great a proportion of Homo sapiens carrying capacity to assign to animal protein from large animal. A good rule of thumb for modern hunter gatherers is 80% gathered food and 20% animal protein. In arctic conditions the reliance on animal protein is likely to much greater. A 5% impact would still be considered conservative. The model which produced the graph below, was based on an outflow of carrying capacity of only 3% of the kill rate of herbivores (in animal units AU). (Graph 2: Interactive Carrying Capacity - 3% degradation). (For a diagram of the system relationships see Appendix A - Diagrams. For the equations see Appendix B - Equations.

Introducing a connection between prey death and the amount of carrying capacity remaining, decreases Homo sapiens births. This keeps population levels of Homo sapiens from reaching the maximum and allows herbivore populations to survive. The link of the hunting rate and the carrying capacity, makes the carrying capacity responsive. It is the only change made to Whittington and Dyke's model.

Conclusion

In conclusion, examination of what constitutes carrying capacity must be fully explored before assigning it an arbitrary value. Since Homo sapiens is limited by food more than by space it is likely that the loss of a major food supply would degrade carrying capacity at 5% or greater. Yet a reduction of only 3%. decreases Homo sapiens populations enough to allow herbivores to avoid extinction. This result points out the necessity of examining the assumptions upon which any model is based. Any model is also a test of a particular modeling method. Systems dynamics supports more complete models with better defined assumptions. This may give us new insights into the extinction events.

References

Appendix A - Diagrams.

Appendix B - Equations.

The two sleuths discuss the presentation of their own extinction model and some additional problems with Whittington and Dyke (1989)

Background - Follow the Clews with Skylark Holmes and Dr. Janet Watson Scientific Investigators in "The Case of the Aboricidal Megaherbivores"