With these basic parameters, both prey and hunter-gatherer population dynamics can be modeled using a discrete-time logistic equation, whose basic form is. For extinct preys, the population growth rates can only be estimated by the relationship with body mass, thus also obtained from Alroy, :. In the simulations, I conservatively assumed that prey populations were at optimal equilibrium values K when humans arrived. Notice that hunting could be introduced directly into standard logistic models by reducing growth rate r , but I separated "natural" mortality, implicit in the growth parameter, from "hunt mortality".
I did this because the last parameter can be adjusted to human population growth. Also, the N R value, rather than as a rate, can be given based on human nutritional needs and established in terms of number of individuals removed.
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I then assumed, following Brown , p. After estimating population density, I assumed an area of 2,, km 2 for the great plains in North America south of the Laurentia icesheet at the end of the Pleistocene 12, years ago , and then obtained the absolute number of preys N t by simply multiplying this area by density D see Ward, However, it bears consideration that a reduction in hunting rates would occur if a prey had become rare, so that N R in fact represents a maximum theoretical value defined by human needs that would be satisfied with this specific prey. In this way, the actual number of preys removed from the population deviates from the maximum predicted by human needs when prey population size decreases and is no longer represented by its initial value.
Thus, the final model for prey population dynamics is given by:. The N R values must be recalculated for each generation of the simulation, because human population is simultaneously growing under a logistic model, thus forming a Lotka-Volterra-like system.
Peter Ward (paleontologist)
Since a non-preferential use of these preys occurs, the extinction of one of them does not affect human population dynamics since other can replace it. Using the equations described above, I derived carrying capacities initial population sizes N t and growth rates r for the 41 preys, based on their body mass, and generated independently of their population dynamics. For example, for a kg prey such as Cervus elaphus , the initial abundance would be slightly higher than 4,, individuals and the intrinsic growth rate r would be equal to 3.
At the same time, the human population was growing almost exponentially, under a logistic model with a very high carrying capacity of almost 28,, individuals suggested by the same macroecological model, assuming a 70 kg average for human body size. For a multi-prey system, out of the 41 prey species 14 survived using the parameters described above. For the 27 species that did not, the average time for extinction to occur was equal to 1, In other words, the species that survive and those that became extinct tend to be associated in real data and in the model.
Peter Ward (paleontologist) - Wikipedia
Because the parameters of the simple macroecological model presented here are almost entirely based on body masses, it is not surprising that extinction times are associated with body mass, although this relationship is not well described by simple mathematical functions such as power and exponentials Fig. The relationship seems to be better explained by a threshold, above which extinction becomes highly probable. For example, the four species that survived the extinction events at the end of the Pleistocene but vanished in the macroecological model presented here, also did so in Alroy's model.
The current explanation is that these species expanded their distribution in the direction of the Laurentia ice sheet up to Canada, escaping overkill. From several points of view, the model developed here is simpler than the one developed by Alroy First of all, the present model is deterministic and does not include stochastic variations see Gotteli, Also, in my model, initial prey densities are derived from a maximum theoretical value predicted by the macroecological relationship with body mass, and no spatial diffusion component for human populations or spatial distribution of preys was included.
Thus, collapse of prey populations is modeled here as a regional broad-scale effect caused by a global hunt, and I had to assume that both humans and preys were randomly distributed in the Great Plains 12, years ago. On the other hand, in Alroy's simulations, there is a diffusion process in which advancing waves of humans affect local prey populations and the recurrence of these local effects tends to produce regional extinction processes. Despite random distribution of humans and preys in space and time being obviously unrealistic, the convergence between the results of the two models suggests that spatial components original spatial distribution of preys and diffusion of human populations are not critical in corroborating the overkill hypothesis.
Probably, the accumulation of local extinction events matches a regional extinction event, in terms of overall population dynamics. Consequently, hunting pressures are unrealistically high here because of the very large human population size. In the original overkill scenario, small nomadic human populations advanced as a colonization wave, never in excess of 1,, people. However, two points are important and ensure the validity of the model presented here: 1 although human densities suggested by the upper limit of the macroecological relationship between density and body mass are certainly overestimated, it is important to remember that prey populations may also be overestimated for the same reasons see below ; 2 the small human populations at the wave front will also hunt relatively small preys in local populations, so that, in any case, impact is high at a local spatial scale.
This may be equivalent to a large human population hunting a large prey population. In fact, Alroy included a similar scenario with no human diffusion, and obtained similar results in terms of predicting the fate of the species. Despite these many differences, I believe that the most important feature of my model is that it is quite conservative. Firstly, prey populations are assumed to be in equilibrium K and, even so, for all species they are at the maximum possible K predicted by macroecological models based on body mass see Brown, Anyway, it is quite possible that prey densities would be lower than assumed here, increasing their probability of extinction.
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This is especially likely if there had been simultaneous environmental stress, generated by the strong climatic changes directly affecting prey densities or causing changes in plant communities, as argued by some researchers Zimov et al. In that case, preys would have become extinct faster than indicated here.
Bison were also residents of the open plains, able to sprint up to 35 miles per hour, and they did not go extinct — and horses could run even faster. Ward introduces us to the climate change hypothesis.
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During the two million year Ice Age the Pleistocene , there were at least 18 glaciation cycles. Until the last cycle, the megafauna had mostly survived.
The last one began 18, years ago, and it was the most intense of all. It ended 12, years ago. The ice pack melted, forest advanced, and habitats rapidly changed. The mammoth tundra fragmented and shrank, which split the herbivore population into isolated groups. Ward also studied the extinction of dinosaurs.
They roamed the Earth for million years, and then disappeared. Ward was an early advocate of the notion that the dinosaur mass extinction was sudden, caused by an asteroid strike near Chicxulub, Mexico.
Some say it resulted in a decade of near-freezing temperatures on a planet that was largely tropical. Throughout the dinosaur era, small mammals also existed — insect eating night creatures. The extinction of dinosaurs eliminated large animals, and made the age of mammals possible. If not for the asteroid, humans and elephants would have never evolved.
Mammoth country once ranged from France to Siberia to New York. Our primate ancestors evolved in the trees. Their tropical homeland was eventually chilled by an era of glaciation. It thinned the rainforest, and expanded savannahs, which encouraged the evolution of large herbivores, including our hominid ancestors. Thus, you and I are the children of climate change and asteroids. Evolution is a process that creates and deletes species. New species can only emerge when a group becomes isolated, evolves unique traits, and eventually becomes unable to interbreed with their old kin.
Homo sapiens come in many sizes, shapes, and colors, but all belong to the same species, because we can all interbreed. Ward expects white skinned people to disappear in a few thousand years, because of their increasing vulnerability to skin cancer. Our cultural myths tell us that humans are continuously getting smarter.
Once a new species emerges, it changes little thereafter. Humans are the last species of the hominids, and this has risks. A gene pool has better odds for long-term survival when it diversifies into multiple species, as the ants have. Another way for critters to avoid extinction is to become generalists, like humans, rats, and cockroaches, who have adapted to many different ecosystems around the world.
Today, humans live everywhere. There is no place a group could remain isolated for millennia. So, there is little chance for a new hominid species to emerge. Evolution is random, like tossing dice. The process is influenced by ongoing environmental change, natural selection, and genetic drift chance genetic changes. Many gene pools that work well in one set of conditions will fail to adapt to sudden shifts. The golden rule of evolution is adapt or die. We are, by far, the world champion resource parasites. We are hurling countless species into the abyss in our insane impossible quest for perpetual economic growth.
In an extremely quirky twist, Ward celebrates human supremacy at causing mass extinction.