Oscillations lynx population

Figure 4.10.30 (a, b) Oscillations in population density changes in the abundance ofthe lynx and snowshoe hare, indicated by the number of pelts (per year) received by the Hudson Bay Company from 1885-1900 [(a) oscillations of populations with time, (b) limit cycle]. 

The oscillations in the two populations result from the difference in phases between rabbit and lynx reproduction. The rabbits reproduce because their main food source (grassland) is plentiful. The lynx population will also increase, but only after the rabbit population has grown. Once the lynx population becomes too high, rabbits will be eaten more rapidly than new rabbits are born, and their population will begin to decrease, which in turn will lead to a decrease in the lynx population. The rabbit population can then begin to rise again. Thus there will be a time lag between changes in the two populations. 

It is worth adding that in the studied populations of hares and lynxes, occurring in Canada, oscillations in their abundance have been actually observed. 

Many population cycles have the unusual property that their period length remains remarkably constant while their abundance levels are highly erratic. Fig. 15.8a demonstrates these features for one of the most celebrated time series in Ecology - the Canadian hare-lynx cycle. In [28, 29] is was shown that such more complex oscillations can be achieved in simple predator-prey models by including more trophic levels. To describe the main dynamics of the lynx the following ecological foodweb model was presented... 

As shown in Fig. 15.1(1 in a spatial lattice of patches, only small levels of local migration are required to induce broad-scale phase synchronization. The re.sult of the simulation in the phase synchronized regime is visualized ill Fig. 15.11, which demonstrates that all populations in the lattice are phaselocking to the same collective rhythm. Similar to the synchronized oscillations of the Canadian lynx, also in the lattice simulation despite the... 

FIGURE 6.20.3 One-hundred-year record of population cycles of the snowshoe hare Lepus americanus) and the Canada lynx (Lynx canadensis), based on pelt records of the Hudson s Bay Company in Canada. Lack of anticipation in predator-prey systems lead to unstable population oscillations. (From Gotelli, N.J., A Primer of Ecology, Sinauer Associates, Sunderland, MA, 1998. With permission.)... 

A key feature of this system, and of most chemical systems that exhibit oscillations, is autocatalysis, which means that the rate of growth of a species, whether animal or chemical, increases with the population or concentration of that species. Even autocatalytic systems can reach a steady state in which the net rate of increase of all relevant species is zero— for example, the rate of reproduction of rabbits is exactly balanced by that species consumption by lynxes, and lynxes die at the same rate that baby lynxes are born. Mathematically, we find such a state by setting all the time derivatives equal to zero and solving the resulting algebraic equations for the populations. As we shall see later, a steady state is not necessarily stable-, that is, the small perturbations or fluctuations that always exist in a real system may grow, causing the system to evolve away from the steady state. 

Figure 1.2 shows the number of lynx furs turned in to the Hudson Bay Company from 1820 to 1920. Distinct oscillations are seen with a period of about nine years. No data were available on the rabbit population, so we cannot be certain that the oscillations are due to a predator-prey interaction. However, controlled experiments have been performed in the laboratory with paramecia (Paramecium aurelia) that eat the yeast Saccharomyces exiguns (Figure 1.3). Notice how the predator population lags behind the population changes in the prey.

Dynamic behavior and oscillations are also found in nature, such as predator-prey interactions. A classical example of interacting populations is shown in Figure 4.10.30 for the snowshoe hare and the Canadian lynx, a specialist predator. The lynx-hare... 

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