The lynx-snowshoe hare population dynamic pictured here represents an example of population: A growing hare population provides more food for the lynx, which then reproduce at higher rates. Snowshoe hares (prey) Lynx (predator) Population size Time Lynx eat too many hares, thereby reducing their food source and causing their own population to crash, which enables the hare population to grow. exponential growth. oscillation. explosion.
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Scientists have been tracking the population numbers of snowshoe hares, lynx, and coyotes in northern Canada over many years. In this region, lynx and coyote are the primary predators of the snowshoe hare. The graph below shows the population numbers for all three animals over a ten-year period. GRAPH 1: LYNX, COYOTE, AND HARE POPULATIONS Number of Lynx Number of Coyotes Number of Hares 2.0 1.5 1.0 0.5 0.0 1987 1988 1989 1990 1991 1992 1993 1994 1995
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Snowshoe hare and Canadian lynx live in the boreal forest of Canada. The snowshoe hare is the main prey species of the Canadian lynx. They usually live 1 to 2 years and have four to six offspring at one time. The Canadian lynx is a large cat, which lives up to 15 years and has one to four cubs each year. In spring when vegetation is plentiful, the hare population increases quickly. When the hare population becomes more numerous, they are easy to track and catch, and the Canadian lynx population increases. The Canadian lynx hunts the snowshoe hare and causes their population numbers to drop over time. The snowshoe hare would most likely have which kind of population growth? Logistic Regulating Exponential Community
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The relationship between the number of rabbits $y(t)$ and the number of foxes $x(t)$ at any time $t$ is given by $$-C \ln y+D y=A \ln x-B x+E$$ where $A, B, C, D,$ and $E$ are constants. This relationship is based on a model by Lotka $(1880-1949)$ and Volterra (1860-1940) for analyzing the ecological balance between two species of animals, one of which is a prey and the other a predator. Use implicit differentiation to find the relationship between the rate of change of the rabbit population in terms of the rate of change of the fox population.
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