Chapter 2.7, Problem 35E

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8th Edition

James Stewart

ISBN: 9781285740621

Textbook Problem

In the study of ecosystems, *predator-prey models* are often used to study the interaction between species. Consider populations of tundra wolves, given by *W(t),* and caribou, given by *C(t),* in northern Canada. The interaction has been modeled by the equations

(a) What values of *dC/dt* and *dW/dt* correspond to stable populations?

(b) How would the statement “The caribou go extinct” be represented mathematically?

(c) Suppose that *a =* 0.05, *b =* 0.001, *c =* 0.05, and *d =* 0.0001. Find all population pairs (*C, W*) that lead to stable populations. According to this model, is it possible for the two species to live in balance or will one or both species become extinct?

To determine

**Part (a)**

**To find:**

Values of

Explanation

**1) Given:**

**2) Calculation:**

When the population is stable then the growth rate is neither positive nor negative

Therefore,

To determine

**Part (b)**

**To find:** How would the statement “The caribou go extinct” be represent mathematically

To determine

**Part(c)**

**To find:**

All population pairs (C, W) that lead to stable population.

And According to this model is it possible for the two species to live in balance or will one or will both species become extinct

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