1) 4pts. From p. 867. Rancher Jane is thinking of changing from cattle to Americ
ID: 33201 • Letter: 1
Question
1) 4pts. From p. 867. Rancher Jane is thinking of changing from cattle to American bison (Bison bison) to capitalize on the market for lean and more healthy meat, but she needs to know how well bison will do on her ranch first. She buys 50 female bison who are already inseminated and places 10 of them randomly into their own pasture. These 10 females serve as a sample from which Jane collects demographic data over one year. Use her data to answer the questions below. a. What is the total number of births and deaths in this sample population? b. What are the estimated average per capita birth and death rates (b and d) for the entire bison herd, based on this sample? c. What is the estimated per capita growth rate (r)? d. Based on these estimates, what is the size of Jane's entire bison herd at the end of the year? 2. (2pts) a. In the population growth model dN/dt = r N * (K-N)/K. What is measured by K? b. When N = K, what is delta N?Explanation / Answer
1)
a) Based on the given data, the total number of births and deaths in this sample population are:
b)
Calculation of per capita (per person) basis:
The total number in this population, N = 10
The birth rate (bx) = 5/10 = 0.5
The death rate (dx) = 2/10 = 0.2
Mx = bx/nx
Mx = 0.5/0.2
= 2.5
Thus, the estimated per capita is 2.5.
c)
Estimated per capita growth rate is:
r = b-d therefore r = (0.5 - 0.2) = 0.3
d) Based on these estimates, the size of Jane’s entire bison heat at the end of the year is: 13.
2)
a) dN/dt = rN [K - N/K], it is a logistic growth rate equation.
The logistic growth equation is an effective tool for modelling intraspecific competition despite its simplicity, and has been used to model many real biological systems. At low population densities, N(t) is much smaller than K and so they may determinant for population growth is just the per capita growth rate. However, as N(t) approaches the carrying capacity the second term in the logistic equation becomes smaller, reducing the rate of change of population density.
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