BIO 440 Wildlife Ecology
Exercise 2: Statistics & Population Dynamics
Due: In class on 15Oct2010
Worth 38 points
1) A 3-year, limited hunting season on mourning doves (Zenaida macroura) was opened in a handful of southern Michigan counties during 2004. At the end of this 3-year trial hunting season, wildlife managers planned to evaluate the impacts, if any, of the hunt on
the Michigan mourning dove population. Results of these analyses will be used in
evaluating whether to open a season state-wide or place a moratorium on hunting of doves. As a wildlife manager, please outline the monitoring program that you would
implement to best determine the impact of hunting on dove populations. In your
discussion of a monitoring program: (10 points)
a)describe the type of data that need to be collected;
b)how it will be collected;
c)how you might analyze these data; and
d)whether or not the 3-year time frame is long enough to answer your questions.
2) Between 1993 and 1997, the following data were collected on the number of Grasshopper Sparrow nestsfound using surveys on CREP and non-CREP grasslands: (10 points)
CREPLand
/ Non-CREPLandYear / # nests / Year / # nests
1993 / 13 / 1993 / 9
1994 / 22 / 1994 / 16
1995 / 9 / 1995 / 7
1996 / 14 / 1996 / 11
1997 / 27 / 1997 / 14
Examine these data using parametric and non-parametric statistics. You should explicitly state the hypotheses that you are testing, show your work, and explain your results from both a statistical and ecological perspective. Attached are potentially useful test statistics and critical values for a range of significance levels (i.e., -levels). Be sure to defend your choice of -level and your choice of a 1-tailed vs. 2-tailed tests.
3) Apply natural logarithms (base e) to the following: (4 points)
a)Y = 8te4t
b) Nt = N0λt
4) Calculate dy/dx for the following: (4 points)
a) y = 4 – 8x
b) y = e-8x
5) Six islands of the same size were chosen as release sites for captive-reared Sumatran rhinos.
In 1995, 10 individuals were released on each of the 6 islands. Carrying capacities are
not known on any of the islands, although biologists suspect that the islands can each
support 200 to 400 individuals. Two years after the release, rhino populations had grown
to 22 (island 1), 16 (island 2), 29 (island 3), 11 (island 4), 14 (island 5), and 18 (island 6).
a) Calculate the mean r for the 6 island populations, expressed on an annual basis.
(4 points)
6) A population exhibits density-dependent growth characterized by an instantaneous per capita
birth rate, b = 2 – (N/225), and an instantaneous per capita death rate, d = 0.02 + 0.01N.
(6 points)
a) Determine the instantaneous per capita rate of change when N = 225.
b) Determine the equilibrium population size (i.e., N when b – d = 0).
c) Is an Allee effect evident in this population? Explain your answer.
Potentially Useful Statistical Information
,
where:
means for sample 1 and sample 2, respectively
pooled standard deviation for sample 1 and 2
where:
sp2 = pooled variance
n1 and n2 = sample size for sample 1 and sample 2, respectively
where:
SS = sum of squares = done for each sample
df = degrees of freedom = (n-1) done for each sample
two-tailed t-test critical values:
t0.01, 8 = 3.355t0.05, 8 = 2.306t0.10, 8 = 1.860
one-tailed t-test critical values:
t0.01, 8 = 2.896t0.05, 8 = 1.860t0.10, 8 = 1.397
,
where:
n1 and n2 = sample size of sample 1 and sample 2, respectively
R1 = sum of the ranks for sample 1
two-tailed U-test critical values:
U0.01, 5,5 = 25U0.05, 5,5 = 23U0.10, 5,5 = 21
one-tailed U-test critical values:
U0.01, 5,5 = 24U0.05, 5,5 = 21U0.10, 5,5 = 20