Question
Wildlife management introduces 135 ducks to a reservoir in an effort to restore the duck population in the area. The growth rate of the
population (rmax) is 0.074 ducks/year.
Which of the following is the best estimate of the size of this duck population after one year?
(A) 135
(B) 141
(C) 145
(D) 152
▶️Answer/Explanation
Ans:
(C) \(\frac{dN}{dt}=r_{max} N = (0.074)(135) = 10\) ducks in one year. Since the starting
population size is 135 ducks, after one year, there will be 135 + 10 =
145 ducks.
Question
In 1986, the quail population in Golden Gate Park in San Francisco was 140 birds. Hunting by feral cats reduced the number of quail to 32 birds by 2016.
If the birth rate of quail over this period averaged 20.4 quail/year, what was the average death rate of quail during this period?
(A) 2.4 quail/year
(B) 3.6 quail/year
(C) 24 quail/year
(D) 36 quail/year
▶️Answer/Explanation
Ans:
(C) \(\frac{dN}{dt}=B\) (birth rate) – D (death rate). So The average death rate would be D = B – \(\frac{dN}{dt}\). The death rate is D = 20.4 quail / year – \(\frac{(32-140) quail}{30 years} = 20.4 – (-3.6) = 20.4 + 3.6 = 24\) quail/year.
Question
A population of 190 jackrabbits lives in McInnis Park in San Rafael, California. The carrying capacity of the park for jackrabbits is
approximately 200 rabbits.
If the rmax for the jackrabbit population is 1.5 surviving jackrabbits per year, what is the estimated increase in the
number of jackrabbits in one year?
(A) 10
(B) 14
(C) 285
(D) 300
▶️Answer/Explanation
Ans:
(B) Since there is a carrying capacity in this environment, use this equation. \(\frac{dN}{dt} = r_{max} N(\frac{K-N}{K})=(1.5)(190)(\frac{200-190}{200})\) = 14.25. Choice (B) is the closest estimate to this number and is therefore the correct answer.
Question
Which of the following statements describes a population that could experience exponential growth?
(A) a population that was limited by density-dependent factors
(B) a population whose size is beyond the carrying capacity of the
environment
(C) a population in which there are no limiting factors
(D) a K-selected population
▶️Answer/Explanation
Ans:
(C) Populations grow exponentially if there are no limiting resources
or predators that would limit the population size. If the population was
limited by density-dependent factors, its growth would be logistic, so
choice (A) is incorrect. Choice (B) is incorrect because if the size of the
population was beyond the carrying capacity of the environment, its numbers would be declining, not growing. K-selected populations
experience logistic growth, so choice (D) is also incorrect.