Population Growth Questions Answer Key - Bates

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Bio 270 Practice Population Growth Questions
Population Growth Questions Answer Key
1. Distinguish between exponential and logistic population growth. Give the equations for
each.
Exponential growth is continuous population growth in an environment where resources are
unlimited; it is density-independent growth.
dN/dt = rN where,
dN/dt = change in population size; r = intrinsic rate of increase (= per capita rate of increase and
equals birth rate minus death rate); N = population size.
rt
N
= N
e
where,
t
o
N
= population size at time t; N
= original population size, r = intrinsic rate of increase and t =
t
o
time
Logistic growth is continuous population growth in an environment where resources are
limited; it is density-dependent growth. Logistic growth is characterized by a sigmoidal, or S-
shaped growth curve.
dN/dt = rN [K - N/K] where,
dN/dt = change in population size; r = intrinsic rate of increase; N = population size; K = carrying
capacity (upper asymptote).
2. What is carrying capacity? Why do populations fluctuate around some estimated value
of K?
The carrying capacity (K) is the maximum population size that can be supported or sustained
by a given environment. At K, population growth ceases. Environmental conditions fluctuate
and cause K to fluctuate. Time lags in a population's response to environmental conditions will
cause the population size to oscillate around K - the population will slightly overshoot K and
when individuals die due to lack of resources, the population size will decrease and will slightly
undershoot K. Since there are enough resources below K, the population will start to grow
again and the cycle repeats itself. We think of K as some "average" value for the environment.
3. As of 1995, the human population was expected to double within 50 years. Calculate r
for the human population.
t
= ln (2)/ r
double
Therefore, r = ln (2)/t
t = 50 years, and so r = ln (2)/50 = 0.0139 individuals/(individuals x years)
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