Fall 1998

Your answers to these questions should be complete, yet succinct. Extraneous
material will count against you. * Show all work for the problems,
and label the axes of your graphs*. Each correct answer is worth
five points unless otherwise noted.

**1. Define and illustrate graphically population regulation.**

- Regulation is homeostasis, which in populations is the negative feedback
between density (

- The predictive solution to the exponential growth equation

*N _{t }= N_{0}e^{rt}*

…more easily solved as: *lnN _{t} = lnN_{0} + rt*

Now we substitute, where *N _{0} = *150;

…which gives the answer *lnN _{10} = *5.11, so

Now, to solve for doubling time from 150 to 300, solve the equation
for *t*:

*t = *(* lnN _{t} - lnN_{0}*)

**t = 69+ **years

- The parameter

- A logistic population has the sigmoid growth form generated by the
equation:

*dN/dt = rN(1 - N/K)*

*…*and the growth with the above numbers would be:

*dN/dt = *0.02(40)(1 - 40/250)

= 0.67

- The inflection point, where

- Logistic growth assumes that a population will be responsive to the
carrying capacity of the environment ("

- The growth curve of humans on a global scale has been exponential.
Much of this can be explained by raising the birth rate and carrying capacity
through agriculture and industry, and lowering death rate by improvements
in medical care. Establishment of a numerical value for global carrying
capacity is a thorny issue, but a reasonable standard of living would put
the value between one and two billion people, or about a third of the current
population size.

- The ability of an individual to choose a mate based on heritable behavioral
or morphological traits involved in mating behavior constitutes sexual
selection. It is like natural selection, in that an individual's fitness
depends upon how well it can attract a mate relative to others in the deme,
with mate choice being the selective agent. The handicap hypothesis assumes
that secondary traits that make one sex (usually male) more conspicuous
to the other also make it more attractive to predators. Thus, the female,
by choosing the conspicuous male, selects for a handicap in terms of escape
from predation.

- An oak tree is

- Parental investment is the proportion of an organism's energy budget
expended on reproduction. It can involve expenditure on mating behavior
(courtship, territoriality, etc.), care of offspring, and number of offspring.
The trade-offs between semelparity and iteroparity can also be interpreted
as different strategies of parental investment: whether to put all your
eggs in "one basket" or to spread out reproduction over several breeding
seasons. These trade-offs are illustrated by the mathematical relationship
of brood size and age of first reproduction on the relative difference
between semelparity and iteroparity in terms of fitness (

The longer first reproduction is delayed the lowerris, and the less difference brood size makes inr:

**12. Define competition, and differentiate between interference and
exploitation.**

Competition occurs when two or more organisms exploit the same, limiting, resource. This interaction negatively affects all competitors, but not necessarily to an equal degree (i.e., most competition is asymmetrical). Competition can be intraspecific or interspecific. Interference occurs when "access to a resource is limited by a the presence of a competitor" (from Smith's text), which means both competitors are present at the same time in the same place. This can result in "scramble" competition, in which none of the participants is able to acquire sufficient resource to survive. Exploitation, or "niche preemption," occurs when one competitor makes the resource (usually space) unavailable to its competitors, usually by being there before the others. Intraspecific competition is mainly by interference.

If competing species have identical resource requisites, eventually the inferior competitor will go extinct. The greater the differences in exploitation (methods or subsets of a resource), the lower the intensity of competition. Guilds are groups of species that exploit the same class of resources, but generally are to some degree dissimilar in their preferred methods, area of foraging, or size class of resources. These differences allow coexistence, but whether they arise as the "ghost of competition past" or are merely preadaptive is usually undetermined.

Disturbance reduces competition, because it lowers population densities of competing species relative to the amount of limiting resource (i.e., makes the resource less limiting). The intermediate disturbance hypothesis suggests there is an optimal level of disturbance that allows a maximum number of potentially competing species to coexist. Less than this level of intensity allows competition to reduce diversity; greater than this level constitutes "overgrazing" which can cause extinction.

- The outcome of competition can depend upon patterns in the
environment that may favor one species in one location, and the other in
another location; similarly, the environment may shift in time to favor
first one and then the other (

- Competitive networks, sometimes called non-transitive competition,
are groups of species for which the outcomes of competition are not linear
or hierarchical. One species may outcompete a second species, the loser
may in turn win over a third species, but the third species can outcompete
the first. This may result from a difference in competitive strategies
and susceptibilities among species. It is uncertain how important this
kind of interaction is in nature; most demonstrations have involved space
as the limiting resource.

- Intraspecific competition should force less fit members of
a population to seek sub-optimal resources, thus widening the repertoire
for the population as a whole: niche width increases. The mating system
of the grouse is an example, wherein less fit males are forced to display
for mates on the periphery of the optimal spatial position in the lek.
Essentially, intraspecific competition means there is not enough of the
optimal resource to go around, so inferior individuals must seek lesser
portions of that niche factor. Interspecific competition, by contrast,
produces greatest selection against sub-optimal individuals in the zone
of overlap among competing species; hence, niche width is decreased. The
shape of the resource niche at any given time thus depends on a balance
between these two opposing forces.

- The Lotka-Volterra equation is a simple modification of the
logistic equation to account for the effect of a second species on the
growth of the first. In the logistic, the term

*dN _{1}/dt = r_{1}N_{1}(1 - N_{1}/K
- a N_{2}/K)*

We first need the relationship between carrying capacities and competition coefficients, in order to establish intercepts for both axes:

K179;_{1}/a =K, so_{2}/b = 1666Kand_{1}/a < K_{2}K>_{2}/bK_{1}

Since the isocline definingdNis everywhere above the isocline for species 1, species 2 wins, no matter what the initial conditions._{2}/dt