This
class will be split into two parts. In
the first part I will provide an overview of (a) what population dynamics are,
(b) why we might want to predict what populations will do, and (c) how we can
go about making those predictions.
The
second part of the demonstration will involve an interactive discussion and
will demonstrate how we can use a simple population model to learn some basic
information about how management might be used to change the dynamics of a
population.
This
second half of the demonstration is the (very) short version of a series of
labs that I would (in a real class setting) use to give students a hands-on
sense of how population modeling can be used by managers. For a summary of the long version of this
training, I have added a separate web page (click
here).
1. Introduction
A) What are population dynamics?
i)
The
term “population dynamics” simply
refers to the way in which a population changes over time. For example, a graph showing changes in the
number of mule deer in a population over time tells you something about the
population’s dynamics.
ii)
The
study of population dynamics involves trying to understand what it is that
causes these population changes.
B) Why is it useful to predict population dynamics?
i)
Many
aspects of wildlife management focus on trying to understand why populations
are the size that they are, and how managers can alter population size.
ii)
One
of the best ways to determine whether you really understand the events that
influence a population’s size, is to try to predict
how that population will change in the future.
Consequently, attempting to predict population dynamics is a good way to
test whether your understanding of the population is any good.
iii)
Since
managers frequently want to change the size of populations, the ability to
predict the consequences of different management options is also very
important.
2. Predicting population dynamics has many
uses
A) Rare/endangered species
i)
Making
predictions for rare species is frequently called population viability analysis and often focuses on predicting the
risk of the species going extinct.
Although the terminology and focus is somewhat different compared to
other types of management question, the basic approaches are the same.
ii)
Example: Hawaiian stilts are
listed as an endangered species, but their populations have been increasing
steadily for many years resulting in the idea that they may no longer need to
be listed as endangered. By developing a
way to predict the population dynamics of this population, however, it became
clear that the intensive management that they receive because they are
endangered is critical to their persistence.
B) Declining species
i)
A
detailed understanding of the biological events that influence population
dynamics can be used to determine which aspects of a population’s life cycle
should be the target for management.
ii)
Example: Research on sea turtle
populations has shown that changes in adult survival rates are far more
important than changes in breeding success.
This has caused managers to shift their focus towards reducing adult
turtle mortality at sea, rather than concentrating primarily on managing baby
turtle survival on nesting beaches.
C) Harvest management
i)
For
hunting to be sustainable over the long term it is important to ensure that the
number of individuals that are killed is not so great as to cause the
population to decline.
ii)
Example: Bag limits are frequently determined by predicting the
population dynamics that can be expected for different hunting levels.
D) Many other examples …
i)
The
range of situations where it could be useful to predict population dynamics is
wide. Here are a few other areas where they could be useful.
ii)
Wildlife
damage control.
iii)
Controlling
invasive species.
iv)
Planning
a reintroduction program for a species that has been extirpated from an area.
3. How do we predict population dynamics?
A) Population models
i)
A
mathematical model is simply a quantitative way of describing how something
functions. And, a demographic population
model is simply a set of equations that describe how a population will change
in size over time.
ii)
Making
a basic population model is much easier than it often seems, and the same basic
approach can be used to try to answer all of the management problems described
above (plus many more). Consequently, it
is very useful to learn how to make these models.
B) The basics of demographic population modeling
i)
In
its simplest terms most population modeling involves determining how the size
of a population will change in the future.
To do this, we simply need to know how many individuals will be added
and how many will be lost during each time step (usually this means each year).
ii)
To
figure out how many to add, we need to estimate the number of breeders there
are in the population and how many young each of those breeders will produce.
iii)
To
determine how many are lost, we need to know the mortality rate (i.e., how many
will die), preferably with some sort of break-down for different aged animals
(e.g., juveniles usually have higher death rates than adults, so it is
important to include this information).
iv)
Then,
just to complicate things, we also have to account for whether there will be
immigrants (which get added) or emigrants (which get subtracted). If an entire population is being modeled (as
is often the case with endangered species), immigration/emigration can be
ignored.
v)
To
put this in mathematical terms, Nt+1
= Nt + Births – Deaths + Immigrants –
Emigrants. (Nt is the current population size; Nt+1
is the population size one time step in the future.) In very simple terms, if (B+I) is larger than (D+E) then the population will grow, and if
(D+E) is larger than (B+I) the population will decline.
vi)
Once
a model has been created it is important to test it to see if it accurately
predicts changes in the size of the real population. Example: Martha Ellis’s study of mute
swans in
B) Incorporating variation
i)
A
key element of a demographic model is that it must provide information about
the potential variability in the system.
When we estimate the numbers that go into a model, we know that there is
uncertainty about each of them. This
uncertainty arises both because we often do not have very good information
(i.e., our estimates have errors), but also because of stochasticity - random variation - inherent in the system. For example, not every individual produces
exactly the same number of young, not every individual gets to breed, not every year is as good as the others, and so on.
ii)
This
stochasticity is incorporated by telling the computer on which you are building
the model not to use a single number for each part of the equation, but rather
to pick a number from a range of possible numbers. Some numbers may be more likely to be picked
than others (can you think which kind of numbers these might be – e.g., in
terms of mean, mode, median?), but it is not certain which specific values will
be used in each simulation.
iii)
Models
that incorporate variability in this way are referred to as stochastic, rather than deterministic (a deterministic model
will produce exactly the same result every time you run the simulation).
iv)
Once
variation has been incorporated into the model, you can run it repeatedly (say
100 times). Each simulation will produce
a slightly different result, but by looking at all of the simulations it will
be possible to estimate the range of likely outcomes for the real
population. It will also be possible to
say how likely different types of outcomes are (e.g., how likely it is that a
population will increase, how likely it is that it will go extinct, etc.)
Go
to worksheet for the second half of the class.