We will incorporate the DD forces via logistic influences of a population's densityimpact on itself. The DD forces produce humped dN/dt curves (look back at Fig. 6.1
of Lecture 6). "Good" DD years have higher maxima (top of the hump) and
larger K (how far
What other demographic aspects of populations might we want to consider besides
their survival and mortality rates? At least two other features are sex ratio and age
structure (age ratios). Each of these can affect population dynamics in interesting
Reproductive values: (a left eigenvector will be a horizontal 1X4 vector) cfw_1., 2.20,
2.12, 0 Note that the reproductive value of the fourth-year individuals is 0.
That's because they will not survive to reproduce again.
Typically reproductive value cur
A matrix population model is a demographic technique for understanding phenomena
at the population level based on information from the individual level (birth, death,
and growth rates of individuals; we'll call these demographic rates the vital rates).
The "waves" in the age structure disappear as we approach equilibrium at the stable
(st)age distribution, SSD. Note that the equilibrium for the matrix model is defined in
terms of the age structure. Thatcontrasts with the stable equilibrium in the logist
Female applicants to Berkeley were turned down at a rate considerably higher than
that for men. Their test scores (GREs) were higher than the men's. Bias? Actually not;
department by department, female acceptance rates were higher than those for males
Reminder of how to do a derivative for power functions:
derivative of cxa = acxa-1
The derivative of a constant times the quantity "[x to the power of a]" is the exponent
(a) times the constant (c) times the inside-the-brackets-quantity "[x to the power o
Do populations normally grow exponentially? Why not?
Adding (a little ) realism
In most cases, if we model curves like those in Fig. 4.1 (previous lecture) in the light
of real world populations, we can tell immediately that something is wrong.
If a model
Let's look at another interesting aspect of the behavior of the discrete logistic with
high values of r (> 2.692) in the chaos region. Our 1-dimensional map with N(t)
vs. N(t+1) actually provides an illusion of order. If we know the population size at t i
Examples of dynamic population patterns
Changes within a population (intrinsic or endogenous)
Change in sex ratio: increase in females may lead to increase in birth rate if
constraints on female offspring production limit growth.
E.g., much of the practi
From deterministic to stochastic models. Up to this point in the course all the
population models we have considered have been deterministic. That is, we assume
that the vital rates (such as birth, death, immigration and emigration) are constant and
Necessary and sufficient conditions - the best kind of explanation
In ecology and evolution, we are often interested in the conditions that cause a
particular phenomenon to occur. The most satisfactory explanations are those
that describe conditions that
How do populations change in size? Four major processes are at work:
(symbols used in Eqn
Birth, death, immigration and emigration.
We will start simple, and ignore immigration and emigration for the moment. So now
we are looking at birth