In working with this tutorial,
you should be learning about the following questions:
What
biological phenomena can be studied with models?
How
are models used to test hypotheses?
What
are the procedures needed to use Populusâ?
How
should results be compiled?
How
should results be presented?
The word “theory” has very different meanings.
Some people use it in a negative sense (the flat earth theory). It
can describe an idea that is reasonable, but unproven (the theory that overgrazing causes a catastrophic shift
of short-grass prairie to desert). It can describe a set of concepts
in science that are highly explanatory, integrative, and essentially proven (the theory of relativity, the theory
of natural selection). And finally, sets of mathematical equations
derived to represent real-world processes comprise a “theory” about how those processes actually work.
In this tutorial, you will be using “theory” in the sense of using equations to model the real world.
Just about any process can be approached with a
mathematical model. One needs to be able to identify objects (such
as genotypes), have a way to quantify (such as counts), and have reasonable guesses about factors that influence
changes in the objects (such as mortality, reproductive success). If
we want to understand how the relative abundance of different genotypes changes over generations, we can construct
equations that represent the abundance of each genotype and the fitness of each genotype.
Of course, a mathematical model must simplify the
complexity of the real world. The basic question is, can we capture
the essence of biological process with our simpler model? The model
provides predictions about how organisms might react to differences in conditions (such as different fitnesses),
but these predictions must be tested against the real world. If the
models are too simple to accurately predict experimental outcomes or observations in the real world, then we can
increase reality (?) to the simple equations by adding more complex interactions (e.g., allow fitness to change
with the abundance of each genotype).
As indicated above, we start with a set of equations
and parameters. Theoretical biologists (e.g., biologists that develop
mathematical theories – not “hypothetical biologists”) apply two approaches to see what predictions are derived
from those equations and parameters. The analytical approach
solves sets of equations to derive predictions about the state of the system after it reaches equilibrium.
Much of population genetics is analytical. The simulation
approach calculates changes in the system with each cycle of time (e.g., each generation of survival and reproduction),
to provide numerical patterns of change. Obviously, computers are
quite handy for the simulation approach. The analytical approach
has great advantages in being more general in its predictions, while the simulation approach allows for more complexity
and more quantitative predictions. We will be using the simulation
approach in this tutorial.
The software that you saw used in class (Populusâ)
is available for free for educational use. The program has models
for many different ecological and evolutionary processes; we are using just a small set of these models (but feel
free to play around with models for population growth, competition, and predation).
In the autosomal selection model, Populusâ
uses the simple equations that are given in the text and in class to calculate changes in genotype frequency, given
particular fitnesses for each genotype. You will set the parameters
of genotype fitness. In doing so, you can simulate no selection,
directional selection, stabilizing selection and diversifying selection.
You also can simulate different forms of developmental influence such as dominance, co-dominance, or intermediate
dominance. After recalculating genotype frequencies over many
generations (you can control the number of “iterations”), the software provides clear pictures of how the system
changes, using different ways of looking at the system and it also is possible to examine numerical results.
