Thursday’s Lesson — Budgie Populations

by Paul Horwitz

Budgerigars (“budgies” for short) are complicated birds. They come in four colors—green, blue, yellow, and white—with an interesting genetic background, emerging from the interplay of two sets of genes. One of these genes codes for yellow pigment, the other for blue; when both pigments are present, the resulting color is green. Absence of both pigments gives rise to the white variety. Moreover, each pigment is dominant, in that a single copy of the active form (the “dominant allele”) of the gene for that pigment will ensure that it shows up in the color of the offspring. This results in a simple, but surprising pattern: when two budgies mate, the color of their offspring depends not only on the parents’ color (their phenotype), but also on their particular genetic makeup (their genotype). Two white parents, lacking any dominant alleles, can only have white babies, but the offspring of a white and either a yellow or a blue budgie can resemble either parent—the exact proportions depend on whether the colored parent bird carries one or two dominant genes. Finally, the mating of a blue and a yellow budgie can result in green, blue, yellow, or even white offspring (see note).

Population over time

What happens when a randomly distributed population of budgies is allowed to interact over many generations? A new Concord Consortium model—Population Explorer—will help you find out.

Access the Population Explorer on the enclosed CD or at our website.

When the model opens, you will see an empty green field denoting a model budgie habitat. (The green represents a generic food source: “grass.” It turns paler and paler as the food is consumed.)

1. Place budgies in random positions in the field by clicking the "Add organisms" button. A dialog box will open. For now, we suggest that you keep the default selection, which includes 100 male and 100 female birds with a uniform (random) distribution of genotypes. The small squares represent male budgies, the circles, females.
2. Using the arrow tool, double-click on a square or circle to see what the budgie looks like and also to view its chromosomes (see figure 1).
3. Click "Play" and each organism will cycle through four actions in quick succession: it will move, eat, mate (if a suitable partner is nearby), and possibly die. Whether an organism lives or dies depends on three factors: its age, whether or not it is hungry (these budgies cannot go more than five cycles without food), and its state of health.
4. Let the simulation run for about a minute. What do you observe?

As the graph in figure 2 shows, the populations of all four colors of budgies tend to grow rapidly until they outrun their food supply. At that point, the numbers start to decline, finally reaching steady, though fluctuating, values. The green budgies are more numerous simply because a larger fraction of the genetic combinations available lead to green. By the same reasoning, the doubly recessive white budgies are most rare in the population.

Variables affect populations

In the simple case outlined above, none of the color groups has any particular survival advantage, or disadvantage, compared to the others. But that is not always the case in nature. What if we introduce a new factor to the environment—a disease, say, that adversely affects the health of the green budgies? Clearly, we expect the numbers of green birds to decline, but what effect will this change have on the genetically related blue and yellow budgies? And what about the white ones, which are entirely unaffected by the disease? Will their numbers increase? Let’s find out.

1. Click the "Edit Rules…" button to open a dialog box. Leave the "Terrain" popup in its default ("ANY") state. Choose the only genetic trait these budgies have — color — and select "green."
2. Change the setting for "Health" from its default value of 5 to 4. This is a small change, but it will have dramatic consequences, as you will see!
3. Click "Back" to exit the dialog box and start the simulation. The green budgies will start to die off at a slightly younger age than the yellow, blue, and white ones. At first, it's not very obvious, but observe what happens if you wait a while…

Nine minutes and about 150 generations later, not only have the green budgies died out (that small health disadvantage actually drove them to extinction!), but so have the yellow ones—and the white ones aren’t faring too well, either. The demise of the yellow budgies is easy to explain: whenever they mated with a blue budgie, they had a chance of having one of those unfortunate greens—in other words, though they themselves were not affected by the change, they tended to have fewer healthy offspring. So in the presence of blue budgies, the yellow budgies had a selective disadvantage. And vice versa—the blues suffered a loss of fertility in the presence of the yellow. In other words, the presence of blue and yellow together was unstable. Once the yellow budgies were gone, however, the blue population stabilized and now it dominates the population.

So why are the white budgies dying out? (Hint: try running the model many times—it doesn’t always do the same thing!)

Models help students explore

Amazing, isn’t it, how such a simple model can have such unexpected consequences? The Population Explorer model allows for additional explorations. For instance, you can create multiple terrains and set up different rules for each.

1. Click on the paintbrush tool for a menu of four choices of terrains: grass, water, desert, and mountains.
2. Select a terrain, then click and drag over a section of the screen to fill a rectangular region with that terrain.
3. Create your own rules to govern the health (or the speed, age of maturity, or food consumption) of any color budgie on any terrain. To get you started, you might try giving each color a special advantage when it is on the terrain of its own color (consider why this would be the case). Notice what happens in each terrain.

You can switch to a different species (e.g., dragons). You can also create your own mutations that change one allele into another, either randomly or whenever you click on a button. Just click “Edit Mutation…” and follow directions.

The Population Explorer is an incredibly rich environment to help students explore what happens when genetically related organisms interact over many generations. Stay tuned for Ecologica, which will have multiple species interact, each species adapting its genetic mix in response to challenges from the others.

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Paul Horwitz (paul@concord.org) directs the Modeling Center at the Concord Consortium.