AP Biology · Unit 8 · Topic 8.3
Give a population unlimited resources and its growth has a shape that is worth seeing rather than being told about. Run it, and find out how quickly unlimited becomes impossible.
Learning objective 8.3.A Describe factors that influence growth dynamics of populations.
Start with the equation that is always true. A population changes by however many are born minus however many die, and the sign of that difference is the entire story. Everything else in this topic and the next is this equation with more detail added.
Two populations. One has a birth rate six times higher than the other. Predict which one survives before you look.
| Population | Birth rate | Death rate | B − D | After 30 steps |
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When nothing is limiting a population, the number added each interval is proportional to the number already there. That one sentence is the whole model. Pick an rmax and watch what it does — but watch the doubling time rather than the size, because the doubling time is what makes growth exponential.
The same starting size, and a rival that gains exactly fifty individuals every interval no matter what. For nearly half the run the flat one is winning.
Those three words are doing all the work in the exponential model, and it is worth finding out what happens if you take them literally. One bacterium. Divides every twenty minutes. Nothing at all limits it.
| Situation | Why nothing is limiting it yet |
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The next topic supplies the missing term. Everything here stays true — the equation is not wrong — but one factor gets added that makes the growth rate depend on how full the environment already is, and the curve bends over. It is worth arriving at that topic already knowing that something has to be added, and roughly what it has to do.
| Factor | Symbol | Effect on dN/dt | What influences it |
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| Adaptation | Resource it secures | Which term it acts on | How |
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Answer these in your own words before you open the answers.
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