8.3.ATwo patterns of growth
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The subtopic in the middle and five tasks round it: label two diagrams, complete a table and fill 13 gaps. Every box rests on a learning objective of the topic in the AP Biology course and exam description. Type into the blanks and check them, or print it on A4, Letter or A3 with an answer key.
A population of 500 mice has a per capita growth rate r of 0.10 per month, with no limits. Its growth rate is dN/dt = rN = 0.10 × 500 = mice per month. If the same population lives where the carrying capacity K is 1000, dN/dt = 0.10 × 500 × (1000 − 500) / 1000 = 25 mice per month. The growth rate under limits is , and it falls to zero when the population reaches K.
| Exponential | Logistic | |
|---|---|---|
| Rate of change | dN/dt = r N | dN/dt = r N (K − N) / K |
| Shape | J-shaped; the growth rate increases | S-shaped; the rate falls as N nears K |
| When | resources are unlimited | resources are |
| Growth stops at | it does not stop |
A survivorship curve plots how many of a group of births are still alive at each age. Humans and other large mammals that care for their young have a curve, with most dying in old age. Species with a constant chance of dying, such as many birds, show a type II curve. A type III curve, with huge numbers of offspring that mostly die young, is shown by oysters and most plants.
| Exponential | Logistic | |
|---|---|---|
| Rate of change | dN/dt = r N | dN/dt = r N (K − N) / K |
| Shape | J-shaped; the growth rate increases | S-shaped; the rate falls as N nears K |
| When | resources are unlimited | resources are limited |
| Growth stops at | it does not stop | K |
A population of 500 mice has a per capita growth rate r of 0.10 per month, with no limits. Its growth rate is dN/dt = rN = 0.10 × 500 = 50 mice per month. If the same population lives where the carrying capacity K is 1000, dN/dt = 0.10 × 500 × (1000 − 500) / 1000 = 25 mice per month. The growth rate under limits is lower, and it falls to zero when the population reaches K.
A survivorship curve plots how many of a group of births are still alive at each age. Humans and other large mammals that care for their young have a type I curve, with most dying in old age. Species with a constant chance of dying, such as many birds, show a type II curve. A type III curve, with huge numbers of offspring that mostly die young, is shown by oysters and most plants.