We have discussed how population ecologists have tried to develop a model (the logistic growth model) that helps them to understand the factors that affect population growth.
We talked a lot about the graph plotting how the population size would vary over time in a population that started much smaller than the carrying capacity (the s-curve). Why does logistic growth show this pattern?
Initially, the population is growing slowly. When populations are small the per capita growth rate is large but because there are only a few individuals in the population rN is small. Over time, the population growth rate increases becasue populations are still small enough that r is still relatively large and now a larger N allows rN to be a bigger number. Population growth rate starts to slow as populations reach their carrying capacity because in large populations the per capitat growth rate is small and even though N is large rN is small. When the population reaches its carrying capacity b = d, so population growth stops.
Density Dependent Population Regulation
We notice that populations don't keep increasing in size forever. That is because populations are naturally self regulating. As population size increases the per capita birth rate declines for the biological reasons that we discused earlier. (When a parameter decreases as population size increases that parameter is said to be negatively density dependent. As population size increases the per capitat death rates increase for the biological reasons that we discussed earlier. (when a parameter increases as the population size increases that parameter is said to be positively density dependent). Thus, the per capita birth and death rates are naturally density dependent in such a way that eventually causes the population size of species to stop growing.
Past Test Questions (answers at bottom of post)
1. In logistic growth, what is the per capita growth rate when N = 1/2K?
(a) rmax
(b) 2(rmax)
(c) ½ (rmax)
(d) it is a maximum
(e) you can not answer this questions with the information provided.
2. How can you calculate the population growth rate?
(a) subtract B from D
(b) add the per capita death rate to the per capita birth rate
(c) multiply r by N
(d) divide dN/dt by N
(e) a and c
3. Why don’t we expect raccoons to show exponential growth?
(a) per capita birth rates increase as population sizes increase
(b) per capita death rates increase as population sizes increase
(c) per capita birth rates decrease as population sizes increase
(d) b and c
(e) none of the above
4. Which of the following are true when populations are at their carrying capacity?
(a) dN/dt > 0
(b) r < 0
(c) b = d
(d) B > D
(e) a and d
answers- 1.e, 2.c, 3.d, 4.c
Why would the answer to question #1 not be answer choice a? When N=1/2K, doesn't that mean that r begins to become less positive as N approaches K? Therefore, when N=1/2K, r would be at its maximum rate.
ReplyDeleteHI Chelsea, Because r decreases as N increases at a constant rate when the population size is one half of K the per capita birth rate is one half of r max.
ReplyDeleteSo if one of the answers involved having the highest growth rate, then that would be it?
ReplyDeleteand since there is none involving that, there wouldn't be enough information based off our answer choices or the question?