STUDY QUESTIONS #9 (4/17-4/21) Due in lab week of April 24.

1. In logistic population growth, DN is constantly changing as a function of N. Use the equation we discussed in class to say how this works. It will help you understand this if you consider what DN is when N is very low (near 0) or very high (near K). What happens if N > K?

Under logistic growth, DN /Dt= rmax (K-N /K) N. The term (K-N)/K is what adjusts the growth rate according to density (N). This is what makes population growth density- dependent. Note that this adjustment term does not appear in purely exponential growth. When N is low, this term is approximately = (K-0)/K = 1, so the rate of growth is approximately rmax N. When N is higher, near K, then (K-N)/K = 0, so DN approaches 0. In other words, population growth slows as N increases until at K, population growth is zero. If N > K, then (K-N)/K < 0 and DN becomes negative, meaning that ractual has become negative causing the population to decline. NOTE: This is a good example of how to take an equation and see what happens under different circumstances. Comparing the equation to the graph at low or high N will further help you to see how this equation works to produce the s-shaped curve.

2. One of the requirements of logistic growth and density-dependent population regulation is that birth and death rates change with density. How did the data that I presented in the Daphnia example in lec. 6 show that this is a reasonable assumption?

The experimenter put Daphnia at different densities (that is changed the number of individuals in a constant volume of space and constant amount of food). Then the survivorship curves (showing death rates over the lifetime as the probabilities of survival to particular ages) and fecundity curves (the average number of offspring had by females at particular ages) were compared at different densities. Changes in these curves in the direction of decreases shows that birth and death rates change with density in a way that has an inhibiting effect on population growth.

3 . Briefly explain how human population growth became exponential and discuss the three factors that allowed birth rates to become greater than death rates through time.

A number of limiting factors to population growth were removed that allowed humans to expand into new habitats and climate zones, and resulted in the carrying capacities of occupied environments to increase.

Culture provided adaptations that promoted survival. Learned functions such as fire, shelter, tools, community hunts were communicated within the species, and thus facilitated migration.

A move from hunting to agriculture 11,000 years ago resulted in an increase in the carrying capacity. Two milestones, domestication of plants and animals, and irrigation, were the key to increasing food supplies to support increased population.

Technology and science allowed humans to expand into new habitats and climate zones, and to live at high densities. For example, proper hygiene, sewage disposal and medicine decreased death rates, while learning how to harness the energy from fossil fuels lead to industrialization.

4. Describe two effects of the timing of reproduction on population growth. (by describe, I mean say what the effects are and why they work in the direction that they do). In a population that is not growing, explain why late reproduction might even be an advantage.

1. Early reproduction speeds up population growth because offspring born sooner reproduce sooner themselves.

2. Delayed reproduction slows population growth, because later-born offspring don't start contributing to the population themselves until later.

In a population that is not growing (because it is at or near K), delaying reproduction can be an advantage if it allows individuals to be better competitors for resources themselves (by growing larger or learning more as juveniles), or allows their progeny to be bigger at birth. In this case, the disadvantage of decreases in rate of growth is meaningless because the population is not growing.

5 What is the difference between intraspecific and interspecific competition? How could you show experimentally that interspecific competition affects survival or reproduction in a real population?

Intraspecific competition occurs between members of the same species, while interspecific competition occurs between members of different species. To test for interspecific competition, grow and maintain the two species both separately and together. If K of one or both species is reduced when species are together, this is evidence for interspecific competition. Also, showing that survival, growth or reproduction is decreased by the presence of the other species would work, and might be easier than measuring K.

6. In 1798, Thomas Malthus predicted that humans would soon face famine, poverty and disease. What was the basis of his prediction? Why has this prediction not (yet?) been borne out?

Malthus's prediction was based on the belief that human popuation would grow exponentially, that that food production would not keep pace. However, we have seen dramatic increases in food production over the past 100 years, despite continued exponential growth. Have we simply raised K??

7. Name and describe two factors that can cause a decrease in r within a population. Do they affect b, d, or both?

A decrease can occur in r if birth rates decline due to reduced food, or increased stress, or if death rates rise (less food, more disease, more stress, increase in predationÉ). Since r = b-d, anything that lowers b or increases d will affect it.