This exercise is adapted from a free-access website companion to the textbook
Ecology, by Michael L. Cain, William D. Bowman, and Sally D. Hacker, published
...
Advanced Ecology (second part) - Exercise 1: The Growth/Reproduction Trade-off This exercise is adapted from a free-access website companion to the textbook Ecology, by Michael L. Cain, William D. Bowman, and Sally D. Hacker, published by Sinauer Associates. http://www.sinauer.com/ecology/problem07.html
Introduction Trade-offs are a pervasive feature of life; no organism can be superior in every aspect. A common trade-off is that between growth and reproduction: Changes that increase growth often result in declines in reproduction and vice versa. The following simulation exercise illustrates this growth/reproduction trade-off and its consequences. Consider an organism that can allocate resources either to growth or to reproduction. At what point should it cease growth and start reproducing? That is the question that we will explore in this exercise, and one that many organisms face in nature. Bigger individuals usually can produce more offspring than smaller ones, so delaying reproduction could benefit an organism. On the other hand, organisms face risk of death due to predation and other causes; waiting too long to start reproducing may result in being eaten before one can reproduce. Thus, a balance exists between these two competing pressures, and at some point, reproductive output is maximized. Because the onset of reproduction is usually at least partially heritable, natural selection will shape populations to increase their reproductive output. This simulation exercise revolves around a hypothetical fish, the Doriefish. Doriefish can either grow or they can reproduce; they cannot do both, and once they stop growing, they are unable to resume growing. If a Doriefish is growing, it will gain 5 grams, and up to a maximum of 50 grams. Fish that reach at least 10 grams are able to reproduce, but at the cost of no longer growing. The number of offspring that an individual fish can produce is its weight in grams divided by 5. Thus, a 40-gram fish that is reproductive will produce eight offspring per time period, but a 10-gram fish will only reproduce two offspring in the same time period (provided it is reproductive). Remember: Once a Doriefish is reproductive, it can no longer grow. Predation from larger fish is the major source of mortality in Doriefish. The mortality rate varies, however, because some habitats have more predators than do others. In each simulation exercise, you will be given ten Doriefish, each with an initial weight of 5 grams. This simulation is open-ended. Feel free to explore the consequences of different set-points of size under different predation intensities. Open the simulation generator in the following link:
http://www.sinauer.com/ecology/problem07.html
IMPORTANT: Ignore the questions in the site and follow the questions below: Questions Question 1 To examine the fitness consequences of the size at first reproduction, compare Doriefish fitness when it starts reproducing at the minimum versus maximum possible size, when the predation rate (p) is fixed at 0.1. To do this, set the switchpoint (S) at 10 grams, run the simulation ten times, record the total number of offspring produced in each trial, and calculate the mean and the variance. Then, set S to 50 grams, run ten simulations again, and calculate the same statistics.
Concisely (a few sentences) discuss how size at first reproduction affects Doriefish fitness. If the simulations results do not conform to your expectations, explain why. (Note: It is important to do multiple trials, because there will be quite a bit of variability between trials due to the inherent randomness of predation and the small sample population size.) Question 2 To examine the fitness consequences of different levels of predation rate, repeat the procedure in Question 1 with p changed to 0.5. Run the simulation ten times for both sizes of reproduction switchpoint (S=10 and S=50) recording the total number of offspring produced in each trial, and calculating the mean and the variance. Concisely (a few sentences) discuss how predation rate affects Doriefish fitness, and whether the simulations results conform to your expectations. Contrast your answer to Question 1 above with the simulation results obtained for higher rate of predation. Question 3 Suppose that larger Doriefish did not produce more offspring than smaller individuals. What would you expect to occur under that circumstance? Question 4 We augmented the website exercise with our own simulation for a population of 100000 (rather than 10) individuals. The results are shown in the graphs below. Are these results consistent with yours? If not, explain why. Based on this exercise, summarize how size at first reproduction and predation rate interplay to
The total number of offspring
determine Doriefish fitness.
S (gr)
p
Number of offprings per 100000 individuals
p = 0.5 10000
2
5000
1
0 10 4
x 10
20 4
30
40
50
x 10
4
0 10
p = 0.3 10
x 10
p = 0.4
20 4
30
40
50
40
50
40
50
p = 0.2
8
2
6 0 10 4
x 10
20 5
30
40
50
10
2 0 10
10
p = 0.1
x 10
20 6
30 p = 0.01
5
20
30 S (gr)
40
50
0 10
20
30 S (gr)
