Local mate competition exercise
C. Lively, R. Penny, L. Smith
Local Mate Competition
Today’s lab uses Excel to simulate local mate competition. The file (local mate
competition S318.xls) will be supplied to you. Open the file. Note that there are two
worksheets, “Calcs” and “Graphs.” You will be working within the Graphs worksheet.
In the graphs worksheet there are entries in Blue and in Red. We will be changing the
blue ones only.
The blue values are variables. The first one is k, the number of mates. The ESS is a
function of the number of mates. The second variable is ares, the population mean
allocation to male function. We will be changing these two variables in order to answer
questions regarding the shape of fitness functions, and approaches to the ESS.
The red entries are calculated from the blue entries. For example, the ESS is calculated
as (k-1)/(2k-1). (See your notes from class and the Calcs worksheet for the set-up of the
model.)
We will start with Fisher’s assumption of an infinite number of mates. However, instead
of an infinite number, we will assume large number (k = 1000). We will set the
population to 0.5 for allocation of resources to male function (ares = 0.5).
Answer the following questions:
1. We can think of our target individual as a rare mutant. For this target individual, what
is the shape of the relationship between fitness and allocation to male function (ai)? Why
does it take that shape?
What does the shape of the gray curve mean in terms of the effect of natural selection
vs. genetic drift? (You may have to come back to this one – In question #21).
2. What are the shapes for the gains through female function (Wfemale, red curve) and
male function (Wmale, blue curve) in relation to increases in ai? What does it mean?
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Fitness
Local mate competition exercise
C. Lively, R. Penny, L. Smith
Note that the population is at the candidate for the ESS (ai = 0.5). (The blue triangle is on
the red diamond). This is Fisher’s result: there should be equal allocation to male and
female function at equilibrium in large populations.
3. Now, predict what would happen to the fitness curve for the target individual if you
set the population mean allocation to ¼ (i.e., set ares = 0.25). Draw your prediction below.
Allocation to male function
4. Now, set ares = 0.25. What happened to the individual fitness function? Why? Did it
match your predicted result?
5. Given that the population mean for male allocation is 0.25, what would be the fate of a
rare mutant that decreased male allocation? What would be the fate of a rare mutant that
increased male allocation? Why?
Fitness
6. Considering the slopes of the fitness function, what do you predict would happen if
the population mean increased from 0.25 to 0.35? Draw your prediction.
Allocation to male function
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Local mate competition exercise
C. Lively, R. Penny, L. Smith
7. Increase ares to 0.35. Did the results match your prediction? What is going on?
8. Note the slopes of the lines for gains through male function vs. female function. They
should both appear as straight lines. Why is that?
9. Increase ares to 0.45. What happened to the fitness function? To the population mean?
Will the population mean allocation continue to increase; if so, at what point will it stop
increasing?
Fitness
10. Now we ask, what happens if male allocation in the population is greater than the
candidate ESS? Draw your prediction for what would happen if we increased ares to
0.65?
Allocation to male function
11. Set ares to 0.65. Was your prediction qualitatively correct?
12. Set ares to 0.55. What happened to the fitness function and population mean?
13. Decrease ares to 0.50. What happened to the fitness function and population mean
allocation? What would be the fate of a mutant that deviated from 0.50?
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Local mate competition exercise
C. Lively, R. Penny, L. Smith
So far we have been dealing with a large mating population (k = 1000), and asking about
the fate of mutations that cause deviations from the population mean. You should have
noticed that the gains curve for male function is very close to linear.
Now we want to ask: What happens when there is local competition for mates?
Fitness
14. Draw below your predictions for the shape of the fitness curve if you changed the
number of mates to two (k = 2) and ares to 0.1.
Allocation to male function
15. What happened to the shape of the fitness curve? Was your prediction qualitatively
close? Why did the shape of the curve change with a change in k and ares?
16. How will selection act on male allocation? Will allocation increase? Decrease?
Fitness
17. Predict what would happen if we increased ares to 0.2. Draw your predictions below.
Allocation to male function
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Local mate competition exercise
C. Lively, R. Penny, L. Smith
18. Increase ares to 0.2. What happened to the shape of the curves? Did total fitness
increase or decrease? Why?
Fitness
19. Predict what would happen if we increased ares to 0.3. Draw your prediction below.
Allocation to male function
20. What happened to the fitness function and population mean when ares was increased
to 0.3? When will the population stop evolving?
21. What is the shape of the total fitness curve when population mean allocation is at the
ESS? Compare this to fitness curve when the population is at ares = 0.1? What does that
mean in terms of the drift-selection interaction?
22. Now consider what would happen if average male allocation in the population is
greater than the ESS. Set ares to 0.5. What do you predict? What actually happened?
Why?
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Local mate competition exercise
C. Lively, R. Penny, L. Smith
23. Under these conditions, will selection favor individuals that increase male allocation?
Will selection favor individuals that decrease male allocation? Why or why not?
24. Where is the equilibrium allocation? When will the mean population allocation stop
evolving? What will happen to total fitness in the population as it moves toward the
candidate ESS (assuming our starting condition of ares =0.5)?
25. Set ares to 0.2. Predict what would happen if you increased the number of mates (k)
from 2 to 4.
26. Set k = 4. Was your prediction correct? What happened to the male gains curve, and
to the total fitness curve when you increased the number of mates from 2 to 4? Why did
that happen?
27. Why do the male and female gains curves cross at ares? What does that mean?
ADVANCED POINT:
28. When do you think the male gains curve will be steeper than the absolute value of
the female gains curve? What is the significance of this? In terms of the steepness of the
male and female gains curves, what should be true at the ESS?
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