# How to calculate relative fitness from absolute fitness with recapture data?

In Grant 1986, it says:

For this analysis the absolute fitness of an individual id scored as 0 if it disappeared and 1 if it survived, and these scores are then converted to relative fitness values by dividing them by the mean absolute fitness.

Grant, P. R. 1986. Ecology and Evolution of Darwin's Finches

If we have this dataset (for example):

id x1 x2 x3 x4 x5
1   1  0  1  0  0  0
2   2  0  0  1  1  0
3   3  1  0  1  1  0
4   4  1  0  1  1  1
5   5  1  0  1  0  0
6   6  0  0  0  0  1

Imagine that id is a column of individuals and the rest (x#) are the absolute fitness. Then, how would you calculate the relative fitness? For an example, what would be the relative fitness between x3 and x4? X1 is the first event of capture. I.e. I went on the field and capture birds for examples and noted who was there (0). I went on the field on X2, X3, etc. and noted which bird was there.

• I don't fully understand the data set. Can you please explain what each column $x_n$ mean? Apr 7, 2016 at 2:59
• I edited the question Apr 7, 2016 at 3:13
• An individual cannot have more than one value of absolute fitness. I still don't fully understand the data. I don't understand how can an individual disapear at reappear. I suppose the data just say present/absent (or found/not found). I don't understand why knowing an individual is present at time $t_2$ give us as information about its fitness. Do you know or is it part of what is unclear to you too? Apr 7, 2016 at 3:32
• Let's say you're calculating the fitness of an individual from one year to another (say X3 to X4). ID 2 to 4 are surviving, but ID 5 is not. Than the absolute fitness for year x4 would be 1,1,1,0 (for ID 2 to 5). I wonder how to calculate a relative fitness. Like the citation basically. Apr 7, 2016 at 4:49
• Well for one thing each individual lived at least as long as the interval between first and last capture - e.g. although individual #5 was not captured at time point X2 you know it was alive then because it was captured both at X1 and X3. I don't see where fitness comes in to this - you can score relative lifespan but longevity is a poor proxy for fitness Apr 7, 2016 at 5:08

So the dataset is this:

id   x3 x4
2    1  1
3    1  1
4    1  1
5    1  0

Lets assume that we caught the entire population so that we know that a 0 is really a dead organism (the estimate is proportional to lifetime fitness). Furthermore, there is no density-dependent selection and the generations are non overlapping.

The survival for next year would be the fitness value of all individual. So in year x4, the absolute fitness would be W = c(1,1,1,0). Then the mean absolute fitness would be: W_bar = (1+1+1+0)/4 = 3/4. Then to get w, the relative fitness, you divide W by W_bar. w = c(4/3, 4/3, 4/3, 0). Therefor, if you calculate mean(W/W_bar), it should give you 1.

This is as in Endler, J. A. 1986. Natural Selection in the Wild. Princeton University Press, p. 168.

• Not sure I get your question here, with your capture history you coulde estimate a survival for the populaiton. Therefore you could add covariable to your model like body mass and make a realtion between higher survival and bigger weight by example. A proxy of absolute fitness coulde be surviving until sexual maturity or something like that ... So what your question (objective ) Apr 8, 2016 at 3:32

To illustrate my comment:

id x1 x2 x3 x4 x5 group
1   1  0  1  0  0  0   1
2   2  0  0  1  1  0   0
3   3  1  0  1  1  0   1
4   4  1  0  1  1  1   1
5   5  1  0  1  0  0   0
6   6  0  0  0  0  1   1

Lets say the 1 are the bird with dark wing and the zero the bird with white wing. So You can easily run a model in MARK or Rcapture (or others...) to estimate survival for each group.

Let's say you obtain a survival between X2 and X3 of 0.70 for the dark wing and of 0.85 for the white wings. Assuming that they have the same number of offspring, you can calculate the relative fitness for the white wing :

w(white)= 0.7/0.85 = 0.83

Is that what you want to do ?

• Not exactly, I wanted to calculate relative fitness values, like the Grants. I mean, look at the citation in the yellow box. That's what I mean. Apr 8, 2016 at 21:10
• What's your fitness proxy ? Apr 8, 2016 at 21:36
• Survival, like what the Grants used. Apr 9, 2016 at 3:51