How to Calculate Relative Fitness from Recapture Data

Recapture data can help compare fitness, but the number of animals recaptured is not usually a direct measure of survival: living animals may simply go undetected. First estimate survival while accounting for detection. Then, if survival is the fitness component you want to compare, scale each group’s estimate by a reference value.

What relative fitness means

Absolute fitness is an estimate of an individual’s or group’s contribution to the next generation. In a viability-selection study, survival over a defined interval may be used as absolute fitness. In other studies, fitness includes reproduction, such as the number of offspring that survive and reproduce. Recapture data on their own usually inform survival, not the full reproductive contribution.

Relative fitness expresses a group’s absolute fitness compared with a reference:

$$w_i = W_i/W_{\mathrm{ref}}$$

Here, $W_i$ is the absolute fitness estimate for group $i$. A common choice is to use the highest-fitness group as the reference, making that group’s relative fitness 1. Another convention divides by mean fitness, so the population average is 1. State which convention you use; the relative values will differ.

Estimate survival without confusing it with detection

Let $\Phi$ be the probability an animal survives and remains in the study area until the next sampling occasion, and let $p$ be the probability of detecting it then, given that it is alive and available. In a simple one-interval setting, the chance of seeing a marked animal again is approximately $\Phi p$. Therefore, the fraction of marked animals recaptured is not generally equal to survival.

With repeated capture occasions, capture–recapture models can estimate apparent survival and detection separately. The Cormack–Jolly–Seber model is a standard approach for marked animals that can be missed on some occasions. Its apparent-survival estimate includes permanent emigration from the study area: an animal that survives but leaves permanently is not seen again and is indistinguishable from a death without additional information.

If you have only one recapture occasion, you generally cannot estimate both survival and detection from the recapture fraction alone. You need detection to be known or estimated from suitable additional data or a study design.

Worked example

Suppose two genotypes are marked and released. At the next occasion, 48 of 100 genotype A animals and 36 of 100 genotype B animals are recaptured. Assume a repeated-occasion model estimates detection probabilities of 0.80 for A and 0.75 for B. For this simplified illustration, estimated apparent survival is the recaptured fraction divided by the detection probability:

$$\begin{aligned} \hat{\Phi}_A &= (48/100)/0.80 = 0.60 \\ \hat{\Phi}_B &= (36/100)/0.75 = 0.48 \end{aligned}$$

The raw recapture rates are 48% and 36%, but the detection-adjusted apparent-survival estimates are 60% and 48%. If survival is the fitness measure and A is the reference, then:

$$w_A = 0.60/0.60 = 1, \qquad w_B = 0.48/0.60 = 0.80$$

Under this definition, B has 80% of A’s apparent viability fitness over the interval. Its selection coefficient relative to A is $s_B=1-w_B=0.20$. This describes the survival component measured by the study; it does not show that B’s total lifetime reproductive success is 20% lower.

The calculation $\text{recapture fraction}/p$ is a teaching illustration, not a substitute for fitting an appropriate model to real data. Model-based estimates account for the full encounter histories and their assumptions.

When survival is not the whole fitness measure

If groups differ in reproduction as well as survival, comparing survival alone gives only relative viability fitness. To estimate total fitness, measure or estimate the expected reproductive contribution for each group over the relevant life cycle, such as surviving offspring that themselves reproduce. Combine survival and reproduction using a model that matches the species’ life cycle; simply multiplying unrelated averages can give a misleading result.

Use the same time interval, study conditions, and definition of fitness for every group. If survival is estimated for one year in one group and three years in another, their estimates are not directly comparable without a suitable demographic model.

Common mistakes

• Treating every non-recapture as a death. Some animals survive but are missed. Estimate detection probability or clearly state the assumption that detection is perfect.
• Ignoring permanent emigration. Standard marked-animal estimates often measure apparent survival, not survival anywhere.
• Calling survival total fitness. Survival is only one component unless the study’s definition makes it the complete measure.
• Leaving the reference unstated. Say whether you normalized by the best-performing group, a control, or mean fitness.
• Comparing estimates from incompatible intervals. Relative fitness is meaningful only when the compared estimates refer to comparable groups and periods.