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When talking about growth rate as a proxy for fitness, most authors think of population growth rate (whether in terms of the Malthusian parameter or the net reproductive rate). Such methods are typically used for unicellular that have very short generation time. You seem to be referring to the individual growth rate.
Possible proxies for fitness
There are a number of different proxies for fitness one can use.
- growth rate
- Some phenotypic trait correlated with fitness such as:
- seed production
- body size
- Competitive abilities
- Experimental evolution
How to chose a proxy
The proxy you want to use depends:
- The accuracy you need
- The organism you are working with
- The a priori knowledge on the biology of the organism of interest.
For example, if you have little knowledge of what phenotypic trait could be correlated with fitness and if the organism of interest have a very short generation time, then growth rate might be good (and accurate) proxy to use indeed.
You should probably read some papers that have used a method of potential interest before doing it yourself.
At page 1232 of Kawecki and Ebert 2002, there are a few paragraphs reviewing the different proxies and their usage. They cite key papers you might want to have a look at.
Proxy for fitness in fishes
I know little about fish biology in general but I doubt there is such thing as a generalization of whether "individual growth rate" is a good proxy or not. As you don't specify what species of fish you are working on, I don't think it is possible to answer this question accurately.
You should look at previous work done on the species (or related species) you are working on in order to figure out what would be a good proxy.
Issue in your post
I think it is clear from above that you should indicate what species you are working on.
The paper you link should come with more explanation. You say a paper is a review but a review about what?
You cannot say "I would like to do something like them" and link a paper. You should describe with you own word what you are trying to achieve.