# Which statistical test should I use for my experiment on aggressive interactions in killifish?

I am doing a project on sexual selection (male-male competition) in the turquoise killifish Nothobranchius furzeri.

There are two morphs of male in the population from which my fish are obtained from- one has a red tail and the other has a yellow tail.

My null hypothesis is: Tail colour is not related to dominance/competitive ability.

I will be putting one yellow-tailed male and one red-tailed male in an arena and recording the number or aggressive interactions that take place within 5 minutes and the winner of each. I have 8 red males and 8 yellow males all of similar colour intensity. I originally thought I had about 30 of each and I was going to rank for size and pair them up (i.e. largest red with largest male etc.)which would control for size (the larger fish are more dominant). However with a sample size of only 8 this would not be sufficient to get significant results.

How could I redesign the experiment and which statistical tests could I use?

I don’t have access to any more fish.

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Can all fish interact more than once? While the concept of setting up fish to fight one another makes me feel a bit uneasy, from a statistical perspective repeated measures sounds like an option, could you set up some form of tournament where winners face winners and losers face losers? –  Jeromy Anglim Jun 8 '11 at 5:58
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## 2 Answers

Sophie and I discussed this earlier (she is a student at my university) and I am still not satisfied with any of my suggestions so far. Here are two possibilities for the winner/loser data (assuming you always have a winner).

1) Compete each yellow against each red (64 competitions) and record which colour won. Test whether the proportion of fights won by yellow males is significantly different from that you'd expect if colour has no effect on competitive ability (i.e. significantly different from a binomial distribution with p=q=0.5). This is very simple and ignores weight.

2) Compete each fish against every other fish, regardless of colour (120 competitions). Construct a dominance hierarchy (see, for example, Bang et al. 2009 Anim. Behav. 79:631). Test either a) whether there is a significant difference in median dominance rank between the two colour morphs (e.g. Mann-Whitney test) or b) whether red and yellow are randomly dispersed through the hierarchy using a randomisation test. Better still, see if you can find a bespoke test for effects of phenotypic variables on dominance in the literature.

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You might consider doing a round robin tournament and then estimating the effect of color controlling for weight within a hierarchical paired comparison model. With 120 comparisons, you still will not have much power, but you'll have more than the non-parametric techniques. You can get a little bit more power by having them interact more often, but not much more since you are just improving your estimate of the difference between the same fish.

See Ulf Böckenholt's "Hierarchical Modeling of Paired Comparison Data" also H.A. David's The Method of Paired Comparisons for discussion of different types of designs.

Also, I might worry that your experiment could be changing the behavior you are trying to measure, particularly if the fish are unused to interacting. It might be sound to have more than 120 interactions to evaluate whether there is a habituation or learning effect.

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