The ‘strongest male’ is itself a highly variable component.
How to formalise this as a niche? Preamble. All we have, really, are observations. To put niches into a statistical framework, we only have the expected distributions of those observations (both singly and jointly). Selection (either natural or through our study design) changes the distribution of features, and we observe those changes.
For example, if the sample of breeding males is generally taller than the population of breeding males, then we could presume there is selective pressure on this feature — an important item of information. This could be detected statistical significant (e.g. the distribution differ in a Chiâ€“squared test).
If the distribution of the sample of breeding males is the same as the population then we presume height is not important. If breeding males are significantly taller in some cases and smaller in other cases the feature â€˜heightâ€™ could still be important. As a persistent feature of this species then you could say that height selection is generally important to this speciesâ€™ survival, is a determining factor, etc.
Compare this approach with a typical characterization of a niche (i.e. Hutchinsonian). Here you would record observations that characterise all the breeding males, such as that the height of the breeding males ranges from X to Y. You might describe other aspects of breeding males (e.g. hats, RVâ€™s, flip-flops). You might say that males in this height range with these characters represent â€˜core habitatâ€™ for the species.
But there is no guarantee that males with hats, RVâ€™s and flip-flops are breeding because males in the non-breeding group may also have these features. But to a large degree, the information about breeding malesâ€™ hats, RVâ€™s and flip-flops is just non-significant junk.
The only reason you would be interested in this information is if there was a prior expectation that it was important information. You might find some important characteristics of non-breeding males (e.g. males wearing cowboy hats are non-breeding). This is the case for temperature and rainfall; it is only the limits of the range of temperature and rainfall, i.e. those features of non-suitable habitat.
If the discriminating feature of the sample of breeding males is height (i.e. All tall males are breeding males), this would be useful information; it could be applied to predict in other situations, it could be the basis of theories, conservation practises, and so on. If you want to select people for a mission to Mars you could just select the tall guys.
This would, however, leave out some small males that are also breeding. That is just bad luck (depending on whether the mission is successful of course). You could look for an even stronger bijective relationship (e.g. All tall males are breeding males, AND all breeding males are tall). Chances are, however, that this would be a different feature again that optimizes this two-way relationship.
In the same way there are different logical relationships within data sets, and these may be optimised by different variables and have different uses.
1. Characterization: recording the envelope range of temperature, rainfall, etc that a species lives within and other junk information with no statistical basis.
2. Prediction: recording those features that when present are high probability indicators of the presence of the species.
3. Correlation: recording those features that vary together with the density of the species.
So you can see at least three different ways of describing the nature of the habitat of a species, with three different logical structures (right-if, left-if and iff). These three different logical structures usually result in three different features being identified, and they have three different uses. Moreover, to the extent that any particular analytical method is more like one or the other logical structures, it will identify different features and give different results (eg regression, decision trees, BIOCLIM, etc.).
Lack of appreciation of the logical distinction leads to many errors in ecology. Typically only the characterization model is used for all sorts of things it is the least equipped to do. For example, people who make living out of promulgating vague fears like the Climate Adaptation Flagship who state:
Wrong. Because species are found in a narrow climatic range does not mean they are restricted to a narrow climate range. It is more likely the narrow range is due to resource limitation or accidents of history. And so a moderate shift in climate is unlikely to be negative, and may be neutral or beneficial, as has actually been observed.