According to Andersson (1990), "The only thing generally agreed upon is that variation in phenetic parameters is not continuous and that character states are not combined randomly". In the same work, he defines species as clusters of individuals in a multidimensional space, where each character marks an axis (and thus a dimension).
However, in practice, when conducting taxonomy at the species level, we frequently encounter intermediate states, hybridizations of characters, etc., which can cause us to question whether the compartmentalization of the total character hyperspace that defines a species is, at least in part, a construct of ours rather than of nature.
So the question I would like to ask is: If biological diversity could be expressed as an n-dimensional mathematical function, what type would it be? Clearly, there are not infinite intermediate states between each species (as a continuous function would seem to require) and there does appear to be empty interstices between the hypervolumes, as Andersson asserts, but do the intermediate characters we find in practice not prevent the function from being entirely discrete?
REFERENCE:
Andersson, L. 1990. The driving force: Species concepts and Ecology. Taxon 39(3): 375-382.
Hello Alberto; to go back to the origins of the idea...
1. Homage to Santa Rosalia and those that follow.
2. Grant and Grant on the Galapagos finches.
Niche boundaries, and therefore species boundaries, are evidently in a regular state of flux. That's one of the great joys of working in the field...finding the peaks and valley in ecological space.
Best regards, Jim Des Lauriers
It is continuous within kinds of species, such as fungi, mosses, lizards, or pigeons :)
hi
a very old principle of natural philosophy is that "Natura non facit saltus". More scientifically Darwinian paradigm states that a species always originate from another species through gradual changes. All the biological diversity thus appeared through gradual changes. However, as life is though, most of species are extinct. And this introduces discontinuity, at all the level of biodiversity. Your question can thus be answered only once time scale is given. Cheers
Hello Marc Philippe ,
What an interesting answer! Sure, the problem of delimiting biological diversity starts with Darwin's theory, introducing the "time" dimension to the species concept. This problem is deeply discussed by Mayr and many other authors. Indeed, I don't think there is any doubt (at least today) about the continuity of biodiversity on large time scales; continuity that is imposed by the theory of evolution. In my opinion, I think the argument lies in taking the time scale out of the equation, in "taking a snapshot" of where diversity is today. That is the point at which one can either defend the position of many theorists, that is, that most of the diversity we see is discrete, so biodiversity IS discrete, or one can defend that the intermediate characters that sometimes occur indicate that it is not discrete, or at least not entirely discrete, with all the problems in species concepts that this thesis entails.
Thank you very much for the answer!
Cheers,
Alberto.