Hi Nonlin -
When a biologist models various traits as a continuous, normal distribution, s/he gives up some precision. That seems to bother you. It does not bother the scientist, who is glad to give up some irrelevant precision in return for the enormous explanatory and predictive power that modeling over a gradient provides. So scientists are going to continue using those models, in spite of your protests.
This also applies to gradient models of genetic similarities and divergences. It is true that in a world where all biology research dollars were controlled by you, NonlinOrg, you could insist on purely discrete modeling down to the individual. Species would presumably be represented as clusters within in a hypercubic genomic space.
This research project would run into intractable problems, however. The math would become intractable over such a large number of observations. Moreover, you could never really build a model because you would not be able to gather genomic data from every individual organism in a species, much less every individual organism on the planet.
Given these intractable roadblocks to discrete mathematical modeling of genomics across the biosphere, biologists instead take samples and project them into the global genomic space using continuous mathematical functions. The genomic characteristics of a population are represented as a probability distribution function, which is necessarily a continuous function. There is no other way to perform genomic research, your preferences notwithstanding, NonlinOrg.
Moreover, modeling along gradients allows dynamic features to emerge. Observations of neutral drift, mutations, and selection in experiments such as Lenski’s and in numerous field studies can be applied across the biosphere over time, yielding insights into how life evolves over time. As a Christian, I assert that those biological insights are in fact insights into how God has created, shaped, and upheld the creation.
As discussed ad nauseum in a previous thread, Lenski’s experiments showed that the genetic profile of an E.Coli population changed in important ways over 40,000 generations. The speciating mice of Madeira have been pointed out to you. And speciation over the distance from finch to sparrow takes a very, very long time and certain selection forces in the environment. The examples you cite therefore do not conflict in any way with the theory of evolution.
The fact that you think those examples contradict the theory of evolution, when they in fact do not, suggests that you do not understand the theory of evolution.
In order to keep the discussion of Lenski’s experiment from progressing to ad infinitum, I am going to refer readers to my posts in the previous thread.
Have a great holiday weekend, Nonlin
Grace and peace,
Chris Falter