What is needed to demonstrate that change and the resulting characters were produced by a process of natural selection? (Recall the end of the last post in the series: “we need not to assume natural selection when we speculate or interpret observations, but to demonstrate that some actual observed character change was produced by a process of natural selection.”)

Brief answer: It’s very difficult to do so, because:
a) There are no selectors in nature–it’s a metaphor. (What we observe is as if there were a Selector.)
b) Careful definition of natural selection (see previous post):
Organisms (interactors) enjoy differential (survival and) reproductive success because of the effect of some heritable characteristics they possess (i.e. the apt characteristics increase in frequency in a population).
c) Natural selection is not differential representation of the character. (Differential representation is a promissory note for a natural selective account.)
d) To demonstrate natural selection requires demonstrating both a functional and a temporal correlation between the character and the differential reproductive success, i.e. analysis of the character’s effect and its consistent origin in time with respect to the environmental circumstances/ stress/ challenge.
For example, imagine that the angle of a flower and of its hummingbird pollinator coincide. One could find experimentally that perturbing the flower angle lowers the seed set of the plant. But what if the closest relative of the plant has the same angle without having a hummingbird pollinator in its environment? (Or if the closest relative does not have angle, the hummingbird pollinators are in its territory?) In a cladistic diagram:

(The rise of the cladistic approach to classification since the 1980s has led to precision being demanded in claims about historical branching)

What is needed to demonstrate that change and the resulting characters were produced by a process of natural selection? The short answer: It’s hard work to establish evidence for natural selection. The next installment will discuss how, in practice, people don’t undertake that work or seek out or imagine special conditions that increase the chances of natural selection serving as an explanation of the historical change in the frequency of one character.