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Summary of problems:
Explore Evolution substitutes word games for serious engagement with natural selection. Rather than providing an accurate definition of a key evolutionary concept — fitness — the book defines in in circular terms, then pretends that the fault for this circularity lies with the concept, rather than their own poor writing. This gambit is a long-refuted creationist canard based on a misunderstanding of basic terms. It is irrelevant to the science, and rejected by philosophers of science.
"Creationists have long argued that natural selection has no predictive value and thus is a mere tautology stating the obvious fact that organisms that 'survive' are thereby decreed to have been the 'fittest.'" Henry Morris, the late president of the young earth creationist Institute for Creation Science, may have been wrong about many things, but that quotation from the preface to Scientific Creationism is an accurate account of this argument's heritage. Later he repeats the claim about natural selection and Herbert Spencer's description of it as "survival of the fittest":
It is tautologous. Those who survive in the struggle for existence are the fittest because the fittest are the ones who survive.
Explore Evolution doesn't add much:
Just about everyone has heard the popular description of natural selection as "survival of the fittest," a term Darwin credited to Herbert Spencer. The grassroots appeal of this catchphrase was very great, but it sometimes conceals some sloppy reasoning.
EE later explains that "Some [philosophers] think that biologists can avoid such circularity by carefully and specifically identifying the trait that is responsible for the competitive advantage and reproductive success of the population being studied" (p. 127), but then dismisses the claim without explaining why.
This is unfortunate, because that discussion would give them a chance to define fitness and to discuss some common misconceptions about it. Instead, the examples given merely deepen those misunderstandings. EE defines fitness as "the ability of an organism to survive and produce viable offspring in a given environment" ("Glossary," p. 146). This definition does not match that used by biology textbooks, and those differences are what allows EE to repeat this creationist error.
Mark Ridley's Evolution defines fitness as:
The average number of offspring produced by individuals with a certain genotype, relative to the number produced by individuals with other genotypes.
Campbell and Reece define it:
the contribution an individual makes to the gene pool of the next generation relative to the contributions of other individuals.
Futuyma defines two related concepts:
fitness: The success of an entity in reproducing; hence, the average contribution of an allele or genotype to the next generation or to succeeding generations. Relative fitness is the average contribution of an allele or genotype compared with that of another allele or genotype.
Each of these definitions discusses the fitness of alleles or genotypes rather than the fitnesses of individuals. Explore Evolution only talks about the fitness of individuals, and studiously avoids discussing alleles or genotypes. The reason can be seen in the brief example quoted above, in which "someone might say that a particular organism survived because it was more "fit" than its competitors." Later, EE creates a hypothetical situation in which we observe finches and see that some produce more offspring than others. The authors then complain that a study like this "certainly doesn't tell us why. All we can say is that some finches leave more offspring (our definition of 'survival') because they produce and sustain more eggs (our definition of 'fittest')." By ignoring the role of genetics in defining fitness, they trivialized the concept and confused its place in biological evolution.
A student working with an inquiry-based book which properly defined fitness might have been encouraged to propose an experiment which would help determine the "why." The student would propose looking for some genetic factor shared by individuals which produce more eggs. (The student might also suggest examining whether producing more eggs actually produces more offspring which survive to adulthood and contribute genes to future generations, a key component of the accurate definitions of fitness).
Philosophers do continue to seek an broad philosophical account of fitness, but agree that it is not tautological, and that it does describe a general tendency of a trait or organism, not — as EE prefers — a description of the actual performance of an organism. Thus, an individual can be fit (possess traits which ought to increase its reproductive success) but not reproduce. It could be struck by lightning, for instance. Treating fitness as a tendency eliminates any circularity, just as recognizing that salt tends to dissolve in water allows you to describe salt as soluble even if it never is placed in water. A gene can tend to be more fit without making each individual possessing that trait produce more offspring.