Abstract
We present a logically detailed case-study of Darwinian evolutionary explanation. Special features of Darwin’s explanatory schema made it an unusual theoretical breakthrough, from the point of view of the philosophy of science. The schema employs no theoretical terms, and puts forward no theoretical hypotheses. Instead, it uses three observational generalizations—Variability, Heritability and Differential Reproduction—along with an innocuous assumption of Causal Efficacy, to derive Adaptive Evolution as a necessary consequence. Adaptive Evolution in turn, with one assumption of scale (‘Deep Time’), implies the observational generalization of Adaptation. It is a fascinating methodological task to regiment the premises and make the reasoning both rigorous and clear. Doing so reveals how surprisingly small an amount of mathematics is needed in order to carry out the argument. The investigation also reveals the crucial role played by heritability, and how heritability itself admits of Darwinian explanation.
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Notes
We do not claim any great originality for this idea. That Darwin employed the hypothetico-deductive method is already clear from Darwin’s own accounts, and in modern commentaries on Darwin such as Ghiselin (1969). (See especially pp. 64–5 of the latter work.) What we do claim as original in the present treatment, however, is its detailed rigor in drawing out the deductive consequences from certain hypothetical assumptions (about heritability and reproduction-conduciveness). The combinatorial mathematics, implemented on a spreadsheet, would have been unfeasible for (even if not: foreign to) any contemporary of Darwin; and it delivers qualitative insights into evolutionary processes that can be not just surprising, but quite startling.
Although Walsh (2012) describes Matthen and Ariew (2009) as ‘argu[ing] that the changes in the trait structure of a population, identified as selection, are simple “analytic consequences” of the differential survival and reproduction of individuals’, it should be noted that the latter paper makes no claims of analyticity at all. Matthen and Ariew themselves use only the adjective ‘mathematical’ when formulating their view.
Cf. Millstein (2006), at p. 630, where she speaks of the ‘outcome of selection’ as ‘the change in gene or genotype frequencies from one generation to the next’; and at p. 641, where she writes
Definitions of evolution differ, but one common definition (at least among population geneticists) is change in gene frequencies from one generation to the next.
We need to remind ourselves that our thought-experiment involves being innocent of genetics. We would therefore not be much helped by adopting today’s population-geneticist’s understanding of what evolutionary change consists in. We submit that Darwin and his contemporaries had a perfectly workable understanding of adaptive evolutionary change, according to which it is change in trait-value frequencies. It is the plausibility of Darwin’s theory of evolution, on that understanding of evolutionary change, that we are seeking to enhance, independently of subsequent theoretical developments within the neo-Darwinian synthesis. This is so even though—and because—those developments have tended, on the whole, to make Darwinism even more plausible.
This is a theme well developed in Putnam (1971).
Note that we are simplifying here by not distinguishing the case where only one parent has F from the case where both parents have F. Nothing of importance will turn on this.
The comparison here is between two conditional probabilities with different conditions. The requirement is that the conditional probability
\(p\)(F(Z)\(\mid\)(F(X) or F(Y)) and X and Y begat Z)
exceed the conditional probability
\(p\)(F(Z\('\))\(\mid\)(not-F(X\('\)) and not-F(Y\('\))) and X\('\) and Y\('\) begat Z\('\)).
The modifier ‘highly’ here can be understood easily with reference to increased differences between the two kinds of conditional probabilities just mentioned.
One could, in principle, make this probability a function not only of the individual \(\iota\) but also of the age of individual \(\iota\). Thus \(p_\iota (k,t)\) would be the probability that the individual \(\iota\) has exactly \(k\) offspring by age \(t\). Making the function \(p_\iota\) age-dependent would enable one to address the interesting case of different generation times discussed in Godfrey-Smith (2007). This further layer of mathematical complexity is unnecessary, however, for the basic task of regimentation that we have set ourselves. Carrying out that task even within the idealization of the discrete-generation model is sufficiently challenging.
Note that we avoid the phrases ‘fitness enhancing’ and ‘fitter than’.
The requirement here of nomological possibility is needed in order to take care of cases where respective values of two different phenotypic traits covary, as can happen, say, in cases where a single gene has pleiotropic phenotypic effects. The specific values of the two traits then come together, or not at all. They cannot be ‘uncoupled’.
On this point, cf.Sober (2001), at p. 310.
Note that we can limit ourselves here to mention only of reproduction-conduciveness, rather than reproduction-conduciveness-cum-heritability. This is because with a trait of the form ‘has such-and-such an allele at genetic locus so-and-so’, the heritability factor stabilizes out at \(\frac{1}{2}\), whence one can ‘divide through’ all reproduction-conduciveness-cum-heritability values, so as to be able to deal only with reproduction-conduciveness values.
The biologically informed reader will have noticed, however, that the special heritability matrix under consideration here characterizes (in the case of sexual as opposed to asexual reproduction) a two-allele, single-gene trait with F 1 = aa, F 2 = aA, and F 3 = AA, under conditions of random mating within types, but not mating across types. It could be called a Mendelian matrix.
This is even more surprising than the claims, in Earnshaw-Whyte (2012) at p. 398, that ‘[Evolution by natural selection] can proceed even where there is no heredity’ and ‘variation in heritability can drive evolutionary change’.
It is extremely important to deal with the sexual case, when making general qualitative claims about evolutionary processes. Tennant (1999) criticized Skyrms (1996) for making incorrect qualitative generalizations that were made on the basis of a consideration of only (what amounted to) the case of asexual reproduction.
The appropriate generalization, for the case of sexual reproduction involving all possible (F i , F j )-matings, would be:
for all \(k\) distinct from both \(i\) and \(j\), either \(\phi ^{i,j}_i > \phi ^{i,j}_k\) or \(\phi ^{i,j}_j > \phi ^{i,j}_k\).
As observed in footnote 14, one advantage enjoyed by gene-selectionism is that one can concentrate on reproduction-conduciveness rather than reproduction-conduciveness-cum-heritability. Single alleles have constant heritability (barring the occasional mutation). Polygenic phenotypic traits, however (of the kind that most observable traits tend to be), are both variable and more variable in their heritabilities.
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Acknowledgments
This study had its origins in an Advanced Philosophy of Science course that the author taught in the Spring Term of 2009, devoted in large part to analyzing the hypothetico-deductive structure of explanations in Newtonian and Darwinian science. Earlier versions of the present study have been available as downloads from the public-domain teaching webpage http://people.cohums.ohio-state.edu/tennant9/655.html. The author is grateful to the students in that class, who were willing to embark on an exploration of issues that had no settled outcome guaranteed in advance, and that made considerable demands on their attention in class—for the mathematics in this paper was custom-made, and not drawn from any published sources. The author is grateful also to Elliott Sober and an anonymous referee, for helpful comments, and to the Editor, both for helpful suggestions on overall structure and for eliciting mention of how certain evolutionary phenomena would fit into the general picture on offer here. All remaining errors and oversights are the author’s sole responsibility.
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Tennant, N. The logical structure of evolutionary explanation and prediction: Darwinism’s fundamental schema. Biol Philos 29, 611–655 (2014). https://doi.org/10.1007/s10539-014-9444-0
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DOI: https://doi.org/10.1007/s10539-014-9444-0