By E. J. Dijksterhuis
Dijksterhuis E.J., Dikshoorn t.C., with a brand new bibliographic essay Wilbur R. Knorr. Archimedes (PUP, 1987., 5000)(ISBN 0691084211)(600dpi)(T)(460s)
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As we shall see later, the same constraint tells against certain conceptions of what is required for selection to act at a given hierarchical level, for example, the ‘emergent character’ requirement. Such requirements mistake a product of Darwinian evolution for a prerequisite of it. This is a consideration in favour of the abstract Lewontin characterization. The expressions ‘unit of selection’ and ‘level of selection’ have engendered certain confusion. The following convention will be observed here: if entities at hierarchical level X are units of selection in the Lewontin sense, I shall say that selection ‘operates at level X’.
E. z = n1 n1 zi . So for example, if z were height, then zi would be the height of the ith entity and z the average height of the whole population. If the character z is selectively signiﬁcant, we might expect the quantity z to change over time. To track this change, we need to take account of ﬁtness. We let wi denote the absolute ﬁtness of the ith entity, deﬁned as the total number of offspring entities it produces. For simplicity ⁸ The history of Price’s equation, and its implications for the group selection question in particular, are discussed by Hamilton (1996), Frank (1995a), Sober and Wilson (1998), and Segerstr¨ale (2000).
For each parental entity, we ascertain its own character value zi , and the average character value of its offspring zi ; we then plot the point (zi , zi ) on the scatter diagram. So the diagram does not take account of ﬁtness differences: each parental entity is represented by one point, irrespective of how many offspring it leaves. The heritability of the character z, which we shall denote by ‘h’, then equals the slope of the best-ﬁtting regression line. By standard least-squares theory, it follows that h = Cov (z , z)/Var (z), where the latter term is the variance of z.
Archimedes by E. J. Dijksterhuis