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What Is Adaptation and How Should It Be Measured?

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What Is Adaptation and How Should It Be Measured? Journal of Theoretical Biology 447 (2018) 190–198 Contents lists available at ScienceDirect Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/jtbi What is adaptation and how should it be measured? ∗ Joel R. Peck a, , David Waxman b a Department of Genetics, University of Cambridge, Cambridge, UK b Centre for Computational Systems Biology, ISTBI, Fudan University, Shanghai, China a r t i c l e i n f o a b s t r a c t Article history: Adaptation is a defining property of living systems. It occurs when organisms become better suited to Received 17 May 2017 their environment. The phenomena that people find most fascinating about biological systems are, in gen- Revised 27 February 2018 eral, the result of adaptive processes. Examples include the mammalian central nervous system, the flight Accepted 4 March 2018 of birds and insects, photosynthesis, and the human hand. However, despite the centrality of adaptation Available online 6 March 2018 for biology, there is no generally agreed quantitative way to describe the degree to which an organism Keywords: is adapted. Here, we address this situation by proposing a quantitative measure of adaptation. We also Evolution present results of computer simulations which demonstrate that some changes in parameter values cause Natural selection mean adaptedness and mean relative fitness to change in opposite directions. This indicates that adapt- Biological information edness and relative fitness are distinct concepts. We suggest that the measure of adaptedness proposed Biological complexity in this work may help to resolve questions about ‘units of selection’ and ‘major transitions in evolution’. Population genetics ©2018 Elsevier Ltd. All rights reserved. 1. Introduction Our adaptedness measure is assessed on individual organisms. The adaptedness of an entire population can be assessed by simply tak- Adaptation is a key concept for biological evolution ( Brandon, ing the mean of the proposed adaptedness measure over the pop- 2014; Reeve and Sherman, 1993; Williams, 1966 ). Indeed, the ulation. observation of adaptation was a central motivation for Darwin’s There have been some previous attempts to quantify adapted- development of the theory of evolution by natural selection ness ( Brandon, 2014; Reeve and Sherman, 1993 ). The most perti- ( Darwin, 1859 ). However, at present, scientific investigation of nent idea appears to be that of R. Brandon, who said that if we adaptation is impeded because evolutionary biologists have no sat- compare two organismal types, whether genotypes or phenotypes, isfactory quantitative way to describe the degree to which an or- then the organismal type associated with higher biological fitness ganism is adapted to its environment. (i.e., with higher reproductive success) is also the better adapted A satisfactory quantitative measure of adaptation would al- ( Brandon, 2014 ). If we have a set of many organismal types, Bran- low for investigation into how various environmental and ge- don’s proposal allows us to arrange them in order of adaptedness. netic variables affect the development and maintenance of adap- Of course, this ordering is not an intrinsic quality of the organis- tation ( Williams, 1966 ). Such a measure of adaptation can also mal types. Rather, it is a determined, in part, by the nature of the be expected to advance research on ‘units of selection’, and on environment within which the population lives. This is because, in closely-related issues associated with ‘major transitions in evolu- Brandon’s conception, adaptation is a function of the fitness of the tion’ ( Keller, 1999; Lewontin, 1970; Maynard Smith and Szathmáry, various possible organismal types, and fitness depends on environ- 1995; Williams, 1966 ). To a substantial extent, these two topics re- mental conditions. late to the degree to which biological adaptation occurs at the level Brandon’s proposal seems to accord with the natural-language of groups of organisms. Thus, a tool that allows for the quantitative meaning of adaptedness, and the work reported here is based upon measurement of adaptedness may well prove to be indispensable it. However, Brandon’s proposal does not provide a satisfactory for the solution of some of the deepest and most vexing problems quantitative measure, since it does not convey the degree to which in contemporary evolutionary biology. one type is more (or less) adapted than another. That is to say, it Here, we propose a quantitative measure of adaptation, and is merely an ‘ordinal measure’ of adaptedness ( Stevens, 1946 ). we test it using computer simulations of biological populations. Perhaps the reason that we have no satisfactory quantitative measure of adaptation is that such a measure may appear to be redundant. At first glance, it seems that the concept of biologi- ∗ Corresponding author. E-mail addresses: [email protected] (J.R. Peck), [email protected] (D. cal fitness already provides such a measure. After all, fitness is a Waxman). continuous variable, and, as Brandon suggests, if one type is fitter https://doi.org/10.1016/j.jtbi.2018.03.003 0022-5193/© 2018 Elsevier Ltd. All rights reserved. J.R. Peck, D. Waxman / Journal of Theoretical Biology 447 (2018) 190–198 191 than another, then it is also sensible to say that it is better adapted 2. A quantitative measure of adaptedness ( Brandon, 2014; Futuyma, 2013 ). However, some reflection reveals that fitness can easily fail as To begin our development of a quantitative measure of adapta- a measure of adaptation. To see why, let us begin by consider- tion, let us consider a species in which we can identify different ing the simple case of absolute fitness for a population of asexual types of individual. A particular organismal type may be defined organisms with discrete generations and with no ‘class structure’ by any aspect of an individual’s genotype or phenotype, or by a ( Grafen, 2006a, 2015 ). Here, the absolute fitness of a newborn indi- description that includes aspects of both genotype and phenotype. vidual is the expected number of offspring that the individual will We number these different organismal types 1 , 2 , 3 , . , , and contribute to the next generation. Thus, absolute fitness is equal to will refer to the collection of all types as the comparison set. expected reproductive success, and it takes into account both via- Let wi represent the relative fitness of newborn individuals that bility and fertility. That is to say, absolute fitness is affected both by have the ith organismal type. That is, wi represents the expected the probability that a newborn individual will survive to reproduc- reproductive success of type i newborns, divided by the expected tive age, and by the expected number of offspring that the new- reproductive success of newborn individuals that have an organ- born individual will have, if it survives. ismal type that confers the maximum-possible level of expected Let us assume, for the asexual organism under consideration, reproductive success (maximising over all members of the com- ≤ ≤ that the population size stays approximately constant from gen- parison set). Thus, 0 wi 1. eration to generation. Under this assumption, in a population like In light of the foregoing discussion, we propose the following the one just described, the mean value of absolute fitness must two requirements for a quantitative measure of adaptedness: be approximately equal to one. This is true regardless of whether (1) A quantitative measure of adaptedness should be an increas- all population members have the best-possible organismal type, ing function of relative fitness. That is, if, in a given environ- or if their organismal types are far from optimal. Accordingly, the ment, w > w , then type i is better adapted than type j in mean of absolute fitness for the population is independent of the i j that environment. appropriateness of the organismal types present in the population (2) The value of adaptedness, for a given organismal type, for the current environmental conditions. As such, absolute fitness should reflect how special that type is for a particular en- cannot be a good measure of adaptedness ( Barton, 2017 ). vironment. That is, it should indicate the extent to which One might think that the problems associated with using abso- the organismal type is unique with respect to how high its lute fitness to measure adaptedness could be eliminated by using relative fitness is in the environment. relative fitness instead. The relative fitness of a newborn individual is equal to the individual’s absolute fitness divided by the absolute We now propose a particular measure of adaptedness which is fitness of a newborn with some reference organismal type. Here, both reasonably simple, and which satisfies both of these require- we will take the reference type to be an organismal type with the ments. α maximum-possible value of absolute fitness. Unfortunately, relative Let i denote the adaptedness of type i. Let Q i represent the fitness also fails as a measure of adaptedness. The reason for this number of organismal types in the comparison set that have a is more subtle than in the case of absolute fitness. level of relative fitness that equals or exceeds the relative fitness of To understand the problems with using relative fitness as an organismal-type i in a given environment. Our measure of adapt- adaptedness measure, it is helpful to consider the case of purifying edness is selection that constrains a phenotypic trait to be close to a partic- ular optimum state. We might, for instance, imagine an organism αi = log 2 , (1) Q that is occasionally afflicted with a parasite. Assume that this or- i α ganism can produce a particular protein that inhibits the parasite where log2 denotes a logarithm to base 2. We will refer to i sim- ≤ ≤ and thus enhances relative fitness. Assume further that there is an ply as the adaptedness of type i.
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