Modeling in Theory and Practice

Anya Plutynskitt Univerllily of Pcnnsylvani:t

This paper use~ d number Df ~);al1lples of Jiven;e types and lundions or models in LO argue that the demarcation belw~'en theory and practice. or "theory model" and "dala model." is often dini,,;ult 10 make. II is Shll\Vll IlOw both mathematical and laboratory model~ funclion a,; plausibility arguments. e1'.islem:e proofs. and refutations in the investigation of que81ions about the pattern and process of eVolutionary history. J consider the consequences of this fOf the semantic approach to theories and Iho;:ory confinnation. The paper attempts to reconcile the insights of both cnlies and advocates I)f Ihe semamic approach to theories.

1. Introduction. In lAws and Symmetry, van Fraassen comments that phi­ losophers of science have focused on the product of science. !he theory, to the exclusion of the "aim, conditions. and processes of production" (1989, 189). This paper aims to fill this lacuna. especially with regard to evolutionary biology. In particular, I take a closer look at the use of mod­ cis in the practice of evolutionary biology. The product/process analogy assimilates science to industry, implying that the aim of science is the production of theories, and that a strict demarcation can be made between the product, theories. and the process, scientific practice. One of the aims of this paper is 10 challenge this strict demarcation. I argue that the diverse types and functions of models and modeling in biology are not easily categorized as either product or process. A further aim is to consider the consequences of blurring the line of demarcation between theory and prac­ tice for the semantic approach to scientific theories.

tSend requests for reprints to the author. Deparlment of Philosophy. University of Pennsylvania. Philadelphia. PA 19104; email;p!U\ynski@\:aTlhlink.net. tl would like to thank Dr. Gary Hallleld. Dr. Paul Sniegowski, Dr. Warren Ewcns, Dr. David Magnus, and an anonymous reviewer for commenting on earlier drafts of this paper.

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S225 5226 ANYA PLUTYNSKI

The classic scman tic view of van Franssen (1980, 1989) characterizes theories as fa milies of models. A theory is empirically adequate if the empirical substructures of one's "theory model"' are isomorphic or struc­ turally idcnlicallO one's "data modeL" So. confirmation is essentially fit between model and data. As I will demonstrate below. co nfi rmation as identity of structure between theory and data model is inadequate 10 de­ scribe the ways in which many models afC deployed in evolutionary bi­ ology. This paper thus rollows the route of Downes ( 1992) and Griesemer ( 1990, 1991). who have each advocated a more "liberal" or "extended" semantic view ofthenrics. They question whether isomorphism is the right way \0 conceive of the relation between theory and world , and whether the metamathcmatical senSe of model adopted by the semantic view can serve as a template for all models in science. Beally (198 1). Lloyd ( 1988). and Thompson (1985. 1989) have each appropriated the seman ti c view as a way to describe the structure of evo­ lutionary theory. They argue that it resoh'es many of the problems that arise for evolutionary theory on the received, or ';syntactic" view. For instance. they cla im {hat the crilicism (h at evolutionary theory is not a scientific theory beclilise of its alleged lack of laws is rendered moot by the semantic view. However. Ercshefsky (1991) and Slocp and van def Steen (1987) have argued that the semantic view faces some of the same difficulties as the received view. Ereshefsky argues that the semantic ap­ proach cannot dispense with l<,\w5. Moreover. he points out that since evolutionary explanations oft en employ informlltion rrom H number Dr subdisciplines within evolutionary biology, giving a formal account of their structure is forbiddingly comple,'(, whether one adopts the semantic or the syn tactic approach. In other words, the complex rela tion between theory and world is no less complex once one substitutes models and em­ beddability requirements for axioms and partial interpretation rules. Like Ere5hefsky, I am skeptical th

2. On tbe Semantic Picture of Confi rmation. E. Lloyd (198B ) disc\J sses three forms of confirmat ion: fit betwccn some model and data. independent testing of some aspect of a model. and va riety of evidence. Each of these types of confirmation. she argues. is a variant of Ihe sa me genera! type: demonstfllt ion that a natural system is isomorphic in certain respects to a model. While I think that Ll oyd's account is the best we have yet of how evolutionary hypotheses are co nfi rmed, I wish \0 suggesl the follow ing emendations of her view . Isomorphism, whi le it may be an ideal relation between modcl and world, is often neither hoped for nor possible. in evolutionary biology. Lloyd mentions this poi nt in a footnote (1988, 168). but I think that this issue calls for grealer elaboration. Mlllly models arc simulations of natural systems. While one hopes to incorporate as much realism as possible in such cases. laboratory or computer sim ulat ions will ncccssarily b(! ve ry dilTercnt from natural systems. In fac i. it is exactly when a process in naturc is 100 complica tcd to track. or wo uld tClke too long to obscn 'c. that such sim ulations are appropriate. Biologists do not expect sllch simula­ tions \0 be isomorphic 10 natural systems. Rather, sim Ul ation models serve in both an explo ratory and argumentative role. A simu lation can yield S228 Ar-.'"YA PLVTYNSK I

new empirical resuhs, or suggest thaI one or another factor in the evolu­ tionary process is more or less significll nt. I will discll Ss an elegant example below of a simulation of 20,000 generations of evolution using £. coli as an experimental system. Modeling in biology often has the role of demonstrating the plausibi lity of some process or mechanism. While Lloyd mentions this point in her discussion of Beckner, I believe that this important function of modeling in biology gels left to one side in her subsequent discussion. Sometimes. the question is not whether one can gene rate a model whose assumptions are we ll confirmed Of whose results have a good fit with empiric,11 data, but whether one can generate a model at al! that is j ust robust enough to give LIS good reason to c)(pect that some process could occur in nature. Success at constructing such a model can serve as an e)( lstence proof. Rice and Salt 's ( 1988) model of in sympatry is one example (see below). Lloyd devotes some discussion to the problem of counterfactual as­ sumptions or idealizations-we afe warned to be skeptical of models that employ such assumptions. I agree. However. I would argue that there arc some cases where this skepticism oUgh t to be suspended. There are an enormo us number of factors at work in any evol ut ionary process. To incorporate all these factors in a model would quickly make our mathe­ matics intractable. Counterfactual assumptions are thus par for the course in modeli ng evolutionary dynamics. Infi nite population size, haploidy. or random mating, are often unavoidable. ifcounterfactua1. assumptions one needs to make in order to answer specific evolutionary q uestions. Pro­ ponents of the semantic view argue thai models are abstract and often involve ides uming an in fin ite populatio n size or random ma ting is appropriate: it depends both on tbe context and the ri sk one is wi lling to assume. This may seem counteri ntui tive: how can models serve as plausi bility argu ments when the assumptions oftbe model MODELlNG EVOLUTION IN THEOR Y AND PRACTICE S229 are so im plausible? For example. infinite population size is sim ply an im­ possibility. Oughtn't we regard any model assuming this to be suspect? Certainly. counterfactual assumptions may give us reason to doubt the plausibili ty of a model argument. However, in many cases, models that arc si mply false can often be as effective. if not more effective, in furthering theory as those models tbat are true of or similar 10 the world are (Wimsatt 1987). If we were to reject any model argument with counterfactual as­ sumptions. then we would have to side wit h Pearson and Punnett in their initi al rejection of Fisher"s (19 18) paper, where he argued fo r the compat­ ibility ofbiomelry and a gradualist picture of evoluti on with the principles of Mendeli sm. Coun terfactual assumptions are not always rcason to reo gard a model as suspect. In some cases, a model that employs counterfac­ tual assumptions can serve as a compelling arg ument, either for or against the possibilit y of some rela tion, pattern, or process in nature. 1 will give an example below from a debate over the founder model of speciation. According to the classic semantic view, mathematical models are ab­ stract representations of real systems. Laboratory experiments will serve to generate data models. which are then checked against one's theory model. This top-down picture takes mathematical models to be the core expression of fheory, and laboratory models 10 be test ing grounds fo r one's theoretical hypotheses. In the practice of science, this hierarchy is often reversed. Mathematical models. often serve as tools for investigation: the investigative aspect of science is not confined to the lab or field. Math­ ematical or compuler simulation models can function as tests of theoreti· cal questions in the same way as do laboratory experiments. Moreover, there is an interesting division of labor in terms of the scope of qm:stion capable of being investigated in mathematical versus laboratory modeling. Mathematical models can serve to answer questions that cannot be ad­ dressed in a laboratory model. and vice versa. In the examples discussed below, mathematical and material models scrve as independent, comple­ mentary lines of evidence in addressing questions about the pattern and process of evolulio ll, rather than steps in a hierarchy between theory and world.

3, Some Models of Models. Now I will consider three examples of modeling which illustrate the instrumental and argumentative role of diverse types of models in biology. J. Griesemer (1990) has recently brought attention to the role of material models in evolutionary biology. Richard Lenski conducted an experiment using E. coli to investigale the dynamics of evo­ lution over many generations. E. coli have a generation time of about twenty minutes under optimal conditions, yielding many generations a day, and can be transferred in to fresh medium and frozen at - 80°C with- S230 ANYA PLUTYNSKI out damage. T his makes them analogolLs to " machines for time travel" for the st udy of processes of evolutionary change (Lenski and Travisa no 1994). Lenski and T ravisano describe slL ch a system as ro llows: Imagine that you have discove red a well-preserved and clearly strat­ ified foss il bed that provides a record or evolution ex tending thou­ sands of generations for the particular organism that you study .... Imagine that you could resurrect these organisms and reconstruct their environment exactly as it was during thousands of generations preserved in the fossil bcd .... You could travel back in time and manipulate populations by altering their evolutionary history or their environment. and then return to the present to examine the effect of these condi tions on the dyna mics of and diversification. (1994,6808- 6809) Lcnski and others have been conducting a long-term evolution experiment on twelve replicate populations of E. c:uli cultu re with frozen records of approximately 20.000 generations. Fitness (measured as the ratio of the number of doublings of derived vs. anceSlOr strains) of twelve re plicate populations increased by approx.imatcly 45%. with most improvement taking place in the first 2000 generations. The trajectory of mean fitness for the twelve strains approximates an asym ptotic curve, suggesting that there arc constraints on indefllli te improvement. The system allows one 10 investigate the dyn

'"w .. , '"z c:~ w " > ":'i " w .. , '" " , 2000 '000 8000 8000 1000:1 riME (generotions)

Figu re I. Lenski et nl 's (1994) lraj,,;-tories of mean fitness relative tl) the an{.'eSlor in 12 replicate populations of £ ('0/' during 10.000 gene ra tions of evolution in the 1:lboml0ry,

Their long-term experiment was able 10 generate sever:;!1 reproductively isola ted strains or Drosophila through sympalric means, via disruptive se· lection by habital spcciali7.a tion. They constructed a habitat maze where Drosophila chose selective habitats Ih ;:lt differed with respect 10 light. grav­ ity. and choice of chemical vapors. Positive assortative mating evolved as a correlated response to Ihe disruptively selecti ve character. in this case. prererence fo r different habitats within the maze, Key to this ex periment is that selection al one was able to generate isolated strains. There were no population bOl1lenecks or isolation; each entire generat ion of flie s rrom the several habitats were ret urned together to the begin ning of the maze and aUowed to choose their habitats, This is only onc among many experi ments with laboratory populations of Drosophila thaI have been u!)Cd 10 investigatc different hy pot heses about speciation. There has been at least forty years or work on speciation in the lab. Drosophila are the organism or choice, and there have \x.-cn tests orsclectivc divergence, rounder effect. and s)'mplm y (ror a review, sec Rice and Hoslen 1993). Rice and Salt's work challenges what has been the received vi ew among evolutionary biologists. namely that geogruphical or spatial isolation is a crucial condition for speciation. and lhat directional selection alone cannot generate new species. The mai nstream view for ap­ proximately fifty years among evolutionary biologists is that speciation in allopatry (geograph ic

Figure 2. Rice and Salt's (1988) Dro.lIJl'hi/rI hubitat ma1.e for spedation in sympatry. Po­ sitions of the sek-.: th'e habitl!1S are iDdica l ~d by number (1- 8).

Several questions arise ou t of th is material modeling of the speciation process. For exa mple. how re levant are laboratory ex periments to speci­ ation in the wild? Some might question the relevance of Rice and Salt's experiment to natural speciation processes. Others claim that laboratory populations are fun damentall y different from natural populations, and therefore laboratory experiments and breeding experimcnts arc irrelevant to the problcm of how new species arise. This argument is in the tradition of naturalists such as Jordon and Kellogg (1907), who claimed that no product of the botanical ga rden as a result of breeding experiments cou ld count as a c...se of speciation, Addi tio nally, how are we to evaluate the results of these speciation experiments? How isolated is 'reproductively isolated'? Must onc show MODELING EVOLUTION IN THEORY AND PRACTICE S233 complete reproductive incompatibility? Is lowered viability and fe rtility in anempted crossing surticient? When arc two organisms truly new species? Rice and Salt showed that their sympatry experiment yielded populations with lowered viability and assortative mating: Is this a speciation event? Clearly, inferences from the laboratory to the wild are not decisive. Laboratory work is not meant to reproduce all fa ctors relevant in nature. Rather, one or several parameters-e.g .. selection by habitat type. drift, etc.-can be tested either individually or in combination or competition with one another. Models such as Rice and Sal t's arc not decisive tests so much as su pplementary lines of evidence. The standard top-down pict ure of theoretical models being confim1 ed by laboratory or fieldwo rk is not appropria te here. The theory of sympatry is not confirmed by identifyi ng isomorphisms between the laboratory data and the theory model. Rather, the very fact that Rice and Salt were successful at construct ing simulation of speciation in sympatry serves as an argument for its occurri ng in nature. In evolutionary biology, often simply demonst ra ting the possibili ty of some process in the lab is a persuasive case for its occurrence in nature. In this case, lowe red viability in crosses of these lab strains is an a rgument fo r the possibility of sympatry in the wild . Multiple lines of evidence from multiple different subdisciplines within evolutionary biology bear on the question of how important fo r instance, drift is in evolution, or wh ich mode of speciation is possible or prevalent in nature. Evolutionary questions are almost never decided by single "cru­ cial experiments," Biologists construct models such as Lenski's and Rice and Salt's not to p ro~'e the relative significance of one or another fac tor in the evol utionary process, but to provide a plausibility argument In this sense, a laboratory experiment functions in the same way as some theo­ retical or mathematical models in population genetics. Mathematica l models can serve as argumen ts as well. Moreover, mathematical models can answer questions that laboratory models cannot. For example, another line of evidence on the role of founder effect in specia tion is theoretical population genetic models. Two self-professed neo-Darwinians, Barton and Charlesworth (1984), devoted a review paper to theoretical objections to the founder model. They concluded that al­ though founder effects may cause speciation. they are onl y a very rare extreme along a continuous range of possibilities. Complete geographic isolation is unnecessa ry, and selection can brcilk up coadapted systems of alleles. In particular, Ihcy question the "genetic revolution" as a mecha­ nism of speciation, and argue that speciation is more likel y the result of small steps than a single foun der event. While the theoretical arguments are too mathematically complex to reproduce here. Barton and Charlesworth show how unde r both single­ and multi-locus models. reduction in variability induced by drift reduces the chances of peak shifts, i.e. , the transition from one equilibrium undcr 5234 ANYA PLUTYNSKI selection to another. Select ion requires variability to act upon. Loss of heterozygosity during a founder event reduces that vuriabil it y. Mayr (1942. 1963, 1970) argued that reduction in population size was key to speciation. in that such (I reduction would entail an exposure of new gene combinations because of a loss of heterozygosity. The resulting transfor­ mati on of the genetic composition or a population has been called a "ge­ netic revolution:' Barton and Charlesworth co un ter that the loss of het­ erozygosity can occur only in populations that grow so slowl y that they are morc likely to die out than evolve into new species. They also explain that the probability of peak shifts-moving from one peak on Wright's adaptive landscape to ano\hcr- dccrcflses exponentiall y with the size of each step. In other wo rds, the probability that a founder population will undergo a rapid transition to a new selective equilibrium is very low. Re· productive isolation is more likely to evolve in fI series of small steps than in a single " genetic revolution ." Their rna tllematical mode! serves as an argument against the fo under cITect. or more specifically, "genet ic revo· lutions" playing a rolc in speciation. One might argue that the classic semantic view is still appropriate for these e:'l:amples. Fo r instance, the habitat maze is a structure that is true for, or satisfi es, the sentences or the theory or sympatry. However, the useru lness or this metamathematical sense of model is stretched to the limit when it comes to describing how such models function in the practice or evolutionary bio logy. Models such as Rice and Salt's habitat maze, or Ban on and Charlesworth's mathematical model or peak shirts, arc not confi rmations, nor are they theoretical models that await confi rmation. The laboratory model is a caricalllre or what actua ll y goes on in natural populations. Laboratory models such as Rice a nd Salt's runction simu l­ taneously as:I tool ror invesliga tion :lnd a test of the plausibility or one mechanism of speciation. lrsympalry were possible, how would it work? And. can we make it work? Barton and Ch:lrlesworth's model runctions as an argument. not a theory that awaits testing in the lab or fi eld. Multiple different types or models which jointly establish the plausibility or the sa me mechan ism yield a consilicnce or induction in favor or it s existcnce in nature. Confirmation in historical disciplines such as evolutionary bi­ ology is ra rely a mailer or si mply checking the fi t between model and world. Because we can rarely see evolution in action, evolutionary biolo­ gists usc models as tools for investigation, cxistence proors, and arguments ror or against the plausibility of one or another mechanism at work in nature.

4. Conclusion, Biologists more often than not resort to laborator}' si mu· lations and idealized mathematical models as sources or plausibility ar­ guments. Moreover, models and modding can have multi ple, diverse runc- MODELI NG EVOLUTION IN T HI;ORY AND PRACTICE S235 tions, wh ich a re not easily characterized as eit her theory making or confirm ation. Models can yield new q uestions or empirical phenomena not predicted by theory, serve as existence proofs, or as arguments for or against the significance of olle or another mechanism at work in na ture. While the appropriation of fo rmal semantics wa s a helpful way \0 get out of the rut of viewing theories as sets of axioms, the semant' ic view still ca rries the taint of the discovery-justification di vide. In evolutionary bi­ ology, discovery and j ustifica tion, a long with theory and practice, are not so easily demarcated. Models and modeling are not ancillary to theory, but can function as independent tools for investiga tion.

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