Marshall Abrams
Associate Professor, Department of Philosophy,
University of Alabama at Birmingham

email: mabrams at uab dot edu, marshall at logical dot net
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(Most titles are links to PDFs.)

Please feel free to request a copy of any paper for which there's no PDF link.

"Natural Selection with Objective Imprecise Probability", Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications, eds. De Bock, de Campos, de Cooman, Queghebeur, Wheeler, Proceedings of Machine Learning Research, 2019.
(The linked version fixes some minor typos, but the pagination is same as in the published version.)
I argue that natural selection sometimes depends on objective imprecise probabilities.  I give a general argument for the existence of objective imprecise probabilities.  I then argue that natural selection, whether involving objective imprecise probabilities or not, would give rise to organisms whose behavior was imprecisely probabilistic, and that this would mean that other organisms' environments are imprecisely probabilistic.  Since natural selection can be influenced by the environment, it therefore sometimes depends on objective imprecise probability.  I explain why the absence of reports of objective imprecise probability in evolution is nevertheless unsurprising, and provide illustrations of ways to model natural selection with objective imprecise probabilities.

"Modeling the coevolution of religion and coordination in Balinese rice farming", for Beyond the Meme, eds. William C. Wimsatt and Alan C. Love, Minnesota Studies in Philosophy of Science, University of Minnesota Press, 2019.
Culture often seems to exhibit a high degree of harmony or coherence, exhibiting various sorts of ``fit" between cultural patterns in disparate domains.  In this paper, I explore one strategy for explaining some kinds of cultural coherence.  I show how a gradual process by which individuals with different cultural variants influence each other could lead to such coherence.  More specifically, I use computer simulations to model the spread of religious patterns specific to rice growing regions in southern Bali.  These are cultural patterns that exhibit a high degree of of coherence with Balinese beliefs about the natural world.  I show that the religious patterns could have spread through cultural transmission biased by variation in harvest success, under the influence of local social and ecological conditions.  The simulations also highlight the potential importance of what we might call ``population communication structure" in cultural transmission: In the simulations, spread of certain religious cultural patterns was likely only when communication from distant farming regions occurred infrequently.  This communication pattern allowed homogeneity in small regions to develop, creating pragmatic benefits that subsequently made religious practices in those regions attractive to individuals in other areas.  This ability of partial isolation to preserve variation and to support group-beneficial effects is well known from evolutionary biology.  There has previously been a great deal of research on group-level effects in cultural transmission as well as on effects of communication structure on cultural transmission.  There are other proposals according to which group-level effects have played an important role in the spread of certain religious practices The present research, however, illustrates a new way that explanations of harmonious cross-domain cultural patterns may be constrained by effects of communication structure.

"Probability and chance in mechanisms", in The Routledge Handbook of Mechanisms and Mechanical Philosophy, eds. Stuart Glennan and Phyllis Illari, Routledge 2017.
Though many authors recognize that mechanisms can involve stochasticity, there's been little discussion about the nature of the stochastic relationships in mechanisms.  I try to elucidate some issues that arise with stochastic mechanisms and propose new ways of thinking about them.  I'll focus mainly but not exclusively on what I call recurrent mechanisms--token mechanisms that operate in a similar manner at different times, or mechanism types that have many instances that operate in a similar manner.  Scientists' uses of "mechanism" seem to refer primarily to these mechanisms, which have also been the main focus of recent discussions of mechanistic explanation by philosophers. I begin in part 1 with a description of part of the mechanism of bacterial chemotaxis, which provides an illustration I use throughout the chapter, and then make some general remarks about roles for probability in mechanisms.  The rest of the chapter is somewhat arbitrarily divided into two sections (parts 2 and 3), focusing on metaphysical and epistemological issues.  Under metaphysics I include a brief general discussion of interpretations of probability, and a section in which I argue that those interpretations of probability relevant to the functioning of mechanisms are usually what I call causal probability interpretations.  I also suggest that some stochasticity in mechanisms might not involve probabilities per se, but could instead involve what are known as imprecise probabilities.  The epistemology section discusses various strategies for modeling probabilistic mechanisms, as well as evidence for probabilities in mechanisms.  I conclude in part 4 with a discussion of non-recurrent mechanisms.

"Probability and manipulation: Evolution and simulation in applied population genetics", Erkenntnis 80(3, supp), December 2015.
I define a concept of causal probability and apply it to questions about the role of probability in evolutionary processes.  Causal probability is defined in terms of manipulation of patterns in empirical outcomes by manipulating properties that realize objective probabilities.  The concept of causal probability allows us see how probabilities characterized by different interpretations of probability can share a similar causal character, and does so in such way as to allow new inferences about relationships between probabilities realized in different chance setups.  I clarify relations between probabilities and properties defined in terms of them, and argue that certain widespread uses of computer simulations in evolutionary biology show that many probabilities relevant to evolutionary outcomes are causal probabilities.  This supports the claim that higher-level properties such as biological fitness and processes such as natural selection are causal properties and processes, contrary to what some authors have argued.

"Coherence, Muller's ratchet, and the maintenance of culture". A slightly shorter, revised version appears in Philosophy of Science, 82(5), 2015.
I investigate the structure of an argument that culture cannot be maintained in a population if each individual acquires a given cultural variant from a single person.  I note two puzzling consequences of the argument: It appears to conflict with (a) many models of cultural transmission and (b) real-world cases of cultural transmission.  I resolve the first puzzle by showing that one of the models central to the argument is conceptually analogous and mathematically equivalent to one used to investigate the evolution of sexual reproduction.  This analogy clarifies what assumptions are crucial to the argument concerning cultural transmission.  I resolve the second puzzle by arguing that probabilistic models of epistemological coherence can be reinterpreted as models of mutual support between cultural variants.  I develop a model of cultural transmission illustrating this proposal.  I suggest that real-world cases that seem to conflict with the original argument may in fact be instances in which mutually supporting cultural variants are learned from different individuals.

"Cultural variant interaction in teaching and transmission", Behavioral and Brain Sciences 38, January 2015, e32 (2 pages), © 2014 Cambridge University Press.  (Commentary on Michelle Ann Kline's target article.)
Focusing on the way in which cultural variants affect other variants' probabilities of transmission in modeling and empirical work can enrich Kline's conceptualization of teaching. For example, the problem of communicating complex cumulative culture is an adaptive problem; teaching methods that manage transmission so that acquisition of some cultural variants increases the probability of acquiring others provide a partial solution.

"Equidynamics and reliable reasoning about frequencies", Metascience 24(2), 2015. Invited contribution to a book symposium on Michael Strevens' Tychomancy: Inferring Probability from Causal Structure, also including a review by Frederick Eberhardt and a reply by Strevens. The final publication is available at Springer via

"Maintenance of cultural diversity: Social roles, social networks, and cognitive networks", Behavioral and Brain Sciences (2014) 37, 254-255, © 2014 Cambridge University Press.  (In the PDF, my commentary appears immediately after Paul Smaldino's target article.)
Smaldino suggests that patterns that give rise to group-level cultural traits can also increase individual-level cultural diversity.  I distinguish social roles and related social network structures, and discuss ways in which each might maintain diversity.  I suggest that cognitive analogs of "cohesion", a property of networks which helps maintenance of diversity, might mediate the effects of social roles on diversity.

"Environmental grain, organism fitness, and type fitness", in Entangled Life: Organism and Environment in the Biological and Social Sciences; edited by Trevor Pearce, Gillian Barker, and Eric Desjardins; Springer 2014.
Natural selection is the result of organisms' interactions with their environment, but environments vary in space and time, sometimes in extreme ways.  Such variation is generally thought to play an important role in evolution by natural selection, maintaining genetic variation within and between populations, increasing the chance of speciation, selecting for plasticity of responses to the environment, and selecting for behaviors such as habitat selection and niche construction.  Are there different roles that environmental variation plays in natural selection?  When biologists make choices about how to divide up an environment for the sake of modeling or empirical research, are there any constraints on these choices?  Since diverse evolutionary models relativize fitnesses to component environments within a larger environment, it would be useful to understand when such practices capture real aspects of evolutionary processes, and when they count as mere modeling conveniences.  In this paper, I try to provide a general framework for thinking about how fitness and natural selection depend on environmental variation.  I'll give an account of how the roles of environmental conditions in natural selection differ depending the probability of being experienced repeatedly by organisms, and how environmental conditions combine probabilistically to help determine fitness.  My view has implications for what fitness is, and suggests that some authors have misconceived its nature.

"A Moderate role for cognitive models in agent-based modeling of cultural change", Complex Adaptive Systems Modeling 1(16), 2013.  (Please also see this correction.)
Purpose: Agent-based models are typically "simple-agent" models, in which agents behave according to simple rules, or "complex-agent" models which incorporate complex models of cognitive processes.  I argue that there is also an important role for agent-based computer models in which agents incorporate cognitive models of moderate complexity.  In particular, I argue that such models have the potential to bring insights from the humanistic study of culture into population-level modeling of cultural change.
Methods: I motivate my proposal in part by describing an agent-based modeling framework, POPCO, in which agents' communication of their simulated beliefs depends on a model of analogy processing implemented by artificial neural networks within each agent.  I use POPCO to model a hypothesis about causal relations between cultural patterns proposed by Peggy Sanday.
Results: In model 1, empirical patterns like those reported by Sanday emerge from the influence of analogies on agents' communication with each other.  Model 2 extends model 1 by allowing the components of a new analogy to diffuse through the population for reasons unrelated to later effects of the analogy.  This illustrates a process by which novel cultural features might arise.
Conclusions: The inclusion of relatively simple cognitive models in agents allows modeling population-level effects of inferential and cultural coherence relations, including symbolic cultural relationships.  I argue that such models of moderate complexity can illuminate various causal relationships involving cultural patterns and cognitive processes.

"Populations and pigeons: Prosaic pluralism about evolutionary causes", Studies in History and Philosophy of Biological and Biomedical Sciences 44, 2013, pp. 294-301.
Walsh (2007; 2010) was correct to conclude that the way a biological population is described should affect conclusions about whether natural selection occurs, but wrong to conclude that natural selection is therefore not a cause.  After providing a new argument that (Walsh, 2007) ignored crucial biological details, I give a biological illustration that motivates a fairly extreme dependence on description.  I argue that contrary to an implication of (Otsuka et al., 2011), biologists allow much flexibility in describing populations, as contemporary research on recent human evolution shows.  Properly understood, such description-dependence is consistent with descriptions capturing different causal relations involving the same population. I thus show that Walsh's (2007) arguments fail for reasons that have not previously been understood; I argue that Walsh's (2010) more recent "Sure Thing" argument fails for similar reasons.  The resulting view provides a new perspective on causation in evolutionary processes.

"Measured, modeled, and causal conceptions of fitness", Frontiers in Genetics, 3(196), 2012.
This paper proposes partial answers to the following questions:  In what senses can fitness differences plausibly be considered causes of evolution?  What relationships are there between fitness concepts used in empirical research, modeling, and abstract theoretical proposals?  How does the relevance of different fitness concepts depend on research questions and methodological constraints?  The paper develops a novel taxonomy of fitness concepts, beginning with type fitness (a property of a genotype or phenotype), token fitness (a property of a particular individual), and purely mathematical fitness.  Type fitness includes statistical type fitness, which can be measured from population data, and parametric type fitness, which is an underlying property estimated by statistical type fitnesses.  Token fitness includes measurable token fitness, which can be measured on an individual, and tendential token fitness, which is assumed to be an underlying property of the individual in its environmental circumstances.  Some of the paper's conclusions can be outlined as follows:  Claims that fitness differences do not cause evolution are reasonable when fitness is treated as statistical type fitness, measurable token fitness, or purely mathematical fitness.  Some of the ways in which statistical methods are used in population genetics suggest that what natural selection involves are differences in parametric type fitnesses.  Further, it's reasonable to think that differences in parametric type fitness can cause evolution.  Tendential token fitnesses, however, are not themselves sufficient for natural selection.  Though parametric type fitnesses are typically not directly measurable, they can be modeled with purely mathematical fitnesses and estimated by statistical type fitnesses, which in turn are defined in terms of measurable token fitnesses.  The paper clarifies the ways in which fitnesses depend on pragmatic choices made by researchers.

"Implications of use of Wright's FST for the role of probability and causation in evolution", Philosophy of Science, 79(5), December 2012 (© PSA).
Sewall Wright's Fst is a mathematical test widely used in empirical applications to characterize genetic and other differences between subpopulations, and to identify causes of those differences.  Cockerham and Weir's popular approach to statistical estimation of Fst is based on an assumption sometimes formulated as a claim that actual populations tested are sampled from an infinite set of (counterfactual) subpopulations, all derived from a single ancestral population. This provides a particularly interesting context for examining implications of assumptions about counterfactual populations, because of Fst's diverse empirical use and well-developed theory of estimation, because Cockerham and Weir's assumption is more substantive than many similar assumptions made in other contexts in population biology, and because in many applications, the counterfactual populations assumption plays an essential role in allowing Fst to distinguish the effects of drift from those of natural selection or migration.  I argue that Cockerham and Weir's approach to estimation of Fst implies that selection and drift are distinct causal factors in evolution, that evolutionary processes involve objective, causal probabilities, and that a natural interpretation of these probabilities as frequencies--suggested by the counterfactual populations assumption--would be incorrect.  The empirical success and theoretical justification of Cockerham and Weir's approach thereby provide support for a view of evolutionary theory as identifying evolutionary causes; this view is at odds with some recent philosophical accounts of evolutionary theory.

"Mechanistic probability", Synthese 187(2), 2012. The original publication is available at
I describe a realist, ontologically objective interpretation of probability, "far-flung frequency (FFF) mechanistic probability".  FFF mechanistic probability is defined in terms of facts about the causal structure of devices and certain sets of frequencies in the actual world.  Though defined partly in terms of frequencies, FFF mechanistic probability avoids many drawbacks of well-known frequency theories and helps causally explain stable frequencies, which will usually be close to the values of mechanistic probabilities.  I also argue that it's a virtue rather than a failing of FFF mechanistic probability that it does not define single-case chances, and compare some aspects of my interpretation to a recent interpretation proposed by Strevens. (Accepted October, 2010.)

"Mechanistic Social Probability: How Individual Choices and Varying Circumstances Produce Stable Social Patterns", in the Oxford Handbook of the Philosophy of the Social Sciences, ed. Harold Kincaid, Oxford University Press 2012.
Uncorrected proof, Replacements for figures 9.2 and 9.4
This paper applies ideas introduced in my "Mechanistic Probability" to probabilities in the social sciences.  Among other things, I argue that sensitive dependence of individual outcomes on vagaries of individual circumstances are the rule rather than the exception.  I argue that even though such idiosyncratic sequences of events appear peripheral to much work in the social sciences, their commonality is in fact what allows that work to proceed as it does.  More specifically, sensitive dependence of individual outcomes on circumstances helps produce enough stability in social phenomena that they can be studied at all, allowing claims about probabilities of social phenomena to succeed, and making sense of policy interventions.

"Natural selection at genomic regions associated with obesity and type-2 diabetes: East Asians and sub-Saharan Africans exhibit high levels of differentiation at type-2 diabetes regions", in Human Genetics 129(4), 2011. By Yann C. Klimentidis, Marshall Abrams, Jelai Wang, Jose R. Fernandez, and David B. Allison.
Different populations suffer from different rates of obesity and type-2 diabetes (T2D). Little is known about the genetic or adaptive component, if any, that underlies these differences. Given the cultural, geographic, and dietary variation that accumulated among humans over the last 60,000 years, we examined whether loci identified by genome-wide association studies for these traits have been subject to recent selection pressures. Using genome-wide SNP data on 938 individuals in 53 populations from the Human Genome Diversity Panel, we compare population differentiation and haplotype patterns at these loci to the rest of the genome. Using an "expanding window" approach (100 to 1,600 kb) for the individual loci as well as the loci as ensembles, we find a high degree of differentiation for the ensemble of T2D loci. This differentiation is most pronounced for East Asians and sub-Saharan Africans, suggesting that these groups experienced natural selection at loci associated with T2D. Haplotype analysis suggests an excess of obesity loci with evidence of recent positive selection among South Asians and Europeans, compared to sub-Saharan Africans and Native Americans. We also identify individual loci that may have been subjected to natural selection, such as the T2D locus, HHEX, which displays both elevated differentiation and extended haplotype homozygosity in comparisons of East Asians with other groups. Our findings suggest that there is an evolutionary genetic basis for population differences in these traits, and we have identified potential group-specific genetic risk factors.

"The unity of fitness", in Philosophy of Science, 76(5), December 2009. (© PSA)
It's been argued that biological fitness cannot uniformly be defined as expected number of offspring; different mathematical functions are needed to define fitness in different contexts.  Brandon (1990) argues that fitness therefore merely satisfies a common schema.  Other authors (Ariew and Lewontin, 2004; Krimbas, 2004) argue that no unified mathematical characterization of fitness is possible.  I focus on comparative fitness, explaining that it must be relativized to an evolutionary effect which fitness differences help to cause.  Thus relativized, comparative fitness can be given a unitary mathematical definition in terms of probabilities of producing offspring of various types and probabilities of producing various other effects.  Fitness will sometimes be defined in terms of probabilities of effects occurring over the long term, but I argue that these probabilities nevertheless concern effects occurring over the short term.

"Fitness 'kinematics': Biological function, altruism, and organism-environment development", Biology and Philosophy, 24(4), September 2009.
It's recently been argued that biological fitness can't change over the course of an organism's life as a result of organisms' behaviors.  However, some characterizations of biological function and biological altruism tacitly or explicitly assume that an effect of a trait can change an organism's fitness.  In the first part of the paper, I explain that the core idea of changing fitness can be understood in terms of conditional probabilities defined over sequences of events in an organism's life.  The result is a notion of "conditional fitness" which is static but which captures intuitions about apparent behavioral effects on fitness.  The second part of the paper investigates the possibility of providing a systematic foundation for conditional fitness in terms of spaces of sequences of states of an organism and its environment.  I argue that the resulting "organism-environment history conception" helps unify diverse biological perspectives, and may provide part of a metaphysics of natural selection.

"What determines biological fitness?  The problem of the reference environment", Synthese 166(1), January 2009. The original publication is available at
Organisms' environments are thought to play a fundamental role in determining their fitness and hence in natural selection.  Existing intuitive conceptions of environment are sufficient for biological practice.  I argue, however, that attempts to produce a general characterization of fitness and natural selection are incomplete without the help of general conceptions of what conditions are included in the environment.  Thus there is a "problem of the reference environment"--more particularly, problems of specifying principles which pick out those environmental conditions which determine fitness.  I distinguish various reference environment problems and propose solutions to some of them.  While there has been a limited amount of work on problems concerning what I call "subenvironments", there appears to be no earlier work on problems of what I call the "whole environment".  The first solution I propose for a whole environment problem specifies the overall environment for natural selection on a set of biological types present in a population over a specified period of time.  The second specifies an environment relevant to extinction of types in a population; this kind of environment is especially relevant to certain kinds of long-term evolution.

"How do natural selection and random drift interact?", Philosophy of Science, 74(5), December 2007 (© PSA)
One controversy about the existence of so called evolutionary forces such as natural selection and random genetic drift concerns the sense in which such "forces" can be said to interact.  In this paper I explain how natural selection and random drift can interact.  In particular, I show how population-level probabilities can be derived from individual-level probabilities, and explain the sense in which natural selection and drift are embodied in these population-level probabilities.  I argue that whatever causal character the individual-level probabilities have is then shared by the population-level probabilities, and that natural selection and random drift then have that same causal character.  Moreover, natural selection and drift can then be viewed as two aspects of probability distributions over frequencies in populations of organisms.  My characterization of population-level probabilities is largely neutral about what interpretation of probability is required, allowing my approach to support various positions on biological probabilities, including those which give biological probabilities one or another sort of causal character.

"Fitness and propensity's annulment?", Biology and Philosophy, 22(1), January 2007
Recent debate on the nature of probabilities in evolutionary biology has focused largely on the propensity interpretation of fitness, which defines fitness in terms of a conception of probability known as "propensity".  However, proponents of this conception of fitness have misconceived the role of probability in the constitution of fitness.  First, discussions of probability and fitness have almost always focused on organism effect probability, the probability that an organism and its environment cause effects.  I argue that much of the probability relevant to fitness must be organism circumstance probability, the probability that an organism encounters particular, detailed circumstances within an environment, circumstances which are not the organism's effects.  Second, I argue in favor of the view that propensities either don't exist or are not part of the basis of fitness, because they usually have values close to 0 or 1.  More generally, I try to show that it is possible to develop a clearer conception of the role of probability in biological processes than earlier discussions have allowed.

"Infinite populations and counterfactual frequencies in evolutionary theory", Studies in History and Philosophy of Biological and Biomedical Sciences, 37(2), June 2006
One finds intertwined with ideas at the core of evolutionary theory claims about frequencies in counterfactual and infinitely large populations of organisms, as well as in sets of populations of organisms.  One also finds claims about frequencies in counterfactual and infinitely large populations--of events--at the core of an answer to a question concerning the foundations of evolutionary theory.  The question is this: To what do the numerical probabilities found throughout evolutionary theory correspond?  The answer in question says that evolutionary probabilities are "hypothetical frequencies" (including what are sometimes called "long-run frequencies" and "long-run propensities").  In this paper, I review two arguments against hypothetical frequencies.  The arguments have implications for the interpretation of evolutionary probabilities, but more importantly, they seem to raise problems for biologists' claims about frequencies in counterfactual or infinite populations of organisms and sets of populations of organisms.  I argue that when properly understood, claims about frequencies in large and infinite populations of organisms and sets of populations are not threatened by the arguments.  Seeing why gives us a clearer understanding of the nature of counterfactual and infinite population claims and probability in evolutionary theory.

"Teleosemantics without natural selection", Biology and Philosophy 20(1), 2005
Ruth Millikan and others advocate theories which attempt to naturalize wide mental content (e.g. beliefs' truth conditions) in terms of function in the teleological sense, where a function is constituted in part by facts concerning past natural selection involving ancestors of a current entity.  I argue that it is a mistake to base content on selection.  Content should instead be based on functions which though historical, do not involve selection.  I sketch an account of such functions, which defines "function" in terms of changes in objective probabilities due to changes in ancestral traits.

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