Convincing disputes about explanatory reductionism in the philosophy of biology require a clear and precise understanding of what a reductive explanation in biology is. The central aim of this book is to provide such an account by revealing the features that determine the reductive character of a biological explanation. Chapters I-IV provide the ground, on which I can then, in Chapter V, develop my own account of explanatory reduction in biology: Chapter I reveals the meta-philosophical assumptions that underlie my analysis (...) of reduction, Chapter II introduces the previous debate about reduction in the philosophy of biology by pointing out the most crucial lessons one should learn from this debate, Chapter III critically discusses the two perspectives on explanatory reduction that have been proposed in the philosophy of biology so far, and Chapter IV clarifies in what ways the issue of reduction is entangled with the issue of explanation. In Chapter V I present my own account of explanatory reduction. My main claim is that reductive explanations in the biological sciences possess three main characteristics: they explain the behavior of a biological system S, first, exclusively in terms of factors that are located on a lower level of organization than S, second, by focusing on factors that are internal to S , and third, by describing the genuine parts of S only as “parts in isolation”. This account is ontic because it traces the reductivity of an explanation back to certain relations that exist in the world. (shrink)

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. In this paper, we present a model of a new type of intertheoretic relation, called 'Montague Reduction', which is assumed in Montague's framework for the analysis and interpretation of natural language syntax. To motivate the adoption of our new model, we show that this model extends (...) the scope of application of the Nagelian (or related) models, and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

There are two ways evolution by natural selection is conceptualized in the literature. One provides a ‘recipe’ for ENS incorporating three ingredients: variation, differences in fitness, and heritability. The other provides formal equations of evolutionary change and partitions out selection from other causes of evolutionary changes such as transmission biases or drift. When comparing the two approaches there seems to be a tension around the concept of heritability. A recent claim has been made that the recipe approach is flawed and (...) should be abandoned. In this article, I show that the tension is only a superficial one. If one uses a concept of heritability strictly in line with the formal equations of evolutionary change, the recipe approach keeps its validity and generality. To demonstrate that the intuitive concept of heritability is not a general one, I use one formulation of the Price equation formulated by Okasha, show that the concept of heritability in his formulation incorporates both the intuitive notion of heritability as a measure of similarity between parent and offspring characters, and a measure of persistence. I advocate for persistence to be incorporated in the concept of heritability used in recipes for ENS in the same way heredity is, show that this is readily attainable and thereby dissolve any point of tension concerning heritability between the recipe and the analytical approach to ENS. 1 Introduction2 Heritability in the Price Equation2.1 Different approaches to heredity and heritability2.2 Heritability: From recipes to the Price equation3 A Problem for the Recipes?4 Reinterpreting Heritability for Recipes5 Conclusion Appendix. (shrink)

It is illegitimate to read any ontology about "race" off of biological theory or data. Indeed, the technical meaning of "genetic variation" is fluid, and there is no single theoretical agreed-upon criterion for defining and distinguishing populations (or groups or clusters) given a particular set of genetic variation data. Thus, by analyzing three formal senses of "genetic variation"—diversity, differentiation, and heterozygosity—we argue that the use of biological theory for making epistemic claims about "race" can only seem plausible when it relies (...) on the user’s own assumptions about race; the move from biological measures to claims about “race” inevitably amounts to a pernicious reification. We also excavate assumptions in the history of the technical discourse over the concept of "race" (e.g., Livingstone's and Dobzhansky's 1962 exchange, Edwards' 2003 response to Lewontin 1972, as well as contemporary discussions of cladistic "race", and "races" as clusters). We show that claims about the existence (or non-existence) of "race" are underdetermined by biological facts, methods, and theories. Biological theory does not force the concept of "race" upon us; our social discourse, social ontology, and social expectations do. We become prisoners of our abstractions at our own hands, and at our own expense. (shrink)

The classical holism-reductionism debate, which has been of major importance to the development of ecological theory and methodology, is an epistemological patchwork. At any moment, there is a risk of it slipping into an incoherent, chaotic Tower of Babel. Yet philosophy, like the sciences, requires that words and their correlative concepts be used rigorously and univocally. The prevalent use of everyday language in the holism-reductionism issue may give a false impression regarding its underlying clarity and coherence. In reality, the conceptual (...) categories underlying the debate have yet to be accurately defined and consistently used. There is a need to map out a clear conceptual, logical and epistemological framework. To this end, we propose a minimalist epistemological foundation. The issue is easier to grasp if we keep in mind that holism generally represents the ontological background of emergentism, but does not necessarily coincide with it. We therefore speak in very loose terms of the “holism-reductionism” debate, although it would really be better characterised by the terms emergentism and reductionism. The confrontation between these antagonistic paradigms unfolds at various semantic and operational levels. In definitional terms, there is not just emergentism and reductionism, but various kinds of emergentisms and reductionisms. (shrink)

I adopt a cladistic view of species, and explore the possibility that there exists an equally valuable cladistic view of organismic traits. This suggestion seems to run counter to the stress on functional views of biological traits in recent work in philosophy and psychology. I show how the tension between these two views can be defused with a multilevel view of biological explanation. Despite the attractions of this compromise, I conclude that we must reject it, and adopt an essentially cladistic (...) conception of biological traits. (shrink)

Research on the human microbiome has gen- erated a staggering amount of sequence data, revealing variation in microbial diversity at the community, species (or phylotype), and genomic levels. In order to make this complexity more manageable and easier to interpret, new units—the metagenome, core microbiome, and entero- type—have been introduced in the scientific literature. Here, I argue that analytical tools and exploratory statisti- cal methods, coupled with a translational imperative, are the primary drivers of this new ontology. By reducing the (...) dimensionality of variation in the human microbiome, these new units render it more tractable and easier to interpret, and hence serve an important heuristic role. Nonetheless, there are several reasons to be cautious about these new categories prematurely ‘‘hardening’’ into natural units: a lack of constraints on what can be sequenced metagenomically, freedom of choice in taxonomic level in defining a ‘‘core microbiome,’’ typological framing of some of the concepts, and possible reification of statistical constructs. Finally, lessons from the Human Genome Project have led to a translational imperative: a drive to derive results from the exploration of microbiome variation that can help to articulate the emerging paradigm of per- sonalized genomic medicine (PGM). There is a tension between the typologizing inherent in much of this research and the personal in PGM. (shrink)

Philosophy can shed light on mathematical modeling and the juxtaposition of modeling and empirical data. This paper explores three philosophical traditions of the structure of scientific theory—Syntactic, Semantic, and Pragmatic—to show that each illuminates mathematical modeling. The Pragmatic View identifies four critical functions of mathematical modeling: (1) unification of both models and data, (2) model fitting to data, (3) mechanism identification accounting for observation, and (4) prediction of future observations. Such facets are explored using a recent exchange between two groups (...) of mathematical modelers in plant biology. Scientific debate can arise from different modeling philosophies. (shrink)

For evolution by natural selection to occur it is classically admitted that the three ingredients of variation, difference in fitness and heredity are necessary and sufficient. In this paper, I show using simple individual-based models, that evolution by natural selection can occur in populations of entities in which neither heredity nor reproduction are present. Furthermore, I demonstrate by complexifying these models that both reproduction and heredity are predictable Darwinian products (i.e. complex adaptations) of populations initially lacking these two properties but (...) in which new variation is introduced via mutations. Later on, I show that replicators are not necessary for evolution by natural selection, but rather the ultimate product of such processes of adaptation. Finally, I assess the value of these models in three relevant domains for Darwinian evolution. (shrink)

When data are limited, simple models of complex ecological systems tend to wind up closer to the truth than more complex models of the same systems. This greater proximity to the truth, or verisimilitude, leads to greater predictive success. When more data are available, the advantage of simplicity decreases, and more complex models may gain the upper hand. In ecology, holistic models are usually simpler than reductionistic models. Thus, when data are limited, holistic models have an advantage over reductionistic models, (...) with respect to verisimilitude and predictive success. I illustrate these points with models designed to explain and predict the numbers of species on islands. (shrink)

ABSTRACTIn Darwinian Population and Natural Selection, Peter Godfrey-Smith brought the topic of natural selection back to the forefront of philosophy of biology, highlighting different issues surro...

Intertheoretic relations are an important topic in the philosophy of science. However, since their classical discussion by Ernest Nagel, such relations have mostly been restricted to relations between pairs of theories in the natural sciences. This paper presents a case study of a new type of intertheoretic relation that is inspired by Montague’s analysis of the linguistic syntax-semantics relation. The paper develops a simple model of this relation. To motivate the adoption of our new model, we show that this model (...) extends the scope of application of the Nagelian models and that it shares the epistemological advantages of the Nagelian model. The latter is achieved in a Bayesian framework. (shrink)

The Macarthur-Wilson equilibrium theory of island biogeography has had a contradictory role in ecology. As a lasting contribution, the theory has created a new way of viewing insular environments as dynamical systems. On the other hand, many of the applications of the theory have reduced to mere unimaginative curve-fitting. I analyze this paradox in semiotic terms: the theory was mainly equated with the simple species-area relationship which became a signifier of interesting island ecology. The theory is, however, better viewed as (...) a theoretical framework that suggests specific hypotheses on the ecology of colonization of insular environments. This paradox is inherent in the use of simplifying analytic models. Analytic models are necessary and fruitful in the work of ecologists, but they ought to be supplemented with a broader, pluralistic appreciation of the role of theories in general. (shrink)

Ecology is the study of the interactions of organisms and their environments. The methods of ecology fall roughly into three categories: descriptive surveys of patterns of species and resource distribution and abundance, theoretical modeling, and experimental manipulations. Ecological systems are “open” systems, and patterns and processes are products of a huge number of interacting forces. Ecology and the environmental sciences have made enormous advances since the mid-twentieth century in the understanding of ecological systems, as well as in the human impact (...) on the environment. Theory in ecology usually centers on the development of models. Environmental outcomes are uncertain and when making decisions under uncertainty, there are a variety of options available. One option is to carry out a cost benefit analysis based upon expected utilities and other is to adopt the precautionary principle. Uncertainty and under determination of theory by evidence is a fact of life in science. (shrink)

Holism and reductionism are usually seen as opposite and mutually exclusive approaches to nature. Recently, some have come to see them as complementary rather than mutually exclusive. In this book I have argued that, even stronger, they should be seen as mutually dependent and co-operating research programmes. I have discussed holism and reductionism in biology in general and in ecology in particular. After an introductory chapter I have provided an overview of holistic and reductionistic positions in biology, and of the (...) reduction problems to which they relate. I have argued that it is extremely important to distinguish between ontological, epistemological and methodological aspects of these problems. The overview has shown that there are actually several approaches to reduction problems in biology, which can be characterized as more or less radically or moderately holistic or reductionistic. It has shown also that there are three major ’contradistinctions’ between holism and reductionism in biology, to wit the doctrine of emergence versus the reduction thesis; functional explanations versus causal explanations; and phenomenology versus mechanicism. In later chapters I have shown that these ’contradistinctions’ are not really contradistinctions at all. In the next chapters I have discussed the terms ’reduce’ and ’reduction’ in science. In chapter 3 I have discussed the reduction of laws and theories. I have shown that there are many different types of reduction depending on the auxiliary hypotheses that are being used in addition to the reducing theory: approximation-, aggregation, correlation and/or identification-hypotheses. The distinctions between these types has later, in chapter 5, proved to be of great importance in defining the concept of ’emergence’. The major conclusion of chapter 3 was that reduction is an epistemological issue, pertaining to logical relations between statements or systems of statements. It should not be confused, therefore, with ’ontological reduction’, certainly not in one of its ordinary senses, such as diminishing, devaluating or the like. Scientific reductions are, with the exception of instrumentalistic reductions, kinds of explanation, and, moreover, non-eliminative kinds of explanation. This means that a reduced law or theory is not eliminated by the reducing theory but rather consolidated or even reinforced. The ontology of the reduced law or theory is thereby also being consolidated. In chapter 4 I have argued that the same holds for reductions of concepts. Concept reductions are supposed to be accomplished by means of so-called ontological identity relations, which are in turn supposed to connect terms in the law or theory to be reduced, which do not occur in the reducing theory, with theoretical terms of the reducing theory. Because they are called ontological identity relations, several philosophers have thought that concept reductions imply some form of ontological reduction. And because they often occur in the context of micro-reductions, some have even thought that concept reductions are themselves micro-reductions. As a result, the idea has arisen that ontological identity relations are connections between macro-concepts and micro-concepts. However, concept reductions by means of ontological identity relations cannot be micro-reductions, because micro-reduction is, by definition, reduction with an aggregation step. Moreover, ontological identity relations are relations between different representations of and the same type of thing or attribute. That is, they express different epistemological sides of the same ontological coin. Therefore, concept reductions cannot be considered ontological reductions either, certainly not in the ordinary sense of diminishing, devaluating or the like. Thus, concept reduction is, like law or theory reduction, an epistemological issue: it pertains to relations between, in this case, different concepts or representations of one and the same type of thing or attribute. ’Ontological reduction’, then, may, in the context of scientific reductions, actually be considered a contradiction of terms. In chapter 5 I have linked this conclusion to the emergence thesis and to the alleged contradistinction between this thesis and the reduction thesis. I have shown that the doctrine of emergence actually consists of two separate claims, namely an ontological thesis stating that a whole has emergent properties which the component parts do not possess, neither separately nor in other partial combinations; and an epistemological thesis stating that emergent properties of wholes are ’in principle’ irreducible. I have argued that the first claim may be regarded as a valid, universal thesis about relations between properties of wholes and properties of parts, but that the second claim is untenable. I have discussed many emergent properties of wholes, biological as well as physico-chemical, that have proved to be explainable in terms of micro-theories about the component parts and auxiliary hypotheses. Once again, however, it is important to realize that reduction is an epistemological issue, whereas emergence, in the sense of thesis, is an ontological one. It is not ’wholes’ or ’emergent properties of wholes’ that are being reduced but statements about them. Reduction is a kind of explanation, not of explaining-away. Thus, it leaves the ontology of whatever is reduced fully intact. I have developed a new definition of the term ’emergence’ which expresses emergence in terms of the auxiliary hypotheses that may be used in reductions, in particular aggregation-, correlation- and identification-hypotheses. This has even lead to two very remarkable conclusions. First, emergence may be considered the opposite of ontological identity. And second, if there were no emergence, there wouldn’t be any reductions either. to reduce.) In this respect, therefore, there is absolutely no contradistinction between holism and reductionism. On these grounds I have introduced my thesis that holism and reductionism should rather be seen as mutually dependent, and hence co-operating, research programmes than as conflicting views of nature or of relations between sciences. Holistic programmes play an important role in science as guide programmes for reductionistic programmes by discovering or developing macro-laws or -theories about phenomena at the level of wholes, which they themselves, however, cannot explain. For these explanations they depend on the fruits of reductionistic programmes. If the latter succeed in providing the explanations they act as supply programmes for the holistic guide programmes. Reductionistic programmes depend in turn on holistic programmes for providing the macro-laws or -theories that call for these explanations. In chapter 6 I have discussed an example of this mutual dependency in the form of the reduction of the Bohr-effect in animal physiology. I have shown that this law has been reduced to the theory of allostery, applied to hemoglobin molecules in red blood cells, and that this application of the theory of allostery has been reduced to the theory of chemical bonding. I have also shown that at least six research programmes were involved in these reductions, and that the relations between these programmes can be characterized very well in terms of the model of holistic guide programmes and reductionistic supply programmes. The only, but highly significant, qualification appearing from example was that the terms ’holistic’ and ’reductionistic’ are extremely relative and should always be related to a certain given level of organization. In chapter 7 I have resolved the remaining contradistinction between holism and reductionism in biology, viz. the need for functional explanations and the demand that explanations be causal. I have shown that functional explanations are perfectly legitimate explanations which in a sense can be reconstrued as causal explanations. I have argued that functional explanations are indispensable components of more comprehensive, causal-evolutionary explanations, because the latter appeal to the adaptive value, and hence the function, of the property to be explained. In that sense functions can be regarded as adaptations, and functional explanations can be regarded as a sort of ’short-hand’ for evolutionary explanations. Finally, I have shown that in the context of functional explanations, too, co-operation of holistic and reductionistic research programmes occurs. In part 2 I have applied my thesis to ecology. I have shown that in ecology too, holismreductionism disputes notwithstanding, co-operation of holistic and reductionistic research programmes occurs, or, in so far as this appears to be not the case, that it should be strived after. In chapter 8 I have given an overview of reduction problems in ecology and of the various approaches to these problems. I have noticed that in ecology, too, there are several, radical, moderate and anti-reductionistic research strategies, with respect to the levels of both ecosystems, communities and populations. I have also noticed, however, that concrete solutions to reduction problems in ecology are frustrated by what is called the intellectual immaturity or the anomalous status of ecology. This refers to the almost complete lack of general laws and theories in ecology, at least at the higher levels of communities and ecosystems. Of a number of possible causes I have lifted out two, which lend themselves to philosophical analysis and clarification. The first one is the ambiguity of a major part of the ecological vocabulary. This was the subject of chapters 9 and 10. The second is the inhibitory effect which holism-reductionism disputes have on the growth of knowledge. This was the subject of chapter 13. In chapter 9 I have discussed the concept of an community. It appeared that the term ’community’ is used for several different entities at various levels of organization. This ambiguity alone seems to be sufficient for the lack of ’general’ laws and theories about ’communities’. My purpose in chapter 9 was to try and contribute to a solution of this problem. In doing so I have argued, first, that it seems wise to use the term ’community’ only for groups of species belonging to a single taxonomic or phylogenetic group, and to use the term ’biocoenosis’ for the higher level of organization, defined as the biotic component of an ecosystem. Next I have argued that, although species within communities may of course interact with each other, interaction is itself not a necessary or sufficient condition for community membership. Finally, I have hit upon what is known as the most notorious problem in community ecology, to wit the boundary problem, as well as the problem of heterogeneity. I have found that the cause of these problems lies in the fact that communities are almost invariably being seen as groups of populations occurring together in space and time, whereas the empirical fact is rather that populations of different species mostly do not occur together in the same space, and, moreover, that the species composition of communities changes continuously. This has lead to the suggestion that a community had better be defined as the group of individuals of two or more species occurring in the area of intersection of populations of these species. It is only in such intersection areas that one can really talk of the co-occurrence of species. I have shown the empirical adequacy of this definition by discussing various salt marsh plant communities on the Dutch island of Schiermonnikoog. In chapter 10 I have clarified two other important, yet highly controversial, concepts in ecology, to wit habitat and niche. It appeared that there are at least four different habitat concepts in ecology, and as many niche concepts, the additional complication being that two of these habitat concepts correspond to two of these niche concepts, whence the distinction between habitat and niche is blurred. In addition, different habitat concepts appeared to correspond to different environment concepts and also to different biotope concepts. My purpose in chapter 10 was to disentangle all these concepts from one another and to supply each of them with a suitable term. I have done so by keeping a close eye on commonly accepted notions about habitat differentiation and niche differentiation, two ’principles’ allowing one to explain the coexistence or non-coexistence of species in communities. The results can be found in boxes 5 and 7 in chapter 10. In chapter 11 I was finally able to substantiate my claim that in ecology, too, co-operation of holistic and reductionistic research programmes occurs. I have discussed the reduction of the classical competition model of Lotka and Volterra to modern niche theory. The Lotka/Volterra model is a phenomenological model: it describes the possible effects of competition between two species. Modern niche theory, on the other hand, is a mechanistic theory, in which both the objects of competition and a mechanism are being specified. I have shown that the reduction was established with the help of a relatively simple identification hypothesis and two relatively simple aggregation hypotheses, making it yet another example of heterogeneous microreduction in biology. In the reduction, the Lotka/Volterra model acted as a holistic guide programme and modern niche theory acted as a reductionistic supply programme. In chapter 12 I have discussed another example of co-operation in the form of the approximative reduction of MacArthur and Wilson’s equilibrium theory of island biogeography. I have argued that this can be seen as a holistic model, which has been of great unifying and especially heuristic value, but which in time has been found to be a bit too simple and in some respects had to be corrected. Therefore, it can also be seen as an idealization in the sense of the model of idealization and concretization, which subsequent research programmes have concretized. Because these concretizations have a reductive character, we can see in this structure of idealization and concretization yet another example of the co-operation of holistic and reductionistic research programmes in ecology. A philosophically interesting side-conclusion was that the model of idealization and concretization thus appears to apply also to relations between research programmes, and not only to programme-internal developments. In chapter 13 I have discussed an example of the inhibitory effect that holism-reductionism disputes may have on the growth of knowledge. The example concerns a controversy in island biogeography over the role of interspecific competition in structuring communities. This controversy has lasted for about ten years, appeares to have died out rather than to have been resolved, and has produced nothing new in the field of explanations of community structure. I have shown that the major factors underlying the controversy were differing, in casu holistic and reductionistic, views of communities. Though this presented a problem for my thesis, I have argued that, ultimately, the controversy can be resolved, and in a sense has been resolved, in a way that corroborates my thesis. In the epilogue, finally, I have mentioned some remaining problems concerning the adequacy of the present reduction model in dealing with reduction in ecology. These problems pertain to the question of specificty of ecological laws and theories, the likelihood that reductions in ecology generally occur on the basis of several reducing micro-theories, and the possible relationship between the former two points. (shrink)

Edward O. Wilson's forays into human sociobiology have been the target of persistent, vehement attack by his Harvard colleague in evolutionary biology, Richard C. Lewontin. Through examination of existing documents in the case, together with in-depth personal interviews of Wilson, Lewontin, and other biologists, the reasons for Wilson's stance and Lewontin's criticisms are uncovered. It is argued that the dispute is not primarily personally or politically motivated, but involves a conflict between long-term scientific-cum-moral agendas, with the reductionist program as a (...) key issue. It is concluded that it is in the interest of both disputants to keep the controversy alive. (shrink)

This paper revisits the debate over whether the study of facilitation requires ecologists to revise their understanding of the relationship between realized and fundamental niches as conceptualized by Hutchinson. Following Rodriguez-Cabal et al., I argue against Bruno et al.’s claim that facilitation can make a species’ realized niche larger than its fundamental niche. However, I also maintain that the abstract Hutchinsonian conceptualization of the niche makes a whole range of facilitative interactions—which I propose to call ameliorative facilitation—invisible to niche-based approaches (...) to the study of ecological communities. I propose a way to incorporate ameliorative facilitation into such approaches. My proposal involves supplementing the Hutchinsonian realized/fundamental dyad with a third concept: the potential niche. This concept was introduced by ecologists studying the effects of environmental change on species distributions, but I show how it could also be fruitfully used in facilitation studies. I argue that this proposed solution is more appealing than Stachowicz’s suggestion that Hutchinson’s realized/fundamental contrast be applied to a spatial-geographical, as opposed to an abstract-conceptual, notion of the niche. (shrink)

Habitat templets are graphical-qualitative models which describe the development of life-history strategies in specific environmental conditions. In the context of the previous models of life-history strategies, life-history theorists focused on the density-dependent factors as the factors determining life-history strategies. With the use of habitat templets, the focus is oriented towards the environmental causal factors, considering density-dependent phenomena as by-products of the environmental impact. This implies an important shift in causality as well as in the worldview of life-history theorists: population is (...) not considered as a closed system isolated from the environment. The object of study is the organism-in-its-environment, as a complex multilevel system. This shift has also methodological consequences: Life-history theory combines holistic and reductionistic insights, using a variety of heuristic models. This imposes a new conception of generality as well as of the structure of scientific theories. (shrink)

Ecology's reputation as a holistic science is partly due to widespread misconceptions of its nature as well as shortcomings in its methodology. This article argues that the pursuit of empirical laws of ecology can foster the emergence of a more unified and predictive science based on complementary modes of explanation. Numerical analyses of population dynamics have a distinguished pedigree, spatial analyses generate predictive laws of macroecology, and physical analyses are typically pursued by the ecosystem paradigm. The most characteristically ecological laws, (...) however, are found in biotic analyses in the functional trait paradigm. Holistic credentials for ecology may thus be restored on two bases: its accommodating complementary modes of analysis and explanation, and its having some laws within the least reductionistic mode consistent with its subject matter. These claims, grounded in the aspectual theory of Herman Dooyeweerd, lead to some suggestions for enhancing the versatility and usefulness of ecology—and other sciences—by balancing different research paradigms under a holistic vision. (shrink)

The encounter between the Darwinian theory of evolution and Mendelism could be resolved only when reductionist tools could be applied to the analysis of complex systems. The instrumental reductionist interpretation of the hereditary basis of continuously varying traits provided mathematical tools which eventually allowed the construction of the Modern Synthesis of the theory of evolution.When genotypic as well as environmental variance allow the isolation of parts of the system, it is possible to apply Mendelian reductionism, that is , to treat (...) the phenotypic trait as if ti causally determined by discrete genes for the trait. howeverm such a beanbag genetics approach obscures the system's eye-view. The concept of heritability, defined as the proportion of the total phenotypic variance due to (additive) hereditary variation, asserts that genetic elements have discrete effects; but by relating to the genotypic variance, it avoids the trap of reffering to genes for characters. (shrink)