Fisherian and Wrightian perspectives in evolutionary genetics and model-mediated imposition of theoretical assumptions

I investigate how theoretical assumptions, pertinent to different perspectives and operative during the modeling process, are central in determining how nature is actually taken to be. I explore two different models by Michael Turelli and Steve Frank of the evolution of parasite-mediated cytoplasmic incompatility, guided, respectively, by Fisherian and Wrightian perspectives. Since the two models can be shown to be commensurable both with respect to mathematics and data, I argue that the differences between them in the (1) mathematical presentation of the models, (2) explanations, and (3) objectified ontologies stem neither from differences in mathematical method nor the employed data, but from differences in the theoretical assumptions, especially regarding ontology, already present in the respective perspectives. I use my "set up, mathematically manipulate, explain, and objectify" (SMEO) account of the modeling process to track the model-mediated imposition of theoretical assumptions. I conclude with a discussion of the general implications of my analysis of these models for the controversy between Fisherian and Wrightian perspectives.     

Defending information-free genocentrism

Genocentrism, the thesis that the genes play a special role in the causation of development is often rejected in favor of a 'causal democracy thesis' to the effect that all causally necessary conditions for development are equal. Genocentrists argue that genes play a distinct causal role owing to their informational content and that this content enables them to program the embryo. I show that the special causal role of the genome hinges not on its informational status--it has none, or at least no more than computer programs have independent of our interpretations of them--but on its power literally to program the embryo, a power nicely illustrated in the use of polynucleotide sequences to compute solutions to NP hard problems in mathematics.     

Where all the rivers flow west: Maps,abstraction and change in the Papua New Guinea lowlands

‘Abstraction’ has been often identified as a key element in social change. Analyses, however, have often conflated the ideas of abstraction as ‘object’ and as ‘process’. This paper discusses two maps drawn by or on behalf of Kubo men, of the interior lowlands of southern Papua New Guinea. They were drawn in the context of recent exposure to a vast Liquefied Natural Gas project initiated on the land of their neighbours and both, as abstractions from new observations and experiences, were intended as assertions of rights to land. They derived, however, from entirely different logics: one more compatible with ‘Western’ understandings of ownership, the other more in keeping with earlier Kubo understandings of belonging. By reference to these maps, we consider the role of abstraction in social change and argue that while, as object, abstraction is relative as a process it is universal.     

Evolution in health and disease: work in progress.

This article surveys progress in Darwinian medicine since 1991. Evolutionary thinking has been providing an increasing flow of fresh ideas into medical science, ideas that would not be suggested by other perspectives. Recent contributions have shed new light on the evolution of virulence, of antibiotic resistance, of oocytic atresia, of menopause, of the timing of the expression of genetic disease, of links between mate choice and disease resistance, and of genomic conflict between mother and fetus over resource provisioning. An important consequence of changes from the environment of evolutionary adaptedness concerns reproductive cancers; the incidence of reproductive cancers may be linked to changes in the frequency of menstruation in postindustrial societies. Other intriguing developments include some unanticipated and undesirable consequences of good hygiene, hope from an unexpected quarter for progress on nerve and muscle regeneration, evolutionary interpretations of mental disease, and insights from functional genomics into the nature of tradeoffs. The application of evolutionary thinking to problems in medical research and practice has thus yielded an abundant and growing harvest of insights. Some are well founded, others remain speculative. The field is moving from an initial phase dominated by speculation and hypothesis formation into a more rigorous phase of experimental testing of explicit alternatives. Currently the most promising areas, those in which experimental rigor can be applied efficiently, include experimental evolution and functional genomics. The pioneers can be proud of what they have set in motion.     

A Graph Theoretical Approach to Study the Organization of the Cortical Networks during Different Mathematical Tasks

The two core systems of mathematical processing (subitizing and retrieval) as well as their functionality are already known and published. In this study we have used graph theory to compare the brain network organization of these two core systems in the cortical layer during difficult calculations. We have examined separately all the EEG frequency bands in healthy young individuals and we found that the network organization at rest, as well as during mathematical tasks has the characteristics of Small World Networks for all the bands, which is the optimum organization required for efficient information processing. The different mathematical stimuli provoked changes in the graph parameters of different frequency bands, especially the low frequency bands. More specific, in Delta band the induced network increases it’s local and global efficiency during the transition from subitizing to retrieval system, while results suggest that difficult mathematics provoke networks with higher cliquish organization due to more specific demands. The network of the Theta band follows the same pattern as before, having high nodal and remote organization during difficult mathematics. Also the spatial distribution of the network’s weights revealed more prominent connections in frontoparietal regions, revealing the working memory load due to the engagement of the retrieval system. The cortical networks of the alpha brainwaves were also more efficient, both locally and globally, during difficult mathematics, while the fact that alpha’s network was more dense on the frontparietal regions as well, reveals the engagement of the retrieval system again. Concluding, this study gives more evidences regarding the interaction of the two core systems, exploiting the produced functional networks of the cerebral cortex, especially for the difficult mathematics.     

Yeast for Mathematicians: A Ferment of Discovery and Model Competition to Describe Data

In addition to the memorization, algorithmic skills and vocabulary which are the default focus in many mathematics classrooms, professional mathematicians are expected to creatively apply known techniques, construct new mathematical approaches and communicate with and about mathematics. We propose that students can learn these professional, higher-level skills through Laboratory Experiences in Mathematical Biology which put students in the role of mathematics researcher creating mathematics to describe and understand biological data. Here we introduce a laboratory experience centered on yeast (Saccharomyces cerevisiae) growing in a small capped flask with a jar to collect carbon dioxide created during yeast growth and respiration. The lab requires no specialized equipment and can easily be run in the context of a college math class. Students collect data and develop mathematical models to explain the data. To help place instructors in the role of mentor/collaborator (as opposed to jury/judge), we facilitate the lab using model competition judged via Bayesian Information Criterion. This article includes details about the class activity conducted, student examples and pedagogical strategies for success.     

Valéry et l’automatisme psychologique

While the name of Paul Valery is usually associated with that of Leonardo da Vinci or the character, Monsieur Teste, most people are unaware of Valery’s posthumous work, which he considered the most significant of his writings: Cahiers/Notebooks, a voluminous and dense work, in its dimensions (around 30,000 pages) as well as in what it discloses about the daily ponderings of a man who considered himself — in spite of himself — a philosopher. It is a multifaceted work, touching on all fields of thought: history, politics, and the sciences, in all their diversity, from mathematics to physics, and biology to the theory of evolution. Neither philosophy, nor theology, nor linguistics is left in the dark. But he clearly expressed a preference for psychology and, more specifically, the question of mental function: What is it to think? How does the mind link ideas? What is abstraction? What role do feelings play? What is the relationship between the mind and the machine? Must we concede the existence of the unconscious mind. These are some of the questions we address in elucidating the concept of automatism through what makes it work as well as its failings.     

The emergence of abstract ideas: evidence from networks and babies

What is abstraction? In our view, abstraction is generalization. Specifically, we propose that abstract concepts emerge as the natural product of associative learning and generalization by similarity. We support this proposal by presenting evidence for two ideas: first, that children''s knowledge about how categories are organized and how words refer to them can be explained as learned generalizations over specific experiences of words referring to categories; and second, that the path of concepts from concrete to more abstract can be observed throughout development and that even in their more abstract form, concepts retain some of their original sensory basis. We illustrate these two facts by examining, in two kinds of learners--networks and young children--the development of three abstract ideas: (i) the idea of word; (ii) the idea of object; and (iii) the idea of substance.     

Culturally Situated Design Tools: Ethnocomputing from Field Site to Classroom

Ethnomathematics is the study of mathematical ideas and practices situated in their cultural context. Culturally Situated Design Tools (CSDTs) are web-based software applications that allow students to create simulations of cultural arts—Native American beadwork, African American cornrow hairstyles, urban graffiti, and so forth—using these underlying mathematical principles. This article is a review of the anthropological issues raised in the CSDT project: negotiating the representations of cultural knowledge during the design process with community members, negotiating pedagogical features with math teachers and their students, and reflecting on the software development itself as a cultural construction. The move from ethnomathematics to ethnocomputing results in an expressive computational medium that affords new opportunities to explore the relationships between youth identity and culture, the cultural construction of mathematics and computing, and the formation of cultural and technological hybridity.     

The formal darwinism project in outline

The formal darwinism project aims to provide a mathematical framework within which important fundamental ideas in large parts of biology can be articulated, including Darwin's central argument in The Origin (that mechanical processes of inheritance and reproduction can give rise to the appearance of design), modern extensions of evolutionary theory including ESS theory and inclusive fitness, and Dawkins' synthesis of them into a single structure. A new kind of argument is required to link equations of motion on the one hand to optimisation programs on the other, and a major point is that the biologist's concept of fitness maximisation is not represented by concepts from dynamical systems such as Lyapunov functions and gradient functions. The progress of the project so far is reviewed, though with only a brief glance at the rather complicated mathematics itself, and the centrality of fitness maximisation ideas to many areas of biology is emphasised.     

Individual Differences in Inhibitory Control,Not Non-Verbal Number Acuity,Correlate with Mathematics Achievement

Given the well-documented failings in mathematics education in many Western societies, there has been an increased interest in understanding the cognitive underpinnings of mathematical achievement. Recent research has proposed the existence of an Approximate Number System (ANS) which allows individuals to represent and manipulate non-verbal numerical information. Evidence has shown that performance on a measure of the ANS (a dot comparison task) is related to mathematics achievement, which has led researchers to suggest that the ANS plays a critical role in mathematics learning. Here we show that, rather than being driven by the nature of underlying numerical representations, this relationship may in fact be an artefact of the inhibitory control demands of some trials of the dot comparison task. This suggests that recent work basing mathematics assessments and interventions around dot comparison tasks may be inappropriate.     

Quantitative Analysis of the Interdisciplinarity of Applied Mathematics

The increasing use of mathematical techniques in scientific research leads to the interdisciplinarity of applied mathematics. This viewpoint is validated quantitatively here by statistical and network analysis on the corpus PNAS 1999–2013. A network describing the interdisciplinary relationships between disciplines in a panoramic view is built based on the corpus. Specific network indicators show the hub role of applied mathematics in interdisciplinary research. The statistical analysis on the corpus content finds that algorithms, a primary topic of applied mathematics, positively correlates, increasingly co-occurs, and has an equilibrium relationship in the long-run with certain typical research paradigms and methodologies. The finding can be understood as an intrinsic cause of the interdisciplinarity of applied mathematics.     

R A Fisher,design theory,and the Indian connection

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R A Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.     

The significance of Aleš Hrdlička's “Neanderthal phase of man”: A historical and current assessment

Ale? Hrdli?ka's hypothesis on a Neandertal phase of human evolution is examined in light of current data and interpretations on Neandertals. Hrdli?ka's interpretations are related to his ideas regarding the peopling of the New World. A major early statement of Hrdli?ka's views on Neandertal was his Huxley Memorial Lecture of 1927. We assess this formulation and subsequent development of his hypothesis. Hrdli?ka's position is compared with the “presapiens” and “pre-neandertal” hypotheses on the basis of current theory and data.     

Dissipative structures in morphogenetic models of the Turing type

We investigate the general conditions for morphogenesis. It is found that not only the Turing condition shall be satisfied, but also that some other requirements must be fulfilled. Their physical meaning is that the system should have more than one stationary state. In biological terms this means that the competence of differentiation is necessary in order to finish the morphogenesic process. These ideas are illustrated by a simple mathematical model. For this model the bifurcation analysis and computer results are discussed. Furthermore the parametric regulation of the morphogenesis is considered in connection with the role played by the genetic information.     

Mechanism of oxidation of N-hydroxyphentermine by superoxide

Cytochrome P-450 oxidizes N-hydroxyphentermine (MPPNHOH) by an indirect pathway involving superoxide. The chemical details of this oxidation, in which N-hydroxyphentermine is converted to 2-methyl-2-nitro-1-phenylpropane (MPPNO2), have been elucidated by examining the interaction of MPPNHOH with superoxide in aqueous and organic solvents. The role of peroxide, hydroperoxy radicals, and oxygen in the reaction was also examined. The results indicate that superoxide itself is oxidizing MPPNHOH to a nitroxide that disproportionates to MPPNHOH and 2-methyl-2-nitroso-1-phenylpropane (MPPNO). MPPNO is then oxidized to MPPNO2 by O2 or hydroperoxide. Two possible mechanisms for the superoxide oxidation were considered, a proton abstraction and a hydrogen atom abstraction. Stoichiometric and oxygen evolution studies favor the hydrogen abstraction pathway.     

A bio-physical basis of mathematics in synaptic function of the nervous system: A theory

The purpose of this paper is to present a bio-physical basis of mathematics. The essence of the theory is that function in the nervous system is mathematical. The mathematics arises as a result of the interaction of energy (a wave with a precise curvature in space and time) and matter (a molecular or ionic structure with a precise form in space and time). In this interaction, both energy and matter play an active role. That is, the interaction results in a change in form of both energy and matter. There are at least six mathematical operations in a simple synaptic region. It is believed the form of both energy and matter are specific, and their interaction is specific, that is, function in most of the nervous system is stereotyped. It is suggested that mathematics be taken out of the mind and placed where it belongs — in nature and the synaptic regions of the nervous system; it results in both places from a precise interaction between energy (in a precise form) and matter (in a precise structure).Departments of Medicine, Presbyterian-University of Pennsylvania Medical Center and the University of Pennsylvania School of Medicine     

Configuration of the hemoglobin oxygen dissociation curve demystified: a basic mathematical proof for medical and biological sciences undergraduates

The oxygen dissociation curve (ODC) of hemoglobin (Hb) has been widely studied and mathematically described for nearly a century. Numerous mathematical models have been designed to predict with ever-increasing accuracy the behavior of oxygen transport by Hb in differing conditions of pH, carbon dioxide, temperature, Hb levels, and 2,3-diphosphoglycerate concentrations that enable their applications in various clinical situations. The modeling techniques employed in many existing models are notably borrowed from advanced and highly sophisticated mathematics that are likely to surpass the comprehensibility of many medical and bioscience students due to the high level of "mathematical maturity" required. It is, however, a worthy teaching point in physiology lectures to illustrate in simple mathematics the fundamental reason for the crucial sigmoidal configuration of the ODC such that the medical and bioscience undergraduates can readily appreciate it, which is the objective of this basic dissertation.     

Time limits in the control of pollution systems

Exponentially growing pollution systems are examined from the point of view of control. A simplified mathematical model is used. Employing optimal control theory, we show that it is not always possible to drive the state (level of pollution) of such a system to a desired level. We prove that the state has to be smaller than certain bound for the system to be controllable. A specific example illustrates these ideas. The importance of this research lies in the fact that it shows the existence of certain state, and, consequently, time limits in the process of controlling the system.     

Mathematics reflecting sensorimotor organization

 This review combines short presentations of several mathematical approaches that conceptualize issues in sensorimotor neuroscience from different perspectives and levels of analysis. The intricate organization of neural structures and sensorimotor performance calls for characterization using a variety of mathematical approaches. This review points out the prospects for mathematical neuroscience: in addition to computational approaches, there is a wide variety of mathematical approaches that provide insight into the organization of neural systems. By starting from the perspective that provides the greatest clarity, a mathematical approach avoids specificity that is inaccurate in characterizing the inherent biological organization. Approaches presented include the mathematics of ordered structures, motion-phase space, subject-coincident coordinates, equivalence classes, topological biodynamics, rhythm space metric, and conditional dynamics. Issues considered in this paper include unification of levels of analysis, response equivalence, convergence, relationship of physics to motor control, support of rhythms, state transitions, and focussing on low-dimensional subspaces of a high-dimensional sensorimotor space. Received: 28 August 2001 / Accepted in revised form: 11 July 2002 Correspondence to: e-mail: mccollum@ohsu.edu Acknowledgements. I would like to express many thanks for the critical comments on this review offered by William L. Bloch, Jan E. Holly, Gerhard Magnus, and Patrick D. Roberts.