arXiv subjects

Steven A. Frank

Publications and source records attributed to Steven A. Frank.

At least 37 records · Page 2Linked to original sources

arXiv2017

Universal expressions of population change by the Price equation: natural selection, information, and maximum entropy production

The Price equation shows the unity between the fundamental expressions of change in biology, in information and entropy descriptions of populations, and in aspects of thermodynamics. The Price equation partitions the change in the average value of a metric between two populations. A population may be composed of organisms or particles or any members of a set to which we can assign probabilities. A metric may be biological fitness or physical energy or the output of an arbitrarily complicated function that assigns quantitative values to members of the population. The first part of the Price equation describes how directly applied forces change the probabilities assigned to members of the population when holding constant the metrical values of the members---a fixed metrical frame of reference. The second part describes how the metrical values change, altering the metrical frame of reference. In canonical examples, the direct forces balance the changing metrical frame of reference, leaving the average or total metrical values unchanged. In biology, relative reproductive success (fitness) remains invariant as a simple consequence of the conservation of total probability. In physics, systems often conserve total energy. Nonconservative metrics can be described by starting with conserved metrics, and then studying how coordinate transformations between conserved and nonconserved metrics alter the geometry of the dynamics and the aggregate values of populations. From this abstract perspective, key results from different subjects appear more simply as universal geometric principles for the dynamics of populations subject to the constraints of particular conserved quantities

cond-mat.stat-mech↗

arXiv2016

The inductive theory of natural selection: summary and synthesis

The theory of natural selection has two forms. Deductive theory describes how populations change over time. One starts with an initial population and some rules for change. From those assumptions, one calculates the future state of the population. Deductive theory predicts how populations adapt to environmental challenge. Inductive theory describes the causes of change in populations. One starts with a given amount of change. One then assigns different parts of the total change to particular causes. Inductive theory analyzes alternative causal models for how populations have adapted to environmental challenge. This chapter emphasizes the inductive analysis of cause.

q-bio.PE↗

arXiv2016

The invariances of power law size distributions

Size varies. Small things are typically more frequent than large things. The logarithm of frequency often declines linearly with the logarithm of size. That power law relation forms one of the common patterns of nature. Why does the complexity of nature reduce to such a simple pattern? Why do things as different as tree size and enzyme rate follow similarly simple patterns? Here I analyze such patterns by their invariant properties. For example, a common pattern should not change when adding a constant value to all observations. That shift is essentially the renumbering of the points on a ruler without changing the metric information provided by the ruler. A ruler is shift invariant only when its scale is properly calibrated to the pattern being measured. Stretch invariance corresponds to the conservation of the total amount of something, such as the total biomass and consequently the average size. Rotational invariance corresponds to pattern that does not depend on the order in which underlying processes occur, for example, a scale that additively combines the component processes leading to observed values. I use tree size as an example to illustrate how the key invariances shape pattern. A simple interpretation of common pattern follows. That simple interpretation connects the normal distribution to a wide variety of other common patterns through the transformations of scale set by the fundamental invariances.

q-bio.PE↗

arXiv2016

Puzzles in modern biology. III. Two kinds of causality in age-related disease

The two primary causal dimensions of age-related disease are rate and function. Change in rate of disease development shifts the age of onset. Change in physiological function provides necessary steps in disease progression. A causal factor may alter the rate of physiological change, but that causal factor itself may have no direct physiological role. Alternatively, a causal factor may provide a necessary physiological function, but that causal factor itself may not alter the rate of disease onset. The rate-function duality provides the basis for solving puzzles of age-related disease. Causal factors of cancer illustrate the duality between rate processes of discovery, such as somatic mutation, and necessary physiological functions, such as invasive penetration across tissue barriers. Examples from cancer suggest general principles of age-related disease.

q-bio.PE↗

arXiv2016

Puzzles in modern biology. IV. Neurodegeneration, localized origin and widespread decay

The motor neuron disease amyotrophic lateral sclerosis (ALS) typically begins with localized muscle weakness. Progressive, widespread paralysis often follows over a few years. Does the disease begin with local changes in a small piece of neural tissue and then spread? Or does neural decay happen independently across diverse spatial locations? The distinction matters, because local initiation may arise by local changes in a tissue microenvironment, by somatic mutation, or by various epigenetic or regulatory fluctuations in a few cells. A local trigger must be coupled with a mechanism for spread. By contrast, independent decay across spatial locations cannot begin by a local change, but must depend on some global predisposition or spatially distributed change that leads to approximately synchronous decay. This article outlines the conceptual frame by which one contrasts local triggers and spread versus parallel spatially distributed decay. Various neurodegenerative diseases differ in their mechanistic details, but all can usefully be understood as falling along a continuum of interacting local and global processes. Cancer provides an example of disease progression by local triggers and spatial spread, setting a conceptual basis for clarifying puzzles in neurodegeneration. Heart disease also has crucial interactions between global processes, such as circulating lipid levels, and local processes in the development of atherosclerotic plaques. The distinction between local and global processes helps to understand these various age-related diseases.

q-bio.PE↗

arXiv2016

Puzzles in modern biology. I. Male sterility, failure reveals design

Many human males produce dysfunctional sperm. Various plants frequently abort pollen. Hybrid matings often produce sterile males. Widespread male sterility is puzzling. Natural selection prunes reproductive failure. Puzzling failure implies something that we do not understand about how organisms are designed. Solving the puzzle reveals the hidden processes of design.

q-bio.PE↗

arXiv2016

Puzzles in modern biology. II. Language, cancer and the recursive processes of evolutionary innovation

Human language emerged abruptly. Diverse body forms evolved suddenly. Seed-bearing plants spread rapidly. How do complex evolutionary innovations arise so quickly? Resolving alternative claims remains difficult. The great events of the past happened a long time ago. Cancer provides a model to study evolutionary innovation. A tumor must evolve many novel traits to become an aggressive cancer. I use what we know or could study about cancer to describe the key processes of innovation. In general, evolutionary systems form a hierarchy of recursive processes. Those recursive processes determine the rates at which innovations are generated, spread and transmitted. I relate the recursive processes to abrupt evolutionary innovation.

q-bio.PE↗

arXiv2016

Invariant death

In nematodes, environmental or physiological perturbations alter death's scaling of time. In human cancer, genetic perturbations alter death's curvature of time. Those changes in scale and curvature follow the constraining contours of death's invariant geometry. I show that the constraints arise from a fundamental extension to the theories of randomness, invariance and scale. A generalized Gompertz law follows. The constraints imposed by the invariant Gompertz geometry explain the tendency of perturbations to stretch or bend death's scaling of time. Variability in death rate arises from a combination of constraining universal laws and particular biological processes.

q-bio.PE↗

arXiv2016

Common probability patterns arise from simple invariances

Shift and stretch invariance lead to the exponential-Boltzmann probability distribution. Rotational invariance generates the Gaussian distribution. Particular scaling relations transform the canonical exponential and Gaussian patterns into the variety of commonly observed patterns. The scaling relations themselves arise from the fundamental invariances of shift, stretch, and rotation, plus a few additional invariances. Prior work described the three fundamental invariances as a consequence of the equilibrium canonical ensemble of statistical mechanics or the Jaynesian maximization of information entropy. By contrast, I emphasize the primacy and sufficiency of invariance alone to explain the commonly observed patterns. Primary invariance naturally creates the array of commonly observed scaling relations and associated probability patterns, whereas the classical approaches derived from statistical mechanics or information theory require special assumptions to derive commonly observed scales.

math.PR↗

arXiv2015

d'Alembert's direct and inertial forces acting on populations: the Price equation and the fundamental theorem of natural selection

I develop a framework for interpreting the forces that act on any population described by frequencies. The conservation of total frequency, or total probability, shapes the characteristics of force. I begin with Fisher's fundamental theorem of natural selection. That theorem partitions the total evolutionary change of a population into two components. The first component is the partial change caused by the direct force of natural selection, holding constant all aspects of the environment. The second component is the partial change caused by the changing environment. I demonstrate that Fisher's partition of total change into the direct force of selection and the forces from the changing environmental frame of reference is identical to d'Alembert's principle of mechanics, which separates the work done by the direct forces from the work done by the inertial forces associated with the changing frame of reference. In d'Alembert's principle, there exist inertial forces from a change in the frame of reference that exactly balance the direct forces. I show that the conservation of total probability strongly shapes the form of the balance between the direct and inertial forces. I then use the strong results for conserved probability to obtain general results for the change in any system quantity, such as biological fitness or energy. Those general results derive from simple coordinate changes between frequencies and system quantities. Ultimately, d'Alembert's separation of direct and inertial forces provides deep conceptual insight into the interpretation of forces and the unification of disparate fields of study.

q-bio.PE↗

arXiv2015

Commentary: The nature of cancer research

Cancer research reflects an implicit conflict. On the one hand, there is an overwhelming desire to control the disease. We all wish that. On the other hand, we would like to understand why cancer follows so many clearly defined yet puzzling patterns. Why is there such regularity in the rates of progression? Why do different tissues vary so much? There should, of course, be no conflict between control and understanding. But the history of cancer research seems to say that those different goals remain oddly estranged. Peto's 1977 article locates the seeds of this conflict most clearly. He describes what is still the most powerful theoretical perspective for analyzing the causes of cancer. He presents many key unsolved puzzles within that context. He also says why most cancer researchers are not interested in these fundamental issues. The subsequent decades of research grew around this rift, blindly, in the way that research disciplines often grow. Let us revisit Peto, almost 40 years ago. We can learn much about the current nature of cancer research.

q-bio.TO↗

arXiv2014

How to read probability distributions as statements about process

Probability distributions can be read as simple expressions of information. Each continuous probability distribution describes how information changes with magnitude. Once one learns to read a probability distribution as a measurement scale of information, opportunities arise to understand the processes that generate the commonly observed patterns. Probability expressions may be parsed into four components: the dissipation of all information, except the preservation of average values, taken over the measurement scale that relates changes in observed values to changes in information, and the transformation from the underlying scale on which information dissipates to alternative scales on which probability pattern may be expressed. Information invariances set the commonly observed measurement scales and the relations between them. In particular, a measurement scale for information is defined by its invariance to specific transformations of underlying values into measurable outputs. Essentially all common distributions can be understood within this simple framework of information invariance and measurement scale.

stat.OT↗

arXiv2014

Generative models versus underlying symmetries to explain biological pattern

Mathematical models play an increasingly important role in the interpretation of biological experiments. Studies often present a model that generates the observations, connecting hypothesized process to an observed pattern. Such generative models confirm the plausibility of an explanation and make testable hypotheses for further experiments. However, studies rarely consider the broad family of alternative models that match the same observed pattern. The symmetries that define the broad class of matching models are in fact the only aspects of information truly revealed by observed pattern. Commonly observed patterns derive from simple underlying symmetries. This article illustrates the problem by showing the symmetry associated with the observed rate of increase in fitness in a constant environment. That underlying symmetry reveals how each particular generative model defines a single example within the broad class of matching models. Further progress on the relation between pattern and process requires deeper consideration of the underlying symmetries.

q-bio.PE↗

arXiv2014

Microbial metabolism: optimal control of uptake versus synthesis

Microbes require several complex organic molecules for growth. A species may obtain a required factor by taking up molecules released by other species or by synthesizing the molecule. The patterns of uptake and synthesis set a flow of resources through the multiple species that create a microbial community. This article analyzes a simple mathematical model of the tradeoff between uptake and synthesis. Key factors include the influx rate from external sources relative to the outflux rate, the rate of internal decay within cells, and the cost of synthesis. Aspects of demography also matter, such as cellular birth and death rates, the expected time course of a local resource flow, and the associated lifespan of the local population. Spatial patterns of genetic variability and differentiation between populations may also strongly influence the evolution of metabolic regulatory controls of individual species and thus the structuring of microbial communities. The widespread use of optimality approaches in recent work on microbial metabolism has ignored demography and genetic structure.

q-bio.PE↗

arXiv2013

Input-output relations in biological systems: measurement, information and the Hill equation

Biological systems produce outputs in response to variable inputs. Input-output relations tend to follow a few regular patterns. For example, many chemical processes follow the S-shaped Hill equation relation between input concentrations and output concentrations. That Hill equation pattern contradicts the fundamental Michaelis-Menten theory of enzyme kinetics. I use the discrepancy between the expected Michaelis-Menten process of enzyme kinetics and the widely observed Hill equation pattern of biological systems to explore the general properties of biological input-output relations. I start with the various processes that could explain the discrepancy between basic chemistry and biological pattern. I then expand the analysis to consider broader aspects that shape biological input-output relations. Key aspects include the input-output processing by component subsystems and how those components combine to determine the system's overall input-output relations. That aggregate structure often imposes strong regularity on underlying disorder. Aggregation imposes order by dissipating information as it flows through the components of a system. The dissipation of information may be evaluated by the analysis of measurement and precision, explaining why certain common scaling patterns arise so frequently in input-output relations. I discuss how aggregation, measurement and scale provide a framework for understanding the relations between pattern and process. The regularity imposed by those broader structural aspects sets the contours of variation in biology. Thus, biological design will also tend to follow those contours. Natural selection may act primarily to modulate system properties within those broad constraints.

q-bio.MN↗

arXiv2013

Natural selection. VII. History and interpretation of kin selection theory

Kin selection theory is a kind of causal analysis. The initial form of kin selection ascribed cause to costs, benefits, and genetic relatedness. The theory then slowly developed a deeper and more sophisticated approach to partitioning the causes of social evolution. Controversy followed because causal analysis inevitably attracts opposing views. It is always possible to separate total effects into different component causes. Alternative causal schemes emphasize different aspects of a problem, reflecting the distinct goals, interests, and biases of different perspectives. For example, group selection is a particular causal scheme with certain advantages and significant limitations. Ultimately, to use kin selection theory to analyze natural patterns and to understand the history of debates over different approaches, one must follow the underlying history of causal analysis. This article describes the history of kin selection theory, with emphasis on how the causal perspective improved through the study of key patterns of natural history, such as dispersal and sex ratio, and through a unified approach to demographic and social processes. Independent historical developments in the multivariate analysis of quantitative traits merged with the causal analysis of social evolution by kin selection.

q-bio.PE↗

arXiv2013

Natural selection. VI. Partitioning the information in fitness and characters by path analysis

Three steps aid in the analysis of selection. First, describe phenotypes by their component causes. Components include genes, maternal effects, symbionts, and any other predictors of phenotype that are of interest. Second, describe fitness by its component causes, such as an individual's phenotype, its neighbors' phenotypes, resource availability, and so on. Third, put the predictors of phenotype and fitness into an exact equation for evolutionary change, providing a complete expression of selection and other evolutionary processes. The complete expression separates the distinct causal roles of the various hypothesized components of phenotypes and fitness. Traditionally, those components are given by the covariance, variance, and regression terms of evolutionary models. I show how to interpret those statistical expressions with respect to information theory. The resulting interpretation allows one to read the fundamental equations of selection and evolution as sentences that express how various causes lead to the accumulation of information by selection and the decay of information by other evolutionary processes. The interpretation in terms of information leads to a deeper understanding of selection and heritability, and a clearer sense of how to formulate causal hypotheses about evolutionary process. Kin selection appears as a particular type of causal analysis that partitions social effects into meaningful components.

q-bio.PE↗

arXiv2012

Natural selection. V. How to read the fundamental equations of evolutionary change in terms of information theory

The equations of evolutionary change by natural selection are commonly expressed in statistical terms. Fisher's fundamental theorem emphasizes the variance in fitness. Quantitative genetics expresses selection with covariances and regressions. Population genetic equations depend on genetic variances. How can we read those statistical expressions with respect to the meaning of natural selection? One possibility is to relate the statistical expressions to the amount of information that populations accumulate by selection. However, the connection between selection and information theory has never been compelling. Here, I show the correct relations between statistical expressions for selection and information theory expressions for selection. Those relations link selection to the fundamental concepts of entropy and information in the theories of physics, statistics, and communication. We can now read the equations of selection in terms of their natural meaning. Selection causes populations to accumulate information about the environment.

q-bio.PE↗