arXiv subjects

David Waxman

Publications and source records attributed to David Waxman.

14 recordsLinked to original sources

arXiv2025

Effective decoupling of mutations and the resulting loss of biodiversity caused by environmental change

Many biological populations exhibit diversity in their strategy for survival and reproduction in a given environment, and microbes are an example. We explore the fate of different strategies under sustained environmental change by considering a mathematical model for a large population of asexual organisms. Fitness is a bimodal function of a quantitative trait, with two local optima, separated by a local minimum, i.e., a mixture of stabilising and disruptive selection. The optima represent two locally `best' trait values. We consider regimes where, when the environment is unchanging, the equilibrium distribution of the trait is bimodal. A bimodal trait distribution generally requires, for its existence, mutational coupling between the two peaks, and it indicates two coexisting clones with distinct survival and reproduction strategies. When subject to persistent environmental change, the population adapts by utilising mutations that allow it to track the changing environment. The faster the rate of change of the environment, the larger the effect of the mutations that are utilised. Under persistent environmental change, the distribution of trait values takes two different forms. At low rates of change, the distribution remains bimodal. At higher rates, the distribution becomes unimodal. This loss of a clone/biodiversity is driven by a novel mechanism where environmental change decouples a class of mutations.

q-bio.PE↗

arXiv2025

How can we measure the information created by natural selection?

Natural selection can create information. In particular, because of the action of natural selection, we can often learn something about an environment by examining local organisms, and vice versa. For example, the characteristics of a cactus suggest that the local environment is relatively dry, and if a natural terrestrial environment is dry, then we will generally have an enhanced probability of finding drought-resistant plants (like cacti). Here, we propose a measure that can be used to quantify the information that is created by natural selection. We call the proposed quantity reproductive information, and we show that it has an intuitively satisfying relationship to standard quantitative definitions of information. Reproductive information is also approximately equal to a previously defined measure of biological adaptation. In addition, we explain how reproductive information can be measured using phenotypic characters, instead of genotypes. This could facilitate the measurement of reproductive information, and it could also allow for the quantification of the information that is created by natural selection on groups of organisms, instead of just selection on individuals. Thus, the concept of reproductive information has the potential to advance research on the "units of selection", the "major transitions in evolution", and the emergence of "superorganisms" via cooperation among group members.

q-bio.PE↗

arXiv2025

Exact first passage time distribution for nonlinear chemical reaction networks II: monomolecular reactions and a A + B - C type of second-order reaction with arbitrary initial conditions

In biochemical reaction networks, the first passage time (FPT) of a reaction quantifies the time it takes for the reaction to first occur, from the initial state. While the mean FPT historically served as a summary metric, a far more comprehensive characterization of the dynamics of the network is contained within the complete FPT distribution. The relatively uncommon theoretical treatments of the FPT distribution that have been given in the past have been confined to linear systems, with zero and first-order processes. Recently, we presented theoretically exact solutions for the FPT distribution, within nonlinear systems involving two-particle collisions, such as A+B - C. Although this research yielded invaluable results, it was based upon the assumption of initial conditions in the form of a Poisson distribution. This somewhat restricts its relevance to real-world biochemical systems, which frequently display intricate behaviour and initial conditions that are non-Poisson in nature. Our current study extends prior analyses to accommodate arbitrary initial conditions, thereby expanding the applicability of our theoretical framework and providing a more adaptable tool for capturing the dynamics of biochemical reaction networks.

q-bio.MN↗

arXiv2024

A dynamical measure of algorithmically infused visibility

This work focuses on the nature of visibility in societies where the behaviours of humans and algorithms influence each other - termed algorithmically infused societies. We propose a quantitative measure of visibility, with implications and applications to an array of disciplines including communication studies, political science, marketing, technology design, and social media analytics. The measure captures the basic characteristics of the visibility of a given topic, in algorithm/AI-mediated communication/social media settings. Topics, when trending, are ranked against each other, and the proposed measure combines the following two attributes of a topic: (i) the amount of time a topic spends at different ranks, and (ii) the different ranks the topic attains. The proposed measure incorporates a tunable parameter, termed the discrimination level, whose value determines the relative weights of the two attributes that contribute to visibility. Analysis of a large-scale, real-time dataset of trending topics, from one of the largest social media platforms, demonstrates that the proposed measure can explain a large share of the variability of the accumulated views of a topic.

cs.SI↗

arXiv2024

Discrete vs. continuous dynamics in biology: When do they align and when do they diverge?

Many biological systems are governed by difference equations and exhibit discrete-time dynamics. Examples include the size of a population when generations are non-overlapping, and the incidence of a disease when infections are recorded at fixed intervals. For discrete-time systems lacking exact solutions, continuous-time approximations are frequently employed when small changes occur between discrete time steps. Here, we present an approach motivated by exactly soluble discrete time problems. We show that such systems have continuous-time descriptions (governed by differential equations) whose solutions precisely agree, at the discrete times, with the discrete time solutions, irrespective of the size of changes that occur. For discrete-time systems lacking exact solutions, we develop approximate continuous-time models that can, to high accuracy, capture rapid growth and decay. Our approach employs mappings between difference and differential equations, generating functional solutions that exactly or closely preserve the original discrete time behaviour. It uncovers fundamental structural parallels and also distinctions between the difference equation and the `equivalent' differential equation. The findings we present cover both time-homogeneous and time-inhomogeneous systems. For completeness, we also consider discrete-time systems with the most rapid oscillatory behaviour possible, namely a sign change each time step. We show, for exactly soluble cases, that such systems also have a continuous-time description, but that this comes at the expense of generally complex-valued solutions. This work has applications in, for example, population genetics, ecology and epidemic modelling. By bridging discrete and continuous representations of a system, it enhances insights/analysis of different types of dynamics.

q-bio.PE↗

arXiv2024

A comprehensive representation of selection at loci with multiple alleles that allows complex forms of genotypic fitness

Genetic diversity is central to the process of evolution. Both natural selection and random genetic drift are influenced by the level of genetic diversity of a population; selection acts on diversity while drift samples from it. At a given locus in a diploid population, each individual carries only two alleles, but the population as a whole can possess a much larger number of alleles, with the upper limit constrained by twice the population size. This allows for many possible types of homozygotes and heterozygotes. Moreover, there are biologically important loci, for example those related to the MHC complex, the ABO blood types, and cystic fibrosis, that exhibit a large number of alleles. Despite this, much of population genetic theory, and data analysis, are limited to considering biallelic loci. However, to the present, what is lacking is a flexible expression for the force of selection that allows an arbitrary number of alleles (and hence an arbitrary number of heterozygotes), along with a variety of forms of fitness. In this work, we remedy this absence by giving an analytical representation of the force of selection that emphasises the very different roles played by the diversity of the population, and the fitnesses of different genotypes. The result presented facilitates our understanding and applies in a variety of different situations involving multiple alleles. This includes situations where fitnesses are: additive, multiplicative, randomly fluctuating, frequency-dependent, and it allows fitnesses which involve explicit gene interactions, such as heterozygote advantage.

q-bio.PE↗

arXiv2024

Exact first passage time distribution for second-order reactions in chemical networks

The first passage time (FPT) is a generic measure that quantifies when a random quantity reaches a specific state. We consider the FTP distribution in nonlinear stochastic biochemical networks, where obtaining exact solutions of the distribution is a challenging problem. Even simple two-particle collisions cause strong nonlinearities that hinder the theoretical determination of the full FPT distribution. Previous research has either focused on analyzing the mean FPT, which provides limited information about a system, or has considered time-consuming stochastic simulations that do not clearly expose causal relationships between parameters and the system's dynamics. This paper presents the first exact theoretical solution of the full FPT distribution in a broad class of chemical reaction networks involving $A + B \rightarrow C$ type of second-order reactions. Our exact theoretical method outperforms stochastic simulations, in terms of computational efficiency, and deviates from approximate analytical solutions. Given the prevalence of bimolecular reactions in biochemical systems, our approach has the potential to enhance the understanding of real-world biochemical processes.

q-bio.MN↗

arXiv2024

Exact path-integral representation of the Wright-Fisher model with mutation and selection

The Wright-Fisher model describes a biological population containing a finite number of individuals. In this work we consider a Wright-Fisher model for a randomly mating population, where selection and mutation act at an unlinked locus. The selection acting has a general form, and the locus may have two or more alleles. We determine an exact representation of the time dependent transition probability of such a model in terms of a path integral. Path integrals were introduced in physics and mathematics, and have found numerous applications in different fields, where a probability distribution, or closely related object, is represented as a 'sum' of contributions over all paths or trajectories between two points. Path integrals provide alternative calculational routes to problems, and may be a source of new intuition and suggest new approximations. For the case of two alleles, we relate the exact Wright-Fisher path-integral result to the path-integral form of the transition density under the diffusion approximation. We determine properties of the Wright-Fisher transition probability for multiple alleles. We show how, in the absence of mutation, the Wright-Fisher transition probability incorporates phenomena such as fixation and loss.

q-bio.PE↗

arXiv2023

Information encoded in gene-frequency trajectories

In this work we present a systematic mathematical approximation scheme that exposes the way that information, about the evolutionary forces of selection and random genetic drift, is encoded in gene-frequency trajectories. We determine approximate, time-dependent, gene-frequency trajectory statistics, assuming additive selection. We use the probability of fixation to test and illustrate the approximation scheme introduced. For the case where the strength of selection and the effective population size have constant values, we show how a standard result for the probability of fixation, under the diffusion approximation, systematically emerges, when increasing numbers of approximate trajectory statistics are taken into account. We then provide examples of how time-dependent parameters influence gene-frequency statistics.

q-bio.PE↗

arXiv2023

Homogenizing Entropy Across Different Environmental Conditions: A Universally Applicable Method for Transforming Continuous Variables

In classical information theory, a causal relationship between two variables is typically modelled by assuming that, for every possible state of one of the variables, there exists a particular distribution of states of the second variable. Let us call these two variables the causal and caused variables, respectively. We shall assume that both variables are continuous and one-dimensional. In this work we consider a procedure to transform each variable, using transformations that are differentiable and strictly increasing. We call these increasing transformations. Any causal relationship (as defined here) is associated with a channel capacity, which is the maximum rate that information could be sent if the causal relationship was used as a signalling system. Channel capacity is unaffected when the two variables are changed by use of increasing transformations. For any causal relationship we show that there is always a way to transform the caused variable such that the entropy associated with the caused variable is independent of the value of the causal variable. Furthermore, the resulting universal entropy has an absolute value that is equal to the channel capacity associated with the causal relationship. This observation may be useful in statistical applications. Also, for any causal relationship, it implies that there is a 'natural' way to transform a continuous caused variable. We also show that, with additional constraints on the causal relationship, a natural increasing transformation of both variables leads to a transformed causal relationship that has properties that might be expected from a well-engineered measuring device.

cs.IT↗

arXiv2020

Impact of intra and inter-cluster coupling balance on the performance of nonlinear networked systems

The dynamical and structural aspects of cluster synchronization (CS) in complex systems have been intensively investigated in recent years. Here, we study CS of dynamical systems with intra and inter-cluster couplings. We propose new metrics that describe the performance of such systems and evaluate them as a function of the strength of the couplings within and between clusters. We obtain analytical results that indicate that spectral differences between the Laplacian matrices associated with the partition between intra and inter-couplings directly affect the proposed metrics of system performance. Our results show that the dynamics of the system might exhibit an optimal balance that optimizes its performance. Our work provides new insights into the way specific symmetry properties relate to collective behavior, and could lead to new forms to increase the controllability of complex systems and to optimize their stability.

physics.soc-ph↗

arXiv2013

Fluctuating selection models and McDonald-Kreitman type analyses

It is likely that the strength of selection acting upon a mutation varies through time due to changes in the environment. However, most population genetic theory assumes that the strength of selection remains constant. Here we investigate the consequences of fluctuating selection pressures on the quantification of adaptive evolution using McDonald-Kreitman (MK) style approaches. In agreement with previous work, we show that fluctuating selection can generate evidence of adaptive evolution even when the expected strength of selection on a mutation is zero. However, we also find that the mutations, which contribute to both polymorphism and divergence tend, on average, to be positively selected during their lifetime, under fluctuating selection models. This is because mutations that fluctuate, by chance, to positive selected values, tend to reach higher frequencies in the population than those that fluctuate towards negative values. Hence the evidence of positive adaptive evolution detected under a fluctuating selection model by MK type approaches is genuine since fixed mutations tend to be advantageous on average during their lifetime. Never-the-less we show that methods tend to underestimate the rate of adaptive evolution when selection fluctuates.

q-bio.PE↗

arXiv2013

Achieving Precise Mechanical Control in Intrinsically Noisy Systems

How can precise control be realised in intrinsically noisy systems? Here, we develop a general theoretical framework that provides a way to achieve precise control in signal-dependent noisy environments. When the control signal has Poisson or supra-Poisson noise, precise control is not possible. If, however, the control signal has sub-Poisson noise, then precise control is possible. For this case, the precise control solution is not a function, but a rapidly varying random process that must be averaged with respect to a governing probability density functional. Our theoretical approach is applied to the control of straight-trajectory arm movement. Sub-Poisson noise in the control signal is shown to be capable of leading to precise control. Intriguingly, the control signal for this system has a natural counterpart, namely the bursting pulses of neurons --trains of Dirac-delta functions-- in biological systems to achieve precise control performance.

math.OC↗

arXiv2004

Path integral derivation of Bloch-Redfield equations for a qubit weakly coupled to a heat bath: Application to nonadiabatic transitions

Quantum information processing has greatly increased interest in the phenomenon of environmentally-induced decoherence. The spin boson model is widely used to study the interaction between a spin-modelling a quantum particle moving in a double well potential-and its environment-modelled by a heat bath of harmonic oscillators. This paper extends a previous analysis of the static spin boson study to the driven spin boson case, with the derivation of an exact integro-differential equation for the time evolution of the propagator of the reduced spin density matrix. This is the first main result. By specializing to weak damping we then obtain the next result, a set of Bloch-Redfield equations for the equilibrium fixed spin initial condition. Finally we show that these equations can be used to solve the classic dissipative Landau-Zener problem and illustrate these solutions for the weak damping case. The effect of dissipation is seen to be minimised as the speed of passage is increased, implying that qubits need to be switched as fast as possible.

cond-mat.mes-hall↗