Finite Population Model Research Articles

Allele frequencies and selection coefficients in locally adapted populations

Understanding the role of natural selection in driving evolutionary change requires accurate estimates of the strength of selection acting at the genetic level in the wild. This is challenging to achieve but may be easier in the case of populations in migration-selection balance. When two populations are at equilibrium under migration-selection balance, there exist loci whose alleles are selected different ways in the two populations. Such loci can be identified from genome sequencing by their high values of FST. This raises the question of what is the strength of selection on locally-adaptive alleles. To answer this question we analyse a 1-locus 2-allele model of a population distributed between two niches. We show by simulation of selected cases that the outputs from finite-population models are essentially the same as those from deterministic infinite-population models. We then derive theory for the infinite-population model showing the dependence of selection coefficients on equilibrium allele frequencies, migration rates, dominance and relative population sizes in the two niches. An Excel spreadsheet is provided for the calculation of selection coefficients and their approximate standard errors from observed values of population parameters. We illustrate our results with a worked example, with graphs showing the dependence of selection coefficients on equilibrium allele frequencies, and graphs showing how FST depends on the selection coefficients acting on the alleles at a locus. Given the extent of recent progress in ecological genomics, we hope our methods may help those studying migration-selection balance to quantify the advantages conferred by adaptive genes.

Conformity and anti-conformity in a finite population

Conformist and anti-conformist cultural transmission have been studied both empirically, in several species, and theoretically, with population genetic models. Building upon standard, infinite-population models (IPMs) of conformity, we introduce finite-population models (FPMs) and study them via simulation and a diffusion approximation. In previous IPMs of conformity, offspring observe the variants of n adult role models, where n is often three. Numerical simulations show that while the short-term behavior of the FPM with n=3 role models is well approximated by the IPM, stable polymorphic equilibria of the IPM become effective equilibria of the FPM at which the variation persists prior to fixation or loss, and which produce plateaus in curves for fixation probabilities and expected times to absorption. In the FPM with n=5 role models, the population may switch between two effective equilibria, which is not possible in the IPM, or may cycle between frequencies that are not effective equilibria, which is possible in the IPM. In all observed cases of ‘equilibrium switching’ and ‘cycling’ in the FPM, model parameters exceed O(1/N), required for the diffusion approximation, resulting in an over-estimation of the actual times to absorption. However, in those cases with n=5 role models that have one effective equilibrium and stable fixation states, even if conformity coefficients exceed O(1/N), the diffusion approximation matches closely the numerical simulations of the FPM. This suggests that the robustness of the diffusion approximation depends not only on the magnitudes of coefficients, but also on the qualitative behavior of the conformity model.

Causal Inference Under Approximate Neighborhood Interference

This paper studies causal inference in randomized experiments under network interference. Commonly used models of interference posit that treatments assigned to alters beyond a certain network distance from the ego have no effect on the ego's response. However, this assumption is violated in common models of social interactions. We propose a substantially weaker model of “approximate neighborhood interference” (ANI) under which treatments assigned to alters further from the ego have a smaller, but potentially nonzero, effect on the ego's response. We formally verify that ANI holds for well‐known models of social interactions. Under ANI, restrictions on the network topology, and asymptotics under which the network size increases, we prove that standard inverse‐probability weighting estimators consistently estimate useful exposure effects and are approximately normal. For inference, we consider a network HAC variance estimator. Under a finite population model, we show that the estimator is biased but that the bias can be interpreted as the variance of unit‐level exposure effects. This generalizes Neyman's well‐known result on conservative variance estimation to settings with interference.

Integration of Nonprobability and Probability Samples via Survey Weights

Probability sample encounters the problems of increasing cost and nonresponse. The cost has rapidly been increasing in executing a large probability sample survey, and, for some surveys, response rate can be below the 10 percent level. Therefore, statisticians seek some alternative methods. One of them is to use a large nonprobability sample (S_1 ) supplemented by a small probability sample (S_2 ). Both samples are taken from the same population and they include common covariates, and a third sample (S_3 ) is created by combining these two samples; S_1  can be biased and S_2  may have large sample variance. These two problems are reduced by survey weights and combining the two samples. Although S_2  is a small sample, it provides good properties of unbiasedness in estimation and of survey weights. With these known weights, we obtain adjusted sample weights (ASW), and create a sample model from a finite population model. We fit the sample model to obtain its parameters and generate values from the population model. Similarly, we repeat these processes for other two samples, S_1  and S_3  and for different statistical methods. We show reduced biases of the finite population means and reduced variances.as the combined sample size becomes large. We analyze sample data to show the reduction of these two errors.

On Assessing the Performance of IEEE 802.11ad Beamforming Training

In the race for Gigabit wireless links, IEEE introduced 802.11ad, an amendment aimed at delivering Gbps capacities in a WLAN setting by leveraging the 60 GHz band. The key innovation of the standard is its beamforming training protocol. Executed periodically at the beginning of every beacon interval, it enables the formation of directional links. To address contention during the uplink part of beamforming training, 802.11ad introduced A-BFT (Association BeamForming Training), an Aloha-inspired, two-level backoff race. While central to the functionality of 802.11ad networks, the performance of A-BFT, however, remains poorly understood. In this article, we propose an analytical finite-population model for evaluating the performance of IEEE 802.11ad A-BFT under two channel models: loss-free, and a channel introducing a constant bit error rate. After using an open-source simulator to demonstrate its accuracy, we use our model to assess the performance of A-BFT. We find that a counter-intuitive, quit-easily/be-lazy approach by the stations leads to the best overall beamforming training performance.

State dependent queueing models under admission control F-policy: a survey

The optimal F-policy can be used to control the admission of customers in queueing scenarios having limited waiting space. According to F-policy, as soon as the capacity of the system becomes full, the arriving customers are restricted to join the system until there is a drop in the number of customers in the system to a threshold level ‘F’ due to departure of the served customers. In spite of enormous applications of F-policy models in several queueing systems, a limited number of papers has appeared in the queueing literature. The main objective of this article is to provide a state-of-the-art and survey of literature on the state dependent queueing models operating under F-policy. In this article, we describe the mathematical formulation of queueing models operating under F-policy in two categories namely, finite capacity and finite population models. The methodological aspect of non-Markov models with F-policy is presented. The exhaustive list of work done on F-policy is also provided in tabular form.

Why is sterility virulence most common in sexually transmitted infections? Examining the role of epidemiology.

Sterility virulence, or the reduction in host fecundity due to infection, occurs in many host-pathogen systems. Notably, sterility virulence is more common for sexually transmitted infections (STIs) than for directly transmitted pathogens, while other forms of virulence tend to be limited in STIs. This has led to the suggestion that sterility virulence may have an adaptive explanation. By focusing upon finite population models, we show that the observed patterns of sterility virulence can be explained by consideration of the epidemiological differences between STIs and directly transmitted pathogens. In particular, when pathogen transmission is predominantly density invariant (as for STIs), and mortality is density dependent, sterility virulence can be favored by demographic stochasticity, whereas if pathogen transmission is predominantly density dependent, as is common for most directly transmitted pathogens, sterility virulence is disfavored. We show these conclusions can hold even if there is a weak selective advantage tosterilizing.

From Fixation Probabilities to d-player Games: An Inverse Problem in Evolutionary Dynamics.

The probability that the frequency of a particular trait will eventually become unity, the so-called fixation probability, is a central issue in the study of population evolution. Its computation, once we are given a stochastic finite population model without mutations and a (possibly frequency dependent) fitness function, is straightforward and it can be done in several ways. Nevertheless, despite the fact that the fixation probability is an important macroscopic property of the population, its precise knowledge does not give any clear information about the interaction patterns among individuals in the population. Here we address the inverse problem: from a given fixation pattern and population size, we want to infer what is the game being played by the population. This is done by first exploiting the framework developed in Chalub and Souza (J Math Biol 75:1735-1774, 2017), which yields a fitness function that realises this fixation pattern in the Wright-Fisher model. This fitness function always exists, but it is not necessarily unique. Subsequently, we show that any such fitness function can be approximated, with arbitrary precision, using d-player game theory, provided d is large enough. The pay-off matrix that emerges naturally from the approximating game will provide useful information about the individual interaction structure that is not itself apparent in the fixation pattern. We present extensive numerical support for our conclusions.

Modification on PPS Sample Scheme with Replacement

In this paper we have developed an alternative estimator for the Probability Proportional to Size (PPS) with replacement sampling scheme when certain characteristics under study are positively correlated with the selection probability. An analogue to the well-known superpopulation model for finite population is also suggested, using which, we compare the proposed estimator with Hansen and Hurwitz estimator. Finally, an empirical investigation of the performance of the propose estimator has also been made.

The Quasispecies for the Wright–Fisher Model

We consider the classical Wright–Fisher model of population genetics. We prove the existence of an error threshold for the mutation probability per nucleotide, below which a quasispecies is formed. We show a new phenomenon, specific to a finite population model, namely the existence of a population threshold: to ensure the stability of the quasispecies, the population size has to be at least of the same order as the genome length. We derive an explicit formula describing the quasispecies.

Approximating the survival probability in finite life-span population models

We consider the numerical approximation of the survival probability in the case of an unbounded mortality rate related to a finite life-span in age-structured population models. Our numerical approach is based on the approximation of the integral that characterizes this probability function by means of an appropriate quadrature rule. We demonstrate the convergence of this approximation assuming suitable conditions in relation with the unbounded mortality rate that will be reasonable in the real applications of this model. The numerical experiments carried out with typical mortality rates corroborate the interest of this method.

State Estimation for the Individual and the Population in Mean Field Control With Application to Demand Dispatch

This paper concerns state estimation problems in a mean field control setting. In a finite population model, the goal is to estimate the joint distribution of the population state and the state of a typical individual. The observation equations are a noisy measurement of the population. The general results are applied to demand dispatch for regulation of the power grid, based on randomized local control algorithms. In prior work by the authors it has been shown that local control can be carefully designed so that the aggregate of loads behaves as a controllable resource with accuracy matching or exceeding traditional sources of frequency regulation. The operational cost is nearly zero in many cases. The information exchange between grid and load is minimal, but it is assumed in the overall control architecture that the aggregate power consumption of loads is available to the grid operator. It is shown that the Kalman filter can be constructed to reduce these communication requirements,

Inclusive fitness in finite populations-effects of heterogeneity and synergy.

I review recent results concerning the relationship between the inclusive fitness (IF) effect and standard measures of allele fitness in a finite-population, with attention to the effect of heterogeneity in population structure and nonadditive fitness effects. In both cases, existing theoretical work is somewhat technical and I try to provide a more transparent account. In a heterogeneous population it is known that inclusive fitness will generally fail to incorporate the effects of selection on the distribution of alleles among states unless a reproductive-value weighting is used. But even given that, recent work shows that under certain updating rules, the IF effect can fail to be equivalent to standard measures such as fixation probability. In terms of synergistic fitness effects, I review the result that in the finite population model, the IF effect can be calculated using only "additive" relatedness coefficients so that computational difficulties found in the infinite-population model do not arise. In my own work, there is an interaction here in that my 2012 work on synergy with Maciejewski made an assumption about inclusive fitness that my 2014 work on heterogeneity with Tarnita showed to be wrong. I include (Appendix C) a corrected argument for the 2012 result.

Cooperation can emerge in prisoner’s dilemma from a multi-species predator prey replicator dynamic

In this paper we study a generalized variation of the replicator dynamic that involves several species and sub-species that may interact. We show how this dynamic comes about from a specific finite-population model, but also show that one must take into consideration the dynamic nature of the population sizes (and hence proportions) in order to make the model complete. We provide expressions for these population dynamics to produce a kind of multi-replicator dynamic. We then use this replicator dynamic to show that cooperation can emerge as a stable behavior when two species each play prisoner’s dilemma as their intra-species game and a form of zero-sum predator prey game as their inter-species game. General necessary and sufficient conditions for cooperation to emerge as stable are provided for a number of game classes. We also showed an example using Hawk–Dove where both species can converge to stable (asymmetric) mixed strategies.

On the sojourn time distribution in a finite population Markovian processor sharing queue

We consider a finite population processor sharing (PS) queue, with Markovian arrivals and an exponential server. Such a queue can model an interactive computer system consisting of a bank of terminals in series with a central processing unit. For systems with a large population N and a commensurately rapid service rate, or infrequent arrivals, we obtain various asymptotic results. We analyse the conditional sojourn time distribution of a tagged customer, conditioned on the number n of others in the system at the tagged customer's arrival instant, and also the unconditional distribution. The asymptotics are obtained by a combination of singular perturbation methods and spectral methods.We consider several space/time scales and parameter ranges, which lead to different asymptotic behaviours. We also identify precisely when the finite population model can be approximated by the standard infinite population M/M/1 - PS queue.

A paradox of cumulative culture

Culture can grow cumulatively if socially learnt behaviors are improved by individual learning before being passed on to the next generation. Previous authors showed that this kind of learning strategy is unlikely to be evolutionarily stable in the presence of a trade-off between learning and reproduction. This is because culture is a public good that is freely exploited by any member of the population in their model (cultural social dilemma). In this paper, we investigate the effect of vertical transmission (transmission from parents to offspring), which decreases the publicness of culture, on the evolution of cumulative culture in both infinite and finite population models. In the infinite population model, we confirm that culture accumulates largely as long as transmission is purely vertical. It turns out, however, that introduction of even slight oblique transmission drastically reduces the equilibrium level of culture. Even more surprisingly, if the population size is finite, culture hardly accumulates even under purely vertical transmission. This occurs because stochastic extinction due to random genetic drift prevents a learning strategy from accumulating enough culture. Overall, our theoretical results suggest that introducing vertical transmission alone does not really help solve the cultural social dilemma problem.

Conventional Semantic Meaning in Signalling Games with Conflicting Interests

Lewis signalling games are often used to explain how it is possible for simple agents to develop systems of conventional semantic meaning. In these games, all players obtain identical payoffs in every outcome. This is an unrealistic payoff structure, but it is often employed because it is thought that semantic meaning will not emerge if interests conflict. Here it is shown that not only is conventional meaning possible when interests conflict, but it is the most likely outcome in a finite population model of learning known as the Moran process. On the basis of this result it is suggested that evolutionary game theory’s standard models (which presuppose populations that are effectively infinite) may yield results that are systematically distorted for a class of signalling games that have the abstract structure of social dilemmas. 1 Introduction2 The Seduction Game3 Imitation Dynamics with Small Mutations4 Dynamics with Unverifiable Message5 Analysis of a Related Three-Strategy Game6 Conclusion

Some dynamics of signaling games.

Information transfer is a basic feature of life that includes signaling within and between organisms. Owing to its interactive nature, signaling can be investigated by using game theory. Game theoretic models of signaling have a long tradition in biology, economics, and philosophy. For a long time the analyses of these games has mostly relied on using static equilibrium concepts such as Pareto optimal Nash equilibria or evolutionarily stable strategies. More recently signaling games of various types have been investigated with the help of game dynamics, which includes dynamical models of evolution and individual learning. A dynamical analysis leads to more nuanced conclusions as to the outcomes of signaling interactions. Here we explore different kinds of signaling games that range from interactions without conflicts of interest between the players to interactions where their interests are seriously misaligned. We consider these games within the context of evolutionary dynamics (both infinite and finite population models) and learning dynamics (reinforcement learning). Some results are specific features of a particular dynamical model, whereas others turn out to be quite robust across different models. This suggests that there are certain qualitative aspects that are common to many real-world signaling interactions.

A DTN System for Nanosatellite-based Sensor Networks using a New ALOHA Multiple Access with Gateway Priority

This paper presents and evaluates a new communications architecture to provide services to terrestrial sensor networks using a space delay-tolerant networking (DTN)?based solution. We propose a new multiple access mechanism based on extended unslotted ALOHA that takes into account the priority of gateway traffic, which we call ALOHA multiple access with gateway priority (ALOHAGP). We assume a finite sensor population model and a saturated traffic condition where every sensor always has frames to transmit. The performance was evaluated in terms of effective throughput, delay and system fairness. In addition, a DTN convergence layer (ALOHAGP-CL) has been defined as a subset of the standard TCP-CL (Transmission Control Protocol-Convergence Layer). Through simulations, this paper reveals that ALOHAGP/CL adequately supports the proposed DTN scenario, mainly when reactive fragmentation is used.

Estimators for Clustered Education RCTs Using the Neyman Model for Causal Inference

This article examines the estimation of two-stage clustered designs for education randomized control trials (RCTs) using the nonparametric Neyman causal inference framework that underlies experiments. The key distinction between the considered causal models is whether potential treatment and control group outcomes are considered to be fixed for the study population (the finite-population model) or randomly selected from a vaguely defined universe (the super-population model). Both approaches allow for heterogeneity of treatment effects. Appropriate estimation methods and asymptotic moments are discussed for each model using simple differences-in-means estimators and those that include baseline covariates. An empirical application using a large-scale education RCT shows that the choice of the finite- or super-population approach can matter. Thus, the choice of framework and sensitivity analyses should be specified and justified in the analysis protocols.