Theoretical Population Biology最新文献

Interacting Partially Observable DBN to model the dynamics of partially observable metapopulations: Opportunities and open challenges 交互部分可观察DBN来模拟部分可观察元种群的动态：机遇和开放的挑战。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-04-01 Epub Date: 2025-12-26 DOI: 10.1016/j.tpb.2025.12.004

Hanna Bacave , Pierre-Olivier Cheptou , Nathalie Peyrard

Among the mathematical approaches used to model population dynamics, Hidden Markov Models (HMM) are well adapted to the case where the species of interest is difficult to observe. For a broader application of HMM in ecology, two limits need to be overcome. While HMMs can deal with detection errors, another important situation is when only some life stages of the population can be observed while the others remain hidden. The metapopulation level, rather than a single population, makes it possible to incorporate dispersal processes, often linked to hidden life stages. Therefore, there is a need to extend the HMM framework to the case of several couples of hidden and observed life stages interacting via dispersal. We propose a conceptual guide to model and estimate such dynamics using the framework of interacting Partially Observable Dynamic Bayesian Networks (PO-DBN). We show that only four interaction structures are needed to describe the main metapopulation models. We illustrate them on concrete examples. Well known computational challenges apply to inference in metapopulation models with partial observation, due to the problem dimension. We discuss parameter estimation using the EM algorithm and we establish that for two structures the complexity of EM is actually linear in the number of patches, which means that estimation is easily accessible for the associated metapopulations. For the two other structures, the EM complexity is exponential and we discuss methods for approximate inference. This study provides the practical foundations for modelling and estimating the dynamics of a metapopulation with hidden life stages.

在用来模拟种群动态的数学方法中，隐马尔可夫模型（HMM）很好地适应了目标物种难以观察的情况。为了使HMM在生态学中得到更广泛的应用，需要克服两个限制。虽然hmm可以处理检测错误，但另一个重要的情况是，只能观察到种群的某些生命阶段，而其他阶段仍然隐藏。元种群水平，而不是单一种群，使得将分散过程纳入其中成为可能，这些过程通常与隐藏的生命阶段有关。因此，有必要将HMM框架扩展到几对隐藏的和观察到的生命阶段通过分散相互作用的情况。我们提出了一个概念性的指导，使用相互作用的部分可观察动态贝叶斯网络（PO-DBN）框架来建模和估计这种动态。我们表明，仅需要四种相互作用结构来描述主要的元种群模型。我们用具体的例子来说明它们。众所周知，由于问题维度的原因，计算挑战适用于具有部分观测的元种群模型中的推理。我们讨论了使用EM算法的参数估计，并且我们建立了对于两个结构，EM的复杂性实际上在补丁的数量上是线性的，这意味着很容易对相关的元种群进行估计。对于其他两种结构，电磁复杂度是指数的，我们讨论了近似推理的方法。该研究为具有隐藏生命阶段的元种群动力学建模和估计提供了实践基础。

{"title":"Interacting Partially Observable DBN to model the dynamics of partially observable metapopulations: Opportunities and open challenges","authors":"Hanna Bacave , Pierre-Olivier Cheptou , Nathalie Peyrard","doi":"10.1016/j.tpb.2025.12.004","DOIUrl":"10.1016/j.tpb.2025.12.004","url":null,"abstract":"<div><div>Among the mathematical approaches used to model population dynamics, Hidden Markov Models (HMM) are well adapted to the case where the species of interest is difficult to observe. For a broader application of HMM in ecology, two limits need to be overcome. While HMMs can deal with detection errors, another important situation is when only some life stages of the population can be observed while the others remain hidden. The metapopulation level, rather than a single population, makes it possible to incorporate dispersal processes, often linked to hidden life stages. Therefore, there is a need to extend the HMM framework to the case of several couples of hidden and observed life stages interacting via dispersal. We propose a conceptual guide to model and estimate such dynamics using the framework of interacting Partially Observable Dynamic Bayesian Networks (PO-DBN). We show that only four interaction structures are needed to describe the main metapopulation models. We illustrate them on concrete examples. Well known computational challenges apply to inference in metapopulation models with partial observation, due to the problem dimension. We discuss parameter estimation using the EM algorithm and we establish that for two structures the complexity of EM is actually linear in the number of patches, which means that estimation is easily accessible for the associated metapopulations. For the two other structures, the EM complexity is exponential and we discuss methods for approximate inference. This study provides the practical foundations for modelling and estimating the dynamics of a metapopulation with hidden life stages.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"168 ","pages":"Pages 19-31"},"PeriodicalIF":1.3,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145851266","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Evolving genealogies in cultural evolution, the descendant process, and the number of cultural traits 文化演变中的演化谱系，后代的过程，以及文化特征的数量。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-04-01 Epub Date: 2025-12-26 DOI: 10.1016/j.tpb.2025.12.003

Joe Yuichiro Wakano , Hisashi Ohtsuki , Yutaka Kobayashi , Ellen Baake

We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and Ghirlanda (2015) and are closely related to the ancestral selection graph of population genetics, wherefore we call them ancestral learning graphs. We investigate their dynamical behaviour, that is, we are concerned with evolving genealogies. In particular, we consider the total length of the genealogy of the entire population as a function of the (forward) time where we start looking back. This quantity shows a sawtooth-like dynamics with linear increase interrupted by collapses to near-zero at random times. We relate this to the metastable behaviour of the stochastic logistic model, which describes the evolution of the number of ancestors as well as the number of descendants of a given sample.

We superpose types to the model by assuming that new inventions appear independently in every individual, and all traits of the cultural parent are transmitted to the learner in any given learning event. The set of traits of an individual then agrees with the set of innovations along its genealogy. The properties of the genealogy thus translate into the properties of the trait set of a sample. In particular, the moments of the number of traits are obtained from the moments of the total length of the genealogy.

我们考虑了莫兰式的文化进化模型，它描述了特征是如何在群体中出现、传播和消失的。我们的分析侧重于潜在的文化谱系；它们首先由Aguilar和Ghirlanda（2015）描述，并且与群体遗传学的祖先选择图密切相关，因此我们称之为祖先学习图。我们研究它们的动态行为，也就是说，我们关注不断发展的谱系。特别是，我们将整个种群的家谱的总长度视为我们开始回顾的（前）时间的函数。这个量表现出锯齿状的动态，线性增长在随机时间被崩溃中断到接近零。我们将此与随机逻辑模型的亚稳态行为联系起来，该模型描述了给定样本的祖先数量以及后代数量的演变。我们通过假设新的发明在每个个体中独立出现，并且在任何给定的学习事件中，文化父母的所有特征都传递给学习者，从而将类型叠加到模型中。个体的一系列特征与其谱系中的一系列创新相一致。因此，谱系的属性转化为样本特征集的属性。特别地，性状数的矩是由系谱总长度的矩得到的。

{"title":"Evolving genealogies in cultural evolution, the descendant process, and the number of cultural traits","authors":"Joe Yuichiro Wakano , Hisashi Ohtsuki , Yutaka Kobayashi , Ellen Baake","doi":"10.1016/j.tpb.2025.12.003","DOIUrl":"10.1016/j.tpb.2025.12.003","url":null,"abstract":"<div><div>We consider a Moran-type model of cultural evolution, which describes how traits emerge, are transmitted, and get lost in populations. Our analysis focuses on the underlying cultural genealogies; they were first described by Aguilar and Ghirlanda (2015) and are closely related to the ancestral selection graph of population genetics, wherefore we call them <em>ancestral learning graphs</em>. We investigate their dynamical behaviour, that is, we are concerned with <em>evolving genealogies</em>. In particular, we consider the total length of the genealogy of the entire population as a function of the (forward) time where we start looking back. This quantity shows a sawtooth-like dynamics with linear increase interrupted by collapses to near-zero at random times. We relate this to the metastable behaviour of the stochastic logistic model, which describes the evolution of the number of ancestors as well as the number of descendants of a given sample.</div><div>We superpose types to the model by assuming that new inventions appear independently in every individual, and all traits of the cultural parent are transmitted to the learner in any given learning event. The set of traits of an individual then agrees with the set of innovations along its genealogy. The properties of the genealogy thus translate into the properties of the trait set of a sample. In particular, the moments of the number of traits are obtained from the moments of the total length of the genealogy.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"168 ","pages":"Pages 1-18"},"PeriodicalIF":1.3,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145851308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strategies for resolving cellular phylogenies from sequential lineage tracing data 从序列谱系追踪数据中解决细胞系统发育的策略。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-04-01 Epub Date: 2026-01-17 DOI: 10.1016/j.tpb.2026.01.001

Nicola Mulberry , Tanja Stadler

A combination of recent advancements in molecular recording devices and sequencing technologies has made it possible to generate lineage tracing data on the order of thousands of cells. Dynamic lineage recorders are able to generate random, heritable mutations which accumulate continuously on the timescale of developmental processes; this genetic information is then recovered using single-cell RNA sequencing. These data have the potential to hold rich phylogenetic information due to the irreversible nature of the editing process, a key feature of the employed CRISPR-based systems that deviates from traditional assumptions about molecular mutation processes. Recent technologies have furthermore made it possible for mutations to be acquired sequentially. Understanding the information content of these recorders remains an open area of investigation. Here, we model a sequentially-edited recording system and analyse the experimental conditions over which exact phylogenetic reconstruction occurs with high probability. We find, using simulation and theory, explicit parameter regimes over which simple and efficient distance-based reconstruction methods can accurately resolve the cellular phylogeny. We furthermore illustrate how our theoretical results could be used to help inform experimental design.

分子记录设备和测序技术的最新进展使得生成数千个细胞的谱系追踪数据成为可能。动态谱系记录能够产生随机的、可遗传的突变，这些突变在发育过程的时间尺度上不断积累；然后使用单细胞RNA测序来恢复这些遗传信息。由于编辑过程的不可逆性，这些数据有可能包含丰富的系统发育信息，这是基于crispr的系统的一个关键特征，它偏离了关于分子突变过程的传统假设。最近的技术进一步使按顺序获得突变成为可能。了解这些记录仪的信息内容仍然是一个开放的调查领域。在这里，我们建立了一个顺序编辑的记录系统模型，并分析了高概率发生精确系统发育重建的实验条件。我们发现，通过模拟和理论，明确的参数制度，简单有效的基于距离的重建方法可以准确地解决细胞系统发育。我们进一步说明了如何使用我们的理论结果来帮助告知实验设计。

{"title":"Strategies for resolving cellular phylogenies from sequential lineage tracing data","authors":"Nicola Mulberry , Tanja Stadler","doi":"10.1016/j.tpb.2026.01.001","DOIUrl":"10.1016/j.tpb.2026.01.001","url":null,"abstract":"<div><div>A combination of recent advancements in molecular recording devices and sequencing technologies has made it possible to generate lineage tracing data on the order of thousands of cells. Dynamic lineage recorders are able to generate random, heritable mutations which accumulate continuously on the timescale of developmental processes; this genetic information is then recovered using single-cell RNA sequencing. These data have the potential to hold rich phylogenetic information due to the irreversible nature of the editing process, a key feature of the employed CRISPR-based systems that deviates from traditional assumptions about molecular mutation processes. Recent technologies have furthermore made it possible for mutations to be acquired sequentially. Understanding the information content of these recorders remains an open area of investigation. Here, we model a sequentially-edited recording system and analyse the experimental conditions over which exact phylogenetic reconstruction occurs with high probability. We find, using simulation and theory, explicit parameter regimes over which simple and efficient distance-based reconstruction methods can accurately resolve the cellular phylogeny. We furthermore illustrate how our theoretical results could be used to help inform experimental design.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"168 ","pages":"Pages 32-43"},"PeriodicalIF":1.3,"publicationDate":"2026-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146004778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

A clarification of historical concepts of effective population size and their applicability to subdivided populations 澄清有效人口规模的历史概念及其对细分人口的适用性。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-02-01 Epub Date: 2025-12-06 DOI: 10.1016/j.tpb.2025.12.002

Warren Ewens , Ola Hössjer

The great population geneticist Sewall Wright had a lifelong interest in animal breeding programs. He was concerned that, in these programs, genetic variation would tend to be lost (as measured by him in a tendency for genetic heterozygosity to decrease) when a small number of males is mated to a comparatively large number of females. The calculations in his great 1931 paper were designed to quantify this tendency. Decades later other authors noted further cases when population genetic heterozygosity tended to be lost, a classic example being that of a population whose size changes cyclically with some small population sizes arising during the cycle. These observations led to several definitions of the effective population size. Perhaps the two most frequently discussed in the literature are the inbreeding effective population size and the variance effective population size. The first aim of this note is to show that Wright’s (1931) calculations for two-sex populations relate to neither of these, and instead to the far less discussed eigenvalue effective population size. The second aim is to critically assess all three effective population sizes and put two-sex populations into a wider concept of subdivided populations. This analysis reveals some new results, and for two-sex populations without other types of subdivision, we conclude that the eigenvalue effective size is the most relevant type of effective size.

伟大的种群遗传学家休厄尔·赖特（Sewall Wright）一生都对动物育种项目感兴趣。他担心，在这些项目中，当少数雄性与相对较多的雌性交配时，遗传变异可能会丢失（他以遗传杂合性降低的趋势来衡量）。他在1931年的伟大论文中所做的计算就是为了量化这种趋势。几十年后，其他作者注意到群体遗传杂合性趋于丧失的进一步情况，一个典型的例子是，一个群体的规模周期性地变化，在这个周期中出现一些小的群体规模。这些观察结果导致了有效种群大小的几个定义。文献中最常讨论的两个问题可能是近交有效种群大小和方差有效种群大小。本文的第一个目的是表明Wright（1931）对两性种群的计算与上述两种都不相关，而是与较少讨论的特征值有效种群大小有关。第二个目标是严格评估所有三种有效种群规模，并将两性种群纳入更广泛的细分种群概念。本分析揭示了一些新的结果，对于没有其他类型细分的两性群体，我们得出特征值有效大小是最相关的有效大小类型。

{"title":"A clarification of historical concepts of effective population size and their applicability to subdivided populations","authors":"Warren Ewens , Ola Hössjer","doi":"10.1016/j.tpb.2025.12.002","DOIUrl":"10.1016/j.tpb.2025.12.002","url":null,"abstract":"<div><div>The great population geneticist Sewall Wright had a lifelong interest in animal breeding programs. He was concerned that, in these programs, genetic variation would tend to be lost (as measured by him in a tendency for genetic heterozygosity to decrease) when a small number of males is mated to a comparatively large number of females. The calculations in his great 1931 paper were designed to quantify this tendency. Decades later other authors noted further cases when population genetic heterozygosity tended to be lost, a classic example being that of a population whose size changes cyclically with some small population sizes arising during the cycle. These observations led to several definitions of the effective population size. Perhaps the two most frequently discussed in the literature are the inbreeding effective population size and the variance effective population size. The first aim of this note is to show that Wright’s (1931) calculations for two-sex populations relate to neither of these, and instead to the far less discussed eigenvalue effective population size. The second aim is to critically assess all three effective population sizes and put two-sex populations into a wider concept of subdivided populations. This analysis reveals some new results, and for two-sex populations without other types of subdivision, we conclude that the eigenvalue effective size is the most relevant type of effective size.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"167 ","pages":"Pages 11-21"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145709995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Correlation of coalescence times in a diploid Wright–Fisher model with recombination and selfing 二倍体Wright-Fisher模型中合并时间与重组和自交的相关性。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-02-01 Epub Date: 2025-12-10 DOI: 10.1016/j.tpb.2025.11.003

David Kogan , Dimitrios Diamantidis , John Wakeley , Louis Wai-Tong Fan

The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population structure. Based on a diploid Wright–Fisher model with partial selfing and a single mating type for a constant large population of size

N

, we quantify the combined effects of genetic drift and two competing factors, recombination and selfing, on the correlation of coalescence times at two linked loci for samples of size two. Recombination decouples the genealogies at different loci and decreases the correlation while selfing increases the correlation. We obtain explicit asymptotic formulas for the correlation under four different scaling scenarios depending on whether the selfing probability and the recombination probability are of order

O (1 / N)

or

O (1)

as

N

tends to infinity. Our analytical results show that the asymptotic lower bound in King et al. (2018) is sharp when the loci are unlinked and when there is no selfing, and provide a number of new formulas for other scaling scenarios that have not been considered before. We present asymptotic results for the variance of Tajima’s estimator of the population mutation rate for infinitely many loci as

N

tends to infinity. When the selfing probability is of order

O (1)

and is equal to a positive constant

s

for all

N

and if the samples at both loci are in the same individual, then the variance of the Tajima’s estimator tends to

s / 2

(hence remains positive) even when the recombination rate, the number of loci and the population size all tend to infinity.

不同基因座的基因谱系之间的相关性在生物学中是至关重要的，但由于这种相关性取决于包括遗传连锁、重组、自然选择和群体结构在内的许多因素，因此很难理解。基于一个具有部分自交和单一交配类型的二倍体Wright-Fisher模型，我们量化了遗传漂变和两个竞争因素（重组和自交）对两个连锁基因座合并时间相关性的影响。重组对不同基因座的家谱进行了解耦，降低了相关性，而自适应则增加了相关性。当N趋于无穷时，根据自旋概率和重组概率是O（1/N）阶还是O(1)阶，我们得到了四种不同尺度下的相关性的显式渐近公式。我们的分析结果表明，King等人（2018）的渐近下界在位点不链接和不存在自交时是尖锐的，并为以前未考虑过的其他缩放场景提供了许多新的公式。当N趋于无穷时，我们给出了无穷多个位点种群突变率的Tajima估计量方差的渐近结果。当自适应概率为O(1)阶且等于一个正常数s时，如果两个位点的样本都在同一个体中，那么即使重组率、位点数量和总体大小都趋于无穷大，Tajima估计量的方差也趋于s/2（因此仍然为正）。

{"title":"Correlation of coalescence times in a diploid Wright–Fisher model with recombination and selfing","authors":"David Kogan , Dimitrios Diamantidis , John Wakeley , Louis Wai-Tong Fan","doi":"10.1016/j.tpb.2025.11.003","DOIUrl":"10.1016/j.tpb.2025.11.003","url":null,"abstract":"<div><div>The correlation among the gene genealogies at different loci is crucial in biology, yet challenging to understand because such correlation depends on many factors including genetic linkage, recombination, natural selection and population structure. Based on a diploid Wright–Fisher model with partial selfing and a single mating type for a constant large population of size <span><math><mi>N</mi></math></span>, we quantify the combined effects of genetic drift and two competing factors, recombination and selfing, on the correlation of coalescence times at two linked loci for samples of size two. Recombination decouples the genealogies at different loci and decreases the correlation while selfing increases the correlation. We obtain explicit asymptotic formulas for the correlation under four different scaling scenarios depending on whether the selfing probability and the recombination probability are of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>/</mo><mi>N</mi><mo>)</mo></mrow></mrow></math></span> or <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> as <span><math><mi>N</mi></math></span> tends to infinity. Our analytical results show that the asymptotic lower bound in King et al. (2018) is sharp when the loci are unlinked and when there is no selfing, and provide a number of new formulas for other scaling scenarios that have not been considered before. We present asymptotic results for the variance of Tajima’s estimator of the population mutation rate for infinitely many loci as <span><math><mi>N</mi></math></span> tends to infinity. When the selfing probability is of order <span><math><mrow><mi>O</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> and is equal to a positive constant <span><math><mi>s</mi></math></span> for all <span><math><mi>N</mi></math></span> and if the samples at both loci are in the same individual, then the variance of the Tajima’s estimator tends to <span><math><mrow><mi>s</mi><mo>/</mo><mn>2</mn></mrow></math></span> (hence remains positive) even when the recombination rate, the number of loci and the population size all tend to infinity.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"167 ","pages":"Pages 40-68"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145745457","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strong information delay as a driver of epidemic waves: Mathematical modeling for drug trends and epidemic bio-preparedness 强信息延迟作为流行病波的驱动因素：药物趋势和流行病生物准备的数学模型。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-02-01 Epub Date: 2025-12-05 DOI: 10.1016/j.tpb.2025.11.002

Martina Bouka , W. Christopher Strickland

Avoidance behaviors can have a substantial influence on both the spread of an infectious disease and on the long-term dynamics of substance use disorder. However, this behavior is typically reactive based on delayed information related to personal risk as well as both the length of exposure to and retention of that information. This suggests that in epidemic models, feedback delays should be strong — that is, not exponentially distributed (Erlang-1) but instead peaking at a point strictly in the past (Erlang-2 or greater). However, almost all studies of infectivity feedback delays are exponential with qualitatively different results than are seen with strong delays. To address this gap, we analyze two compartmental models for infectious disease epidemiology. Our results demonstrate that sustained oscillations in the total number of active cases may appear even as early as the first two years of an outbreak, suggesting that human behavior may be an explanatory factor for periodic fluctuations evident in recent pandemic time-series data (e.g. COVID-19). We then extend our analysis to a study of the role of information feedback on substance use disorder epidemiology, with a focus on both the transient and asymptotic dynamics of drug waves. We show that under certain conditions, oscillations in substance use disorder can become sustained and that models without strong feedback delays can fail to produce important qualitative transient behavior in substance use incidence rates. To our knowledge, this work represents the first mathematical model exhibiting oscillations with non-contact (linear) pathways to substance use disorder.

回避行为对传染病的传播和物质使用障碍的长期动态都有重大影响。然而，这种行为通常是基于与个人风险相关的延迟信息以及暴露于该信息的时间长度和保留时间的反应性行为。这表明，在流行病模型中，反馈延迟应该是强的——也就是说，不是指数分布（Erlang-1），而是严格在过去的某个点达到峰值（Erlang-2或更大）。然而，几乎所有传染性反馈延迟的研究都是指数型的，其结果与强延迟的结果在质量上有所不同。为了解决这一差距，我们分析了传染病流行病学的两个隔间模型。我们的研究结果表明，活跃病例总数的持续振荡甚至可能早在疫情暴发的头两年就出现，这表明人类行为可能是最近大流行时间序列数据（例如COVID-19）中明显的周期性波动的一个解释因素。然后，我们将分析扩展到信息反馈对物质使用障碍流行病学的作用的研究，重点关注药物波的瞬态和渐近动力学。我们表明，在某些条件下，物质使用障碍的振荡可以持续，没有强反馈延迟的模型可能无法在物质使用发生率中产生重要的定性瞬态行为。据我们所知，这项工作代表了第一个显示非接触（线性）物质使用障碍振荡的数学模型。

{"title":"Strong information delay as a driver of epidemic waves: Mathematical modeling for drug trends and epidemic bio-preparedness","authors":"Martina Bouka , W. Christopher Strickland","doi":"10.1016/j.tpb.2025.11.002","DOIUrl":"10.1016/j.tpb.2025.11.002","url":null,"abstract":"<div><div>Avoidance behaviors can have a substantial influence on both the spread of an infectious disease and on the long-term dynamics of substance use disorder. However, this behavior is typically reactive based on delayed information related to personal risk as well as both the length of exposure to and retention of that information. This suggests that in epidemic models, feedback delays should be strong — that is, not exponentially distributed (Erlang-1) but instead peaking at a point strictly in the past (Erlang-2 or greater). However, almost all studies of infectivity feedback delays are exponential with qualitatively different results than are seen with strong delays. To address this gap, we analyze two compartmental models for infectious disease epidemiology. Our results demonstrate that sustained oscillations in the total number of active cases may appear even as early as the first two years of an outbreak, suggesting that human behavior may be an explanatory factor for periodic fluctuations evident in recent pandemic time-series data (e.g. COVID-19). We then extend our analysis to a study of the role of information feedback on substance use disorder epidemiology, with a focus on both the transient and asymptotic dynamics of drug waves. We show that under certain conditions, oscillations in substance use disorder can become sustained and that models without strong feedback delays can fail to produce important qualitative transient behavior in substance use incidence rates. To our knowledge, this work represents the first mathematical model exhibiting oscillations with non-contact (linear) pathways to substance use disorder.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"167 ","pages":"Pages 22-39"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145702781","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

What drives bacterial extinction? The role of bacteriophages 是什么导致了细菌的灭绝？噬菌体的作用

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2026-02-01 Epub Date: 2025-12-10 DOI: 10.1016/j.tpb.2025.12.001

Mark M. Tanaka , Lindi M. Wahl

Bacterial lineages are relatively short-lived on geological timescales, according to phylogenetic analyses, implying that bacterial extinction occurs at high rates. Since the vast majority of bacteria live in large populations in oceans and soils, many well-studied extinction mechanisms, such as demographic or environmental stochasticity, seem unlikely to drive this pattern. We outline mechanisms for the extinction of large bacterial populations, and discuss the emergence of a new virus as a possible cause of extinction. We use deterministic and stochastic models to characterise the persistence of a bacterial population, demonstrating that when resistance to a new virus does not emerge, large populations are more likely to go extinct than small populations, which contrasts with classically studied extinction mechanisms. When they go extinct, large populations also reach extinction more quickly. When phage-resistant bacteria appear, extinction is rare but its probability increases with population size in some parameter regimes. We also quantify bacterial extinction in spatially distinct subpopulations. We conclude that large bacterial populations are robust to many extinction mechanisms, and typically evolve resistance to new phages, as observed empirically. For bacterial lineages that have gone extinct, however, the failure to evolve resistance to a novel phage is a likely underlying mechanism.

根据系统发育分析，细菌谱系在地质时间尺度上相对较短，这意味着细菌灭绝的速度很快。由于绝大多数细菌在海洋和土壤中大量生活，许多经过充分研究的灭绝机制，如人口统计学或环境随机性，似乎不太可能驱动这种模式。我们概述了大型细菌种群灭绝的机制，并讨论了一种新病毒的出现作为灭绝的可能原因。我们使用确定性和随机模型来描述细菌种群的持久性，证明当没有出现对新病毒的抗性时，大种群比小种群更有可能灭绝，这与经典研究的灭绝机制形成对比。当它们灭绝时，大量种群也会更快地灭绝。当出现抗噬菌体细菌时，灭绝是罕见的，但在某些参数制度下，其概率随着种群规模的增加而增加。我们还量化了空间上不同亚群的细菌灭绝。我们得出结论，根据经验观察，大量细菌种群对许多灭绝机制都很强大，并且通常会进化出对新的噬菌体的抗性。然而，对于已经灭绝的细菌谱系来说，未能进化出对新型噬菌体的抗性可能是一种潜在的机制。

{"title":"What drives bacterial extinction? The role of bacteriophages","authors":"Mark M. Tanaka , Lindi M. Wahl","doi":"10.1016/j.tpb.2025.12.001","DOIUrl":"10.1016/j.tpb.2025.12.001","url":null,"abstract":"<div><div>Bacterial lineages are relatively short-lived on geological timescales, according to phylogenetic analyses, implying that bacterial extinction occurs at high rates. Since the vast majority of bacteria live in large populations in oceans and soils, many well-studied extinction mechanisms, such as demographic or environmental stochasticity, seem unlikely to drive this pattern. We outline mechanisms for the extinction of large bacterial populations, and discuss the emergence of a new virus as a possible cause of extinction. We use deterministic and stochastic models to characterise the persistence of a bacterial population, demonstrating that when resistance to a new virus does not emerge, large populations are more likely to go extinct than small populations, which contrasts with classically studied extinction mechanisms. When they go extinct, large populations also reach extinction more quickly. When phage-resistant bacteria appear, extinction is rare but its probability increases with population size in some parameter regimes. We also quantify bacterial extinction in spatially distinct subpopulations. We conclude that large bacterial populations are robust to many extinction mechanisms, and typically evolve resistance to new phages, as observed empirically. For bacterial lineages that have gone extinct, however, the failure to evolve resistance to a novel phage is a likely underlying mechanism.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"167 ","pages":"Pages 1-10"},"PeriodicalIF":1.3,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145712493","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

An equal-tempered measure of linkage disequilibrium 连杆不平衡的一种均匀测量。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-12-01 Epub Date: 2025-09-12 DOI: 10.1016/j.tpb.2025.09.002

Mark M. Tanaka

Linkage disequilibrium (LD), the association of alleles at two loci, is defined in multiple ways. Because LD measures depend on allele frequencies, it is difficult to compare LD values between populations or loci with different allele frequencies. Here, I consider a geometric interpretation of a commonly used LD measure

r^{2}

which suggests a modification that is frequency-independent in the sense that equal evolutionary forces lead to the same effect at different frequencies. This new measure is a very simple expression that is known elsewhere as the Hamann coefficient and the G index of agreement; it is a linear transformation of the simple matching coefficient. I explore properties of this quantity in comparison with

D

and

r^{2}

, and discuss its interpretation, advantages and disadvantages.

连锁不平衡（LD），等位基因在两个位点的关联，有多种定义。由于LD测量依赖于等位基因频率，因此很难比较具有不同等位基因频率的种群或位点之间的LD值。在这里，我考虑了常用的LD测量r2的几何解释，它表明了一种频率无关的修改，即相等的进化力在不同频率上导致相同的效果。这个新度量是一个非常简单的表达式，在其他地方被称为哈曼系数和G一致指数；它是简单匹配系数的线性变换。通过与D和r2的比较，探讨了这个量的性质，并讨论了它的解释和优缺点。

引用次数: 0

Consistency and central limit results for the maximum likelihood estimator in the Admixture Model 混合模型中最大似然估计量的一致性和中心极限结果

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-12-01 Epub Date: 2025-10-08 DOI: 10.1016/j.tpb.2025.10.001

Carola Sophia Heinzel

In the Admixture Model, the probability of an individual having a certain number of alleles at a specific marker depends on the allele frequencies in

K

ancestral populations and the fraction of the individual’s genome originating from these ancestral populations.

This study investigates consistency and central limit results of maximum likelihood estimators (MLEs) for the ancestry and the allele frequencies in the Admixture Model, complimenting previous work by Pfaff et al. (2004); Pfaffelhuber and Rohde (2022). Specifically, we prove consistency of the MLE, if we estimate the allele frequencies and the ancestries. Furthermore, we prove central limit theorems, if we estimate the ancestry of a finite number of individuals and the allele frequencies of finitely many markers, also addressing the case where the true ancestry lies on the boundary of the parameter space.

Finally, we use the new theory to quantify the uncertainty of the MLEs for the data of the 1000 Genomes Project.

在混合模型中，个体在特定标记上具有一定数量等位基因的概率取决于K个祖先群体中的等位基因频率和个体基因组中来自这些祖先群体的部分。本研究调查了混合模型中祖先和等位基因频率的最大似然估计（MLEs）的一致性和中心极限结果，补充了Pfaff等人（2004）的先前工作；Pfaffelhuber and Rohde（2022）。具体来说，如果我们估计等位基因频率和祖先，我们证明了MLE的一致性。此外，我们证明了中心极限定理，如果我们估计有限个个体的祖先和有限个标记的等位基因频率，也解决了真正的祖先位于参数空间边界的情况。最后，我们利用新理论量化了千人基因组计划数据的mle的不确定性。

引用次数: 0

The Feller diffusion conditioned on a single ancestral founder 费勒扩散以一个单一的祖先奠基人为条件。

IF 1.3 4区生物学 Q4 ECOLOGY

Theoretical Population Biology

Pub Date : 2025-12-01 Epub Date: 2025-09-10 DOI: 10.1016/j.tpb.2025.09.001

Conrad J. Burden , Robert C. Griffiths

We examine the distributional properties of a Feller diffusion

{(X (τ))}_{τ \in [0, t]}

conditioned on the current population

X (t)

having a single ancestor at time zero. The approach is novel and is based on an interpretation of Feller’s original solution according to which the current population is comprised of a Poisson number of exponentially distributed families, each descended from a single ancestor. The distribution of the number of ancestors at intermediate times and the joint density of coalescent times is determined under assumptions of initiation of the process from a single ancestor at a specified time in the past, including infinitely far in the past, and for the case of a uniform prior on the time since initiation. Also calculated are the joint distribution of the time since the most recent common ancestor of the current population and the contemporaneous population size at that time under different assumptions on the time since initiation. In each case exact solutions are given for supercritical, critical and subcritical diffusions. For supercritical diffusions asymptotic forms of distributions are also given in the limit of unbounded exponential growth.

我们研究了Feller扩散(X(τ))τ∈[0，t]的分布特性，条件是当前种群X(t)在时间0时具有单一祖先。该方法是新颖的，基于Feller原始解决方案的解释，根据该解决方案，当前种群由指数分布的家族的泊松数组成，每个家族都来自单个祖先。中间时间的祖先数量分布和接合时间的联合密度是在以下假设下确定的：在过去的特定时间，包括无限远的过去，从一个单一的祖先开始这个过程，以及在开始后的时间有一个均匀的先验。还计算了当前种群从最近的共同祖先开始的时间的联合分布，以及当时在不同假设下的同期种群规模。在每种情况下，都给出了超临界、临界和亚临界扩散的精确解。对于超临界扩散，给出了无界指数增长极限下分布的渐近形式。

{"title":"The Feller diffusion conditioned on a single ancestral founder","authors":"Conrad J. Burden , Robert C. Griffiths","doi":"10.1016/j.tpb.2025.09.001","DOIUrl":"10.1016/j.tpb.2025.09.001","url":null,"abstract":"<div><div>We examine the distributional properties of a Feller diffusion <span><math><msub><mrow><mrow><mo>(</mo><mrow><mi>X</mi><mrow><mo>(</mo><mi>τ</mi><mo>)</mo></mrow></mrow><mo>)</mo></mrow></mrow><mrow><mi>τ</mi><mo>∈</mo><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>t</mi><mo>]</mo></mrow></mrow></msub></math></span> conditioned on the current population <span><math><mrow><mi>X</mi><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></mrow></math></span> having a single ancestor at time zero. The approach is novel and is based on an interpretation of Feller’s original solution according to which the current population is comprised of a Poisson number of exponentially distributed families, each descended from a single ancestor. The distribution of the number of ancestors at intermediate times and the joint density of coalescent times is determined under assumptions of initiation of the process from a single ancestor at a specified time in the past, including infinitely far in the past, and for the case of a uniform prior on the time since initiation. Also calculated are the joint distribution of the time since the most recent common ancestor of the current population and the contemporaneous population size at that time under different assumptions on the time since initiation. In each case exact solutions are given for supercritical, critical and subcritical diffusions. For supercritical diffusions asymptotic forms of distributions are also given in the limit of unbounded exponential growth.</div></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"166 ","pages":"Pages 1-15"},"PeriodicalIF":1.3,"publicationDate":"2025-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145056113","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0