J. Garnier , O. Cotto , E. Bouin , T. Bourgeron , T. Lepoutre , O. Ronce , V. Calvez
{"title":"Adaptation of a quantitative trait to a changing environment: New analytical insights on the asexual and infinitesimal sexual models","authors":"J. Garnier , O. Cotto , E. Bouin , T. Bourgeron , T. Lepoutre , O. Ronce , V. Calvez","doi":"10.1016/j.tpb.2023.04.002","DOIUrl":"10.1016/j.tpb.2023.04.002","url":null,"abstract":"<div><p>Predicting the adaptation of populations to a changing environment is crucial to assess the impact of human activities on biodiversity. Many theoretical studies have tackled this issue by modeling the evolution of quantitative traits subject to stabilizing selection around an optimal phenotype, whose value is shifted continuously through time. In this context, the population fate results from the equilibrium distribution of the trait, relative to the moving optimum. Such a distribution may vary with the shape of selection, the system of reproduction, the number of loci, the mutation kernel or their interactions. Here, we develop a methodology that provides quantitative measures of population maladaptation and potential of survival directly from the entire profile of the phenotypic distribution, without any a priori on its shape. We investigate two different systems of reproduction (asexual and infinitesimal sexual models of inheritance), with various forms of selection. In particular, we recover that fitness functions such that selection weakens away from the optimum lead to evolutionary tipping points, with an abrupt collapse of the population when the speed of environmental change is too high. Our unified framework allows deciphering the mechanisms that lead to this phenomenon. More generally, it allows discussing similarities and discrepancies between the two systems of reproduction, which are ultimately explained by different constraints on the evolution of the phenotypic variance. We demonstrate that the mean fitness in the population crucially depends on the shape of the selection function in the infinitesimal sexual model, in contrast with the asexual model. In the asexual model, we also investigate the effect of the mutation kernel and we show that kernels with higher kurtosis tend to reduce maladaptation and improve fitness, especially in fast changing environments.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"152 ","pages":"Pages 1-22"},"PeriodicalIF":1.4,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9761248","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}
{"title":"A cultural evolutionary model of the interaction between parental beliefs and behaviors, with applications to vaccine hesitancy","authors":"Kerri-Ann Anderson, Nicole Creanza","doi":"10.1016/j.tpb.2023.04.003","DOIUrl":"10.1016/j.tpb.2023.04.003","url":null,"abstract":"<div><p>Health perceptions and health-related behaviors can change at the population level as cultures evolve. In the last decade, despite the proven efficacy of vaccines, the developed world has seen a resurgence of vaccine-preventable diseases (VPDs) such as measles, pertussis, and polio. Vaccine hesitancy, which is influenced by historical, political, and socio-cultural forces, is believed to be a primary factor responsible for decreasing vaccine coverage, thereby increasing the risk and occurrence of VPD outbreaks. Behavior change models have been increasingly employed to understand disease dynamics and intervention effectiveness. However, since health behaviors are culturally influenced, it is valuable to examine them within a cultural evolution context. Here, using a mathematical modeling framework, we explore the effects of cultural evolution on vaccine hesitancy and vaccination behavior. With this model, we shed light on facets of cultural evolution (vertical transmission, community influences, homophily, etc.) that promote the spread of vaccine hesitancy, ultimately affecting levels of vaccination coverage and VPD outbreak risk in a population. In addition, we present our model as a generalizable framework for exploring cultural evolution when humans’ beliefs influence, but do not strictly dictate, their behaviors. This model offers a means of exploring how parents’ potentially conflicting beliefs and cultural traits could affect their children’s health and fitness. We show that vaccine confidence and vaccine-conferred benefits can both be driving forces of vaccine coverage. We also demonstrate that an assortative preference among vaccine-hesitant individuals can lead to increased vaccine hesitancy and lower vaccine coverage.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"152 ","pages":"Pages 23-38"},"PeriodicalIF":1.4,"publicationDate":"2023-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9706795","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}
Michel Benaïm , Claude Lobry , Tewfik Sari , Édouard Strickler
{"title":"Untangling the role of temporal and spatial variations in persistence of populations","authors":"Michel Benaïm , Claude Lobry , Tewfik Sari , Édouard Strickler","doi":"10.1016/j.tpb.2023.07.003","DOIUrl":"10.1016/j.tpb.2023.07.003","url":null,"abstract":"<div><p>We consider a population distributed between two habitats, in each of which it experiences a growth rate that switches periodically between two values, <span><math><mrow><mn>1</mn><mo>−</mo><mi>ɛ</mi><mo>></mo><mn>0</mn></mrow></math></span> or <span><math><mrow><mo>−</mo><mrow><mo>(</mo><mn>1</mn><mo>+</mo><mi>ɛ</mi><mo>)</mo></mrow><mo><</mo><mn>0</mn></mrow></math></span>. We study the specific case where the growth rate is positive in one habitat and negative in the other one for the first half of the period, and conversely for the second half of the period, that we refer as the <span><math><mrow><mo>(</mo><mo>±</mo><mn>1</mn><mo>)</mo></mrow></math></span> model. In the absence of migration, the population goes to 0 exponentially fast in each environment. In this paper, we show that, when the period is sufficiently large, a small dispersal between the two patches is able to produce a very high positive exponential growth rate for the whole population, a phenomena called inflation. We prove in particular that the threshold of the dispersal rate at which the inflation appears is exponentially small with the period. We show that inflation is robust to random perturbation, by considering a model where the values of the growth rate in each patch are switched at random times: we prove that inflation occurs for low switching rate and small dispersal. We also consider another stochastic model, where after each period of time <span><math><mi>T</mi></math></span>, the values of the growth rates in each patch is chosen randomly, independently from the other patch and from the past. Finally, we provide some extensions to more complicated models, especially epidemiological and density dependent models.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"154 ","pages":"Pages 1-26"},"PeriodicalIF":1.4,"publicationDate":"2023-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9976615","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}
{"title":"Digenic genotypes: The interface of inbreeding, linkage, and linkage disequilibrium","authors":"Reginald D. Smith","doi":"10.1016/j.tpb.2023.03.003","DOIUrl":"10.1016/j.tpb.2023.03.003","url":null,"abstract":"<div><p>Many traits in populations are well understood as being Mendelian effects at single loci or additive polygenic effects across numerous loci. However, there are important phenomena and traits that are intermediate between these two extremes and are known as oligogenic traits. Here we investigate digenic, or two-locus, traits and how their frequencies in populations are affected by non-random mating, specifically inbreeding, linkage disequilibrium, and selection. These effects are examined both separately and in combination to demonstrate how many digenic traits, especially double homozygous ones, can show significant, sometimes unexpected, changes in population frequency with inbreeding, linkage, and linkage disequilibrium. The effects of selection on deleterious digenic traits are also detailed. These results are applied to both digenic traits of medical significance as well as measuring inbreeding in natural populations.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"151 ","pages":"Pages 1-18"},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10043390","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}
{"title":"Waiting times in a branching process model of colorectal cancer initiation","authors":"Ruibo Zhang, Obinna A. Ukogu, Ivana Bozic","doi":"10.1016/j.tpb.2023.04.001","DOIUrl":"10.1016/j.tpb.2023.04.001","url":null,"abstract":"<div><p>We study a multi-stage model for the development of colorectal cancer from initially healthy tissue. The model incorporates a complex sequence of driver gene alterations, some of which result in immediate growth advantage, while others have initially neutral effects. We derive analytic estimates for the sizes of premalignant subpopulations, and use these results to compute the waiting times to premalignant and malignant genotypes. This work contributes to the quantitative understanding of colorectal tumor evolution and the lifetime risk of colorectal cancer.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"151 ","pages":"Pages 44-63"},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10061689","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}
{"title":"Copuling population dynamics and diel migration patterns","authors":"Emil F. Frølich","doi":"10.1016/j.tpb.2023.03.004","DOIUrl":"10.1016/j.tpb.2023.03.004","url":null,"abstract":"<div><p>The diel vertical migration is one of the main drivers of population dynamics in the ocean. Population dynamical models of the ocean typically do not incorporate the behavioral aspects of the migration. We demonstrate a model with coupled population dynamics and behavior with the diel vertical migration emerging. We study the population dynamics and behavioral dynamics of a predator–prey system. We impose a cost of motion for both consumers and prey, and model each individual as following an Itô stochastic differential equation. We study the fixed-points of the ecosystem. Our modeling shows that as we increase the basal resource load, the strength of the diel vertical migration increases, as well as maximal velocity. In addition, a bimodal pattern emerges both for predators and consumers. The increase in the magnitude of the diel vertical migration causes a change in the allocation of copepod resources.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"151 ","pages":"Pages 19-27"},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9687761","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}
{"title":"Evolution with recombination as Gibbs sampling","authors":"Jenny M. Poulton , Lee Altenberg , Chris Watkins","doi":"10.1016/j.tpb.2023.03.005","DOIUrl":"10.1016/j.tpb.2023.03.005","url":null,"abstract":"<div><p>This work presents a population genetic model of evolution, which includes haploid selection, mutation, recombination, and drift. The mutation-selection equilibrium can be expressed exactly in closed form for arbitrary fitness functions without resorting to diffusion approximations. Tractability is achieved by generating new offspring using n-parent rather than 2-parent recombination. While this enforces linkage equilibrium among offspring, it allows analysis of the whole population under linkage disequilibrium. We derive a general and exact relationship between fitness fluctuations and response to selection. Our assumptions allow analytical calculation of the stationary distribution of the model for a variety of non-trivial fitness functions. These results allow us to speak to genetic architecture, i.e., what stationary distributions result from different fitness functions. This paper presents methods for exactly deriving stationary states for finite and infinite populations. This method can be applied to many fitness functions, and we give exact calculations for four of these. These results allow us to investigate metastability, tradeoffs between fitness functions, and even consider error-correcting codes.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"151 ","pages":"Pages 28-43"},"PeriodicalIF":1.4,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10043403","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}
Siddharth S. Tomar, Aurélie Hua-Van, Arnaud Le Rouzic
{"title":"A population genetics theory for piRNA-regulated transposable elements","authors":"Siddharth S. Tomar, Aurélie Hua-Van, Arnaud Le Rouzic","doi":"10.1016/j.tpb.2023.02.001","DOIUrl":"10.1016/j.tpb.2023.02.001","url":null,"abstract":"<div><p><span>Transposable elements (TEs) are self-reproducing selfish DNA sequences that can invade the genome of virtually all living species. </span>Population genetics<span> models have shown that TE copy numbers generally reach a limit, either because the transposition rate decreases with the number of copies (transposition regulation) or because TE copies are deleterious, and thus purged by natural selection. Yet, recent empirical discoveries suggest that TE regulation may mostly rely on piRNAs, which require a specific mutational event (the insertion of a TE copy in a piRNA cluster) to be activated — the so-called TE regulation “trap model”. We derived new population genetics models accounting for this trap mechanism, and showed that the resulting equilibria differ substantially from previous expectations based on a transposition–selection equilibrium. We proposed three sub-models, depending on whether or not genomic TE copies and piRNA cluster TE copies are selectively neutral or deleterious, and we provide analytical expressions for maximum and equilibrium copy numbers, as well as cluster frequencies for all of them. In the full neutral model, the equilibrium is achieved when transposition is completely silenced, and this equilibrium does not depend on the transposition rate. When genomic TE copies are deleterious but not cluster TE copies, no long-term equilibrium is possible, and active TEs are eventually eliminated after an active incomplete invasion stage. When all TE copies are deleterious, a transposition–selection equilibrium exists, but the invasion dynamics is not monotonic, and the copy number peaks before decreasing. Mathematical predictions were in good agreement with numerical simulations, except when genetic drift and/or linkage disequilibrium dominates. Overall, the trap-model dynamics appeared to be substantially more stochastic and less repeatable than traditional regulation models.</span></p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"150 ","pages":"Pages 1-13"},"PeriodicalIF":1.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9622940","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}
{"title":"Stability of Rosenzweig–MacArthur models with non-diffusive dispersal on non-regular networks","authors":"Ryusuke Kon , Dinesh Kumar","doi":"10.1016/j.tpb.2023.02.002","DOIUrl":"10.1016/j.tpb.2023.02.002","url":null,"abstract":"<div><p>This paper examines the stability of the Rosenzweig–MacArthur model distributed to identical discrete habitat patches. Migration between patches is assumed to follow the non-diffusive rule that individuals have a fixed rate of leaving their local habitat patch and migrating to another. Under this non-diffusive migration rule, we found that population dispersal on a non-regular and connected habitat network can both stabilize and destabilize the Rosenzweig–MacArthur model. It is also shown that our non-diffusive migration rule apparently becomes diffusive if the habitat network is regular.</p></div>","PeriodicalId":49437,"journal":{"name":"Theoretical Population Biology","volume":"150 ","pages":"Pages 14-22"},"PeriodicalIF":1.4,"publicationDate":"2023-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"9274031","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}