Relevant bibliographies by topics / Plant population genetics Mathematical models

Academic literature on the topic 'Plant population genetics Mathematical models'

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Published: 10 December 2022
Last updated: 28 January 2023

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Journal articles on the topic "Plant population genetics Mathematical models"

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Peck, Joel R., Guillaume Barreau, and Simon C. Heath. "Imperfect Genes, Fisherian Mutation and the Evolution of Sex." Genetics 145, no. 4 (April 1, 1997): 1171–99. http://dx.doi.org/10.1093/genetics/145.4.1171.

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In this paper we present a mathematical model of mutation and selection that allows for the coexistence of multiple alleles at a locus with very small selective differences between alleles. The model also allows for the determination of fitness by multiple loci. Models of this sort are biologically plausible. However, some previous attempts to construct similar models have assumed that all mutations produce a decrease in fitness, and this has led to a tendency for the average fitness of population members to decline when population numbers are finite. In our model we incorporate some of the ideas of R. A. Fisher, so that both deleterious and beneficial mutations are possible. As a result, average fitness tends to approach a stationary distribution. We have used computer simulation methods to apply the Fisherian mutation model to the problem of the evolution of sex and recombination. The results suggest that sex and recombination can provide very large benefits in terms of average fitness. The results also suggest that obligately sexual species will win ecological competitions with species that produce a substantial fraction of their offspring asexually, so long as the number of sites under selection within the genomes of the competing species is not too small and the population sizes are not too large. Our model focuses on fertility selection in an hermaphroditic plant. However, the results are likely to generalize to a wide variety of other situations as well.
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Evans, G. M., and Taing Aung. "Identification of a diploidizing genotype of Lolium multiflorum." Canadian Journal of Genetics and Cytology 27, no. 5 (October 1, 1985): 498–505. http://dx.doi.org/10.1139/g85-074.

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Thirty diploid populations of Lolium multiflorum were screened for genes that were capable of modifying meiosis in species hybrids. A standard genotype of L. temulentum was used as the tester species. Modified pairing at first metaphase of meiosis was identified in some of the hybrid progeny of a single plant from a population from Uruguay and also in one from Portugal. Evidence is presented to show that the high incidence of univalents in diploid hybrids of L. temulentum × L. multiflorum from Uruguay was due to the suppression of homoeologous chromosome association only. A proportion of equivalent triploid and tetraploid hybrids had an excess of bivalents at first metaphase of meiosis. This was confirmed by comparison of the observed meiotic data with that expected from three separate mathematical models. It is concluded that this single plant from the Uruguayan population was heterozygous for genes that suppress chiasmate association of homoeologous chromosomes.Key words: interspecific hybrid, Lolium, chromosome pairing.
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Adams, B. M., H. T. Banks, J. E. Banks, and J. D. Stark. "Population dynamics models in plant–insect herbivore–pesticide interactions." Mathematical Biosciences 196, no. 1 (July 2005): 39–64. http://dx.doi.org/10.1016/j.mbs.2004.09.001.

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Dingkuhn, Michael, Delphine Luquet, Benedicte Quilot, and Philippe de Reffye. "Environmental and genetic control of morphogenesis in crops: towards models simulating phenotypic plasticity." Australian Journal of Agricultural Research 56, no. 11 (2005): 1289. http://dx.doi.org/10.1071/ar05063.

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As molecular biologists are realising the importance of physiology in understanding functional genomics of quantitative traits, and as physiologists are realising the formidable prospects for improving their phenotypic models with information on the underlying gene networks, researchers worldwide are working on linked physiological–genetic models. These efforts are in their early methodological stage despite, or because of, the availability of many different types of models, the problem being to bring together the different ways that scientists see the plant. This paper describes some current efforts to adapt phenotype models to the objective of simulating gene-phene processes at the plant or crop scale. Particular emphasis is given to the models’ capacity to simulate genotype × environment interaction and the resulting phenotypic plasticity, assuming that this permits the defining of model parameters that are closer to specific gene action. Three different types of approaches are presented: (1) a generic, mathematical-architectural model called GREENLAB that simulates resource-modulated morphogenesis; (2) an ecophysiological model of peach tree fruit development and filling, parameterised for a mapping population to evaluate the potential of plugging quantitative trait locus (QTL) effects into the model; and (3) the new model Ecomeristem that constructs plant architecture and its phenotypic plasticity from meristem behaviour, the principal hypothesis being that resource limitations and stresses feed back on the meristems. This latter choice is based on the fact that gene expression happens to a large extent in the meristems. The model is evaluated on the basis of preliminary studies on vegetative-stage rice. The different modelling concepts are critically discussed with respect to their ability to simulate phenotypic plasticity and to operate with parameters that approximate specific gene action, particularly in the area of morphogenesis.
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Gubbins, Simon, and Christopher A. Gilligan. "Biological control in a disturbed environment." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 352, no. 1364 (December 29, 1997): 1935–49. http://dx.doi.org/10.1098/rstb.1997.0180.

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Most ecological and epidemiological models describe systems with continuous uninterrupted interactions between populations. Many systems, though, have ecological disturbances, such as those associated with planting and harvesting of a seasonal crop. In this paper, we introduce host—parasite—hyperparasite systems as models of biological control in a disturbed environment, where the host—parasite interactions are discontinuous. One model is a parasite—hyperparasite system designed to capture the essence of biological control and the other is a host—parasite—hyperparasite system that incorporates many more features of the population dynamics. Two types of discontinuity are included in the models. One corresponds to a pulse of new parasites at harvest and the other reflects the discontinuous presence of the host due to planting and harvesting. Such discontinuities are characteristic of many ecosystems involving parasitism or other interactions with an annual host. The models are tested against data from an experiment investigating the persistent biological control of the fungal plant parasite of lettuce Sclerotinia minor by the fungal hyperparasite Sporidesmium sclerotivorum , over successive crops. Using a combination of mathematical analysis, model fitting and parameter estimation, the factors that contribute the observed persistence of the parasite are examined. Analytical results show that repeated planting and harvesting of the host allows the parasite to persist by maintaining a quantity of host tissue in the system on which the parasite can reproduce. When the host dynamics are not included explicitly in the model, we demonstrate that homogeneous mixing fails to predict the persistence of the parasite population, while incorporating spatial heterogeneity by allowing for heterogeneous mixing prevents fade–out. Including the host's dynamics lessens the effect of heterogeneous mixing on persistence, though the predicted values for the parasite population are closer to the observed values. An alternative hypothesis for persistence involving a stepped change in rates of infection is also tested and model fitting is used to show that changes in some environmental conditions may contribute to parasite persistence. The importance of disturbances and periodic forcing in models for interacting populations is discussed.
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Oryokot, Joseph O. E., Stephen D. Murphy, A. Gordon Thomas, and Clarence J. Swanton. "Temperature- and moisture-dependent models of seed germination and shoot elongation in green and redroot pigweed (Amaranthus powellii, A. retroflexus)." Weed Science 45, no. 4 (August 1997): 488–96. http://dx.doi.org/10.1017/s0043174500088718.

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To predict weed emergence and help farmers make weed management decisions, we constructed a mathematical model of seed germination for green and redroot pigweed based on temperature and water potential (moisture) and expressing cumulative germination in terms of thermal time (degree days). Empirical observations indicated green pigweed germinated at a lower base temperature than redroot pigweed but the germination rate of redroot pigweed is much faster as mean temperature increases. Moisture limitation delayed seed germination until 23.8 C (green pigweed) or 27.9 (redroot pigweed); thereafter, germination was independent of water potential as mean temperatures approached germination optima. Our germination model, based on a cumulative normal distribution function, accounted for 80 to 95% of the variation in seed germination and accurately predicted that redroot pigweed would have a faster germination rate than green pigweed. However, the model predicted that redroot pigweed would germinate before green pigweed (in thermal time) and was generally less accurate during the early period of seed germination. The model also predicted that moisture limitation would increase, rather than delay, seed germination. These errors were related to the mathematical function chosen and analyses used, but an explicit interaction term for water potential and temperature is also needed to produce an accurate model. We also tested the effect of mean temperature on shoot elongation (emergence) and described the relationship by a linear model. Base temperatures for shoot elongation were higher than for seed germination. Shoot elongation began at 15.6 and 14.4 C for green and redroot pigweed, respectively; they increased linearly with temperature until the optimum of 27.9 C was reached. Elongation was dependent on completion of the rate-limiting step of radicle emergence and was sensitive to temperature but not moisture; hence, elongation was sensitive to a much smaller temperature range. Beyond mathematical changes, we are testing our model in the field and need to link it to ecophysiological, genetic, and spatially explicit population processes for it to be useful in decision support for weed management.
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Thompson, Robin N., and Ellen Brooks-Pollock. "Detection, forecasting and control of infectious disease epidemics: modelling outbreaks in humans, animals and plants." Philosophical Transactions of the Royal Society B: Biological Sciences 374, no. 1775 (May 6, 2019): 20190038. http://dx.doi.org/10.1098/rstb.2019.0038.

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The 1918 influenza pandemic is one of the most devastating infectious disease epidemics on record, having caused approximately 50 million deaths worldwide. Control measures, including prohibiting non-essential gatherings as well as closing cinemas and music halls, were applied with varying success and limited knowledge of transmission dynamics. One hundred years later, following developments in the field of mathematical epidemiology, models are increasingly used to guide decision-making and devise appropriate interventions that mitigate the impacts of epidemics. Epidemiological models have been used as decision-making tools during outbreaks in human, animal and plant populations. However, as the subject has developed, human, animal and plant disease modelling have diverged. Approaches have been developed independently for pathogens of each host type, often despite similarities between the models used in these complementary fields. With the increased importance of a One Health approach that unifies human, animal and plant health, we argue that more inter-disciplinary collaboration would enhance each of the related disciplines. This pair of theme issues presents research articles written by human, animal and plant disease modellers. In this introductory article, we compare the questions pertinent to, and approaches used by, epidemiological modellers of human, animal and plant pathogens, and summarize the articles in these theme issues. We encourage future collaboration that transcends disciplinary boundaries and links the closely related areas of human, animal and plant disease epidemic modelling. This article is part of the theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes’. This issue is linked with the subsequent theme issue ‘Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control’.
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Xiao, Sa, Shu-Yan Chen, and Gang Wang. "An ESS for the Height of a Plant Population, or an Optimal Height for an Individual?—Rethinking Game-Theoretic Models for Plant Height." Bulletin of Mathematical Biology 68, no. 4 (April 8, 2006): 957–67. http://dx.doi.org/10.1007/s11538-006-9073-0.

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Benson, Lee, Ross S. Davidson, Darren M. Green, Andrew Hoyle, Mike R. Hutchings, and Glenn Marion. "When and why direct transmission models can be used for environmentally persistent pathogens." PLOS Computational Biology 17, no. 12 (December 1, 2021): e1009652. http://dx.doi.org/10.1371/journal.pcbi.1009652.

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Variants of the susceptible-infected-removed (SIR) model of Kermack & McKendrick (1927) enjoy wide application in epidemiology, offering simple yet powerful inferential and predictive tools in the study of diverse infectious diseases across human, animal and plant populations. Direct transmission models (DTM) are a subset of these that treat the processes of disease transmission as comprising a series of discrete instantaneous events. Infections transmitted indirectly by persistent environmental pathogens, however, are examples where a DTM description might fail and are perhaps better described by models that comprise explicit environmental transmission routes, so-called environmental transmission models (ETM). In this paper we discuss the stochastic susceptible-exposed-infected-removed (SEIR) DTM and susceptible-exposed-infected-removed-pathogen (SEIR-P) ETM and we show that the former is the timescale separation limit of the latter, with ETM host-disease dynamics increasingly resembling those of a DTM when the pathogen’s characteristic timescale is shortened, relative to that of the host population. Using graphical posterior predictive checks (GPPC), we investigate the validity of the SEIR model when fitted to simulated SEIR-P host infection and removal times. Such analyses demonstrate how, in many cases, the SEIR model is robust to departure from direct transmission. Finally, we present a case study of white spot disease (WSD) in penaeid shrimp with rates of environmental transmission and pathogen decay (SEIR-P model parameters) estimated using published results of experiments. Using SEIR and SEIR-P simulations of a hypothetical WSD outbreak management scenario, we demonstrate how relative shortening of the pathogen timescale comes about in practice. With atttempts to remove diseased shrimp from the population every 24h, we see SEIR and SEIR-P model outputs closely conincide. However, when removals are 6-hourly, the two models’ mean outputs diverge, with distinct predictions of outbreak size and duration.
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Trozzi, Francesco, Feng Wang, Gennady Verkhivker, Brian D. Zoltowski, and Peng Tao. "Dimeric allostery mechanism of the plant circadian clock photoreceptor ZEITLUPE." PLOS Computational Biology 17, no. 7 (July 26, 2021): e1009168. http://dx.doi.org/10.1371/journal.pcbi.1009168.

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In Arabidopsis thaliana, the Light-Oxygen-Voltage (LOV) domain containing protein ZEITLUPE (ZTL) integrates light quality, intensity, and duration into regulation of the circadian clock. Recent structural and biochemical studies of ZTL indicate that the protein diverges from other members of the LOV superfamily in its allosteric mechanism, and that the divergent allosteric mechanism hinges upon conservation of two signaling residues G46 and V48 that alter dynamic motions of a Gln residue implicated in signal transduction in all LOV proteins. Here, we delineate the allosteric mechanism of ZTL via an integrated computational approach that employs atomistic simulations of wild type and allosteric variants of ZTL in the functional dark and light states, together with Markov state and supervised machine learning classification models. This approach has unveiled key factors of the ZTL allosteric mechanisms, and identified specific interactions and residues implicated in functional allosteric changes. The final results reveal atomic level insights into allosteric mechanisms of ZTL function that operate via a non-trivial combination of population-shift and dynamics-driven allosteric pathways.
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Dissertations / Theses on the topic "Plant population genetics Mathematical models"

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Pereira, Renato Nunes. "Modelo hierárquico bayesiano na determinação de associação entre marcadores e QTL em uma população F2." Universidade de São Paulo, 2012. http://www.teses.usp.br/teses/disponiveis/11/11134/tde-25042012-161429/.

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O objetivo do mapeamento de QTL (Quantitative Trait Loci ) e identificar sua posição no genoma, isto e, identificar em qual cromossomo esta e qual sua localização nesse cromossomo, bem como estimar seus efeitos genéticos. Uma vez que as localizações dos QTL não são conhecidas a priori, marcadores são usados frequentemente para auxiliar no seu mapeamento. Alguns marcadores podem estar altamente ligados a um ou mais QTL e, dessa forma eles podem mostrar uma alta associação com a característica fenotípica. O efeito genético do QTL e os valores fenotípicos de uma característica quantitativa são normalmente descritos por um modelo linear. Uma vez que as localizações dos QTL não são conhecidas a priori, marcadores são utilizados para representá-los. Em geral, e utilizado um numero grande de marcadores. Esses marcadores são utilizados no modelo linear para proceder ao processo de associação; dessa forma o modelo especificado contem um numero elevado de parâmetros a serem estimados. No entanto, e esperado que muitos destes parâmetros sejam não significativos, necessitando de um tratamento especial. Na estimação bayesiana esse problema e tratado por meio da estrutura de distribuições a priori utilizada. Um parâmetro que e esperado assumir o valor zero (não significativo) e naturalmente especificado por meio de uma distribuição que coloque um peso maior no zero, encolhimento bayesiano. Neste trabalho e proposta a utilização de dois modelos que utilizam distribuições a priori de encolhimento. Um dos modelos esta relacionado com o uso da distribuição a priori Laplace (Lasso bayesiano) e o outro com a Horseshoe (Estimador Horseshoe). Para avaliar o desempenho dos modelos na determinação da associação entre marcadores e QTL, realizou-se um estudo de simulação. Foi analisada a associação entre marcadores e QTL utilizando três características fenotípicas: produção de grãos, altura da espiga e altura da planta. Comparou-se os resultados obtidos neste trabalho com analises feitas na literatura na detecção dos marcadores associados a essas características. A implementação computacional dos algoritmos foi feita utilizando a linguagem C e executada no pacote estatístico R. O programa implementado na linguagem C e apresentado e disponibilizado. Devido a interação entre as linguagens de programação C e R, foi possível executar o programa no ambiente R.
The objective of the mapping of quantitative trait loci (QTL) is to identify its position in the genome, ie, identify which chromosome is and what is its location in the chromosome, as well as to estimate their genetic eects. Since the location of QTL are not known a priori, markers are often used to assist in it mapping. Some markers may be closely linked to one or more QTL, and thus they may show a strong association with the phenotypic trait. The genetic eect of QTL and the phenotypic values of a quantitative trait are usually described by a linear model. Since the QTL locations are not known a priori, markers are used to represent them. Generally is used a large number of markers. These markers are used in the linear model to make the process of association and thus the model specied contains a large number of parameters to be estimated. However, it is expected that many of these parameters are not signicant, requiring a special treatment. In Bayesian estimation this problem is treated through structure priori distribution used. A parameter that is expected to assume the value zero (not signicant) is naturally specied by means of a distribution that put more weight at zero, bayesian shrinkage. This paper proposes the use of two models using priori distributions to shrinkage. One of the models is related to the use of priori distribution Laplace (bayesian Lasso) and the other with Horseshoe (Horseshoe Estimator). To evaluate the performance of the models to determine the association between markers and QTL, we performed a simulation study. We analyzed the association between markers and QTL using three phenotypic traits: grain yield, ear height and plant height. We compared the results obtained in this study with analyzes in the literature on the detection of markers associated with these characteristics. The computational implementation of the algorithms was done using the C language and executed the statistical package R. The program is implemented in C languages presented and made available. Due to the interaction between the programming languages C and R, it was possible execute the program in the environment R.
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Lundy, Ian J. "Theoretical population genetics of spatially structured populations /." Title page, contents and summary only, 1997. http://web4.library.adelaide.edu.au/theses/09PH/09phl962.pdf.

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KOT, MARK. "THE EFFECTS OF PARAMETRIC EXCITATION AND OF DISPERSAL ON THE DYNAMICS OF DISCRETE-TIME POPULATION MODELS." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/184074.

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Parametric excitation and dispersal are added to discrete-time population models. Discrete-time models for growth with dispersal share many of the attributes of reaction-diffusion equations. At the same time, these models readily exhibit period doubling and chaos. Large parametric excitation (seasonality) is inevitably destabilizing, but mild seasonality may have a pronounced stabilizing effect. Seasonality also allows for the coexistence of alternative stable states (equilibria, cycles, chaos). Many examples are presented.
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Gayley, Todd Warwick. "Genetic models of two-phenotype frequency-dependent selection." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184883.

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The aim of this study is to place a wide variety of two-phenotype frequency-dependent selection models into a unified population-genetic framework. This work is used to illuminate the possible genetic constraints that may exist in such models, and to address the question of evolutionary modification of these constraints. The first part of Chapter 1 synthesizes from the literature a general framework for applying a genetic structure to a simple class of two-phenotype models. It shows that genetic constraints may prevent the population from achieving a predicted phenotypic equilibrium, but the population will equilibrate at a point that is as close as possible to the phenotypic equilibrium. The second part of Chapter 1 goes on to ask whether evolutionary modification of the genetic system might be expected to remove these constraints. Chapter 2 provides an example of the application of the framework developed in Chapter 1. It presents re-analysis of a model for the evolution of social behavior by reciprocation (Brown et al. 1982). The genetic results of Chapter 1 apply to this model without modification. I show that Brown et al. were unnecessarily restrictive in their assumptions about the types of genetic systems that support their conclusions. Chapter 3 discusses some models for the evolution of altruism that do not fit the assumptions of Chapter 1, despite their two-phenotype structure. These models violate the fundamental assumption of Chapter 1, this being the way in which individual fitness is derived from the behavioral fitnesses. The first part is a complete, in-depth analysis of diploid sib-sib kin selection. I show that some results from the basic model can be used, provided the behavioral inclusive fitness functions are substituted for the true behavioral fitnesses. The second part is an analysis of the validity of the concept of behavioral structure, as introduced by Michod and Sanderson (1985). I show that this concept is flawed as a general principle. Chapter 4 extends the basic model to the case of sex-allocation evolution. I show how many of the central results of sex-allocation theory can be derived more simply using a two-phenotype framework.
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Gryspeirt, Aiko. "Impact des plantes Bt sur la biologie de Plodia interpunctella: évaluation de l'efficacité de la stratégie agricole "Haute dose - refuge" pour la gestion de la résistance des insectes ravageurs aux plantes Bt." Doctoral thesis, Universite Libre de Bruxelles, 2008. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210542.

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Commercialisées depuis 1996, les plantes génétiquement modifiées produisant une toxine insecticide (toxine Cry) dérivée de Bacillus thuringiensis et appelées plantes Bt ciblent certains Lépidoptères ou Coléoptères ravageurs. Au fil des ans, les surfaces cultivées en plantes Bt sont de plus en plus importantes et contrôlent de larges populations d'insectes. Pour limiter le risque de développement de populations résistantes, une stratégie agricole appelée 'Haute Dose / Zone Refuge' est actuellement recommandée aux Etats-Unis par l'Environmental Protection Agency. Cette stratégie préventive nécessite la plantation d'une 'zone refuge' composée de plantes non-Bt utilisables par le ravageur ciblé et plantée à proximité de la 'zone Bt' qui synthétise une haute dose de toxine Cry.

Mon projet de recherche s’inscrit dans le cadre de l’évaluation de l'efficacité de cette stratégie et s’articule en deux phases :une phase expérimentale et une phase théorique. La première se concentre sur la caractérisation en laboratoire de l'impact des toxines Cry sur la biologie d'un ravageur. Cette phase constitue un support au volet théorique :la mise au point d’un modèle mathématique évaluant l'efficacité de la stratégie HD/R. L'originalité de ce projet repose entre autre sur l'interactivité entre ces deux volets.

Volet expérimental. Impact des toxines Cry sur la biologie de Plodia interpunctella. Nous évaluons séparément l'impact d'une gamme de concentrations de deux toxines Cry (CryXX et CryYY) sur une série de paramètres comportementaux et biologiques d'un insecte commun des denrées stockées: Plodia interpunctella (Hübner) (Lepidoptera :Pyralidae). Ces paramètres sont sélectionnés car leur variation pourrait avoir un impact sur l'efficacité de la stratégie HD/R dans le contrôle de la résistance. Il est donc pertinent de les quantifier pour intégrer dans le modèle des ordres de grandeur réalistes et générer des résultats qui ne sont pas uniquement basés sur des spéculations théoriques.

Volet théorique A. Efficacité de la stratégie HD/R pour des plantes Bt synthétisant une ou deux toxines simultanément. La stratégie 'HD/R' a été développée pour prévenir la résistance envers les plantes Bt synthétisant une seule toxine. Or, depuis 2003, de nouvelles variétés de coton Bt synthétisant simultanément deux toxines Cry sont commercialisées (BollgardII® et WidestrikeTM). Nous évaluons, grâce au modèle que nous avons développé, l'efficacité de cette stratégie lors d'une utilisation exclusive de plantes Bt synthétisant une ou deux toxines.

Volet théorique B. Impact du ralentissement du développement des insectes sur les plantes Bt sur l'efficacité de la stratégie HD/R. Le volet expérimental met en évidence un allongement de la durée du développement des larves se nourrissant sur une diète contaminée en toxine Cry. Ce ralentissement induit une séparation temporelle entre l'émergence des adultes de la zone Bt et de la zone refuge et perturbe une hypothèse principale de la stratégie HD/R: le croisement aléatoire entre adultes, indépendamment du génotype et de la zone d'origine. Dans ce troisième chapitre, nous étudions l'impact de la perturbation du croisement aléatoire sur l'efficacité de la stratégie HD/R. Nous testons également deux options pour optimiser la stratégie en cas d'asynchronie: l'utilisation de plantes Bt synthétisant une faible concentration en toxine (atténuant le décalage entre l'émergence des adultes) ou l'augmentation de la taille de la zone refuge (favorisant la survie des individus porteurs d'allèle de sensibilité et donc optimisant la dilution de la résistance à la génération suivante).

Ce travail s'intègre dans une problématique actuelle et utilise des outils de biologie théorique (théories de la dynamique et de la génétique des populations) ainsi que le développement d'un modèle mathématique. Il apporte des éléments de réponse et de réflexion sur l'optimisation de la gestion de la résistance des insectes mais c'est aussi une illustration de la complémentarité entre la biologie expérimentale et théorique.

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On the market since 1996, genetically modified plants synthesizing an insecticidal toxin (Cry toxin) stemmed from Bacillus thuringiensis, called Bt plants, target several insect pests (Lepidoptera or Coleoptera). Bt crops cover increasingly larger areas and control important pest populations The Insect Resistance Management Strategy (IRM) strategy currently recommended in the U.S.A. to limit the development of resistant populations is the High Dose / Refuge zone (HD/R) strategy. This pre-emptive strategy requires a refuge zone composed by non-Bt plants, usable by the target insect and in close proximity of the Bt zone synthesizing a high toxin concentration.

My research project contributes to the effectiveness assessment of this HD/R strategy. It is structured on two main parts: an experimental, and a theoretical section. The first part characterizes the impact of Cry toxins on the biology of an insect pest. It is the basis of the theoretical part: the implementation of a mathematical model, which evaluates the effectiveness of the HD/R strategy.

The originality of this project is based on the interactivity of these two components.

Experimental section. Impact of the Cry toxins on the biology of Plodia interpunctella. We assess the impact of a range of concentrations of two Cry toxins (CryXX et CryYY) on several behavioural and biological parameters of a common pest of stored products: Plodia interpunctella (Hübner) (Lepidoptera :Pyralidae). These parameters are selected because their variation could influence the effectiveness of a HD/R strategy. So, it is important to quantify these parameters so that realistic values can be integrated in our model. The results of the model are thus not based on theoretical assumptions alone.

Theoretical section A. Effectiveness of a HD/R strategy with Bt plants synthesizing one or two toxins. Initially, the HD/R strategy has been developed to limit the resistance towards Bt plants synthesizing one toxin. However, since 2003, new Bt cotton varieties synthesize two toxins simultaneously (BollgardII® et WidestrikeTM). We assess, with our model, the effectiveness of this strategy for Bt plants synthesizing one or two toxins.

Theoretical section B. Impact of the slowing down of the insect development reared on Bt plants on the effectiveness of the HD/R strategy. The experimental part demonstrates that larvae reared on a Bt diet have a protracted development duration. The consequence of this is a temporal separation between adult emergence in the two zones (Bt zone and refuge zone). This could affect the main assumption of the HD/R strategy, i. e. random mating independently of the genotype and of the native zone. In this third chapter, we study the impact of random mating disruption on the effectiveness of a HD/R strategy. We test two options to optimise the strategy in case of asynchrony: the use of Bt plants synthesizing a lower toxin concentration (limiting emergence asynchrony) or increasing the refuge zone size (favouring the survival of insect carrying one or two susceptible allele and thus optimising the dilution of resistance at the next generation).

This work is applied to a current issue. It uses some of the tools of theoretical biology (theories of population dynamics and population genetics) and develops a mathematical model. It provides some responses and some elements of thought about insect resistance management. It is also an illustration of the complementarity between experimental and theoretical biology.


Doctorat en Sciences
info:eu-repo/semantics/nonPublished

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Tran, Tat Dat. "Information Geometry and the Wright-Fisher model of Mathematical Population Genetics." Doctoral thesis, Universitätsbibliothek Leipzig, 2012. http://nbn-resolving.de/urn:nbn:de:bsz:15-qucosa-90508.

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My thesis addresses a systematic approach to stochastic models in population genetics; in particular, the Wright-Fisher models affected only by the random genetic drift. I used various mathematical methods such as Probability, PDE, and Geometry to answer an important question: \"How do genetic change factors (random genetic drift, selection, mutation, migration, random environment, etc.) affect the behavior of gene frequencies or genotype frequencies in generations?”. In a Hardy-Weinberg model, the Mendelian population model of a very large number of individuals without genetic change factors, the answer is simple by the Hardy-Weinberg principle: gene frequencies remain unchanged from generation to generation, and genotype frequencies from the second generation onward remain also unchanged from generation to generation. With directional genetic change factors (selection, mutation, migration), we will have a deterministic dynamics of gene frequencies, which has been studied rather in detail. With non-directional genetic change factors (random genetic drift, random environment), we will have a stochastic dynamics of gene frequencies, which has been studied with much more interests. A combination of these factors has also been considered. We consider a monoecious diploid population of fixed size N with n + 1 possible alleles at a given locus A, and assume that the evolution of population was only affected by the random genetic drift. The question is that what the behavior of the distribution of relative frequencies of alleles in time and its stochastic quantities are. When N is large enough, we can approximate this discrete Markov chain to a continuous Markov with the same characteristics. In 1931, Kolmogorov first introduced a nice relation between a continuous Markov process and diffusion equations. These equations called the (backward/forward) Kolmogorov equations which have been first applied in population genetics in 1945 by Wright. Note that these equations are singular parabolic equations (diffusion coefficients vanish on boundary). To solve them, we use generalized hypergeometric functions. To know more about what will happen after the first exit time, or more general, the behavior of whole process, in joint work with J. Hofrichter, we define the global solution by moment conditions; calculate the component solutions by boundary flux method and combinatorics method. One interesting property is that some statistical quantities of interest are solutions of a singular elliptic second order linear equation with discontinuous (or incomplete) boundary values. A lot of papers, textbooks have used this property to find those quantities. However, the uniqueness of these problems has not been proved. Littler, in his PhD thesis in 1975, took up the uniqueness problem but his proof, in my view, is not rigorous. In joint work with J. Hofrichter, we showed two different ways to prove the uniqueness rigorously. The first way is the approximation method. The second way is the blow-up method which is conducted by J. Hofrichter. By applying the Information Geometry, which was first introduced by Amari in 1985, we see that the local state space is an Einstein space, and also a dually flat manifold with the Fisher metric; the differential operator of the Kolmogorov equation is the affine Laplacian which can be represented in various coordinates and on various spaces. Dynamics on the whole state space explains some biological phenomena.
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7

Arpin, Sheree. "Using Mathematical Models to Investigate Phenotypic Oscillations in Cichlid Fish: A Case of Frequency-dependent Selection." Diss., The University of Arizona, 2007. http://hdl.handle.net/10150/195981.

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Perissodus microlepis is a species of cichlid fish endemic to Lake Tanganyika (Africa). Adult P. microlepis are lepidophages, feeding on the scales of other living fish. As an adaptation for this feeding behavior P. microlepis exhibit lateral asymmetry with respect to jaw morphology: the mouth either opens to the right or left side of the body. Field data illustrate a temporal phenotypic oscillation in the mouth-handedness, and this oscillation is maintained by frequency-dependent selection. To better understand the oscillation, Takahashi and Hori model frequency-dependent selection in P. microlepis using a population genetic model. Their results are intriguing, and the purpose of this dissertation is to improve and extend their model, which fails to account for important biological aspects.We model P. microlepis with a novel approach that fuses the disparate modeling traditions of population genetics and population dynamics; we account for both processes since, in the case of P. microlepis, they occur on the same time scale (a case of microevolution). We construct our models using systems of difference equations. We prove the existence and uniqueness of a positive equilibrium, which corresponds to a 1 : 1 phenotypic ratio. Using a local stability and bifurcation analysis, we show that the equilibrium becomes unstable when frequency-dependent selection is sufficiently strong. We determine necessary and sufficient conditions for onset of oscillation. Local bifurcation analysis indicates key features of the oscillation that may suggest critical experiments.We determine the role of stage structure and the role of strong and weak intraspecific competition. We show that stage-structure is not necessary for, but enhances, oscillatory behavior. Finally we demonstrate the complicated interplay between population dynamic and population genetic processes. Our findings indicate that classical population genetic models can fail to elucidate complex dynamics.
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Ballard, Todd Curtis. "Mathematical Models of Zea mays: Grain Yield and Aboveground Biomass Applied to Ear Flex and within Row Spacing Variability." TopSCHOLAR®, 2008. http://digitalcommons.wku.edu/theses/41.

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Field studies were conducted during the summers of 2007 and 2008 at the Agricultural Research and Education Complex, Western Kentucky University, Warren County, KY and commercial production fields in Caldwell County, KY, Warrick County IN, and Vanderburgh County, IN. The goals of these studies were to further validate the Duncan grain yield model, the Russell aboveground biomass model, and to study the effect of inconsistent spacing within rows on Zea mays L. yield. Plant spacing other than uniform decreases grain yield and profitability. The population experiments conducted at the Warren County location were a randomized complete block design with three planting densities, three varieties (c.v. DeKalb DKC6547, DeKalb DKC6346, DeKalb DKC6478) in 2007 and (DeKalb DKC6478, DeKalb DKC6342, and DeKalb DKC6544) in 2008, and three replications. Seeds were planted in rows 76 cm apart and 9.1 m long with four rows per plot in a no-till system on a Crider Silt Loam with pH of 6.8 and 1.5% organic matter. The effect of variable within row spacing was evaluated in commercial production fields by randomly selecting five adjacent rows of 5.3 meters in length at each location. Grain yield for each row was then curve fitted both linearly and exponentially. Minimizing interspecies competition was essential to evaluating the effects of competition within Zea mays L. A burn-down application of 2,4-D and glyphosate was used prior to planting. The most common weeds in the plots were Sorghum halepense L. (johnsongrass), Trifolium repens L. (white clover), and Taraxacum officinale L. (common dandelion) . Glyphosate was reapplied throughout the growing season due to reemergence of S. halepense and Ipomoea hederacea Jacq. (ivyleaf morningglory). The weight of each ear was recorded and one row from each plot was randomly selected to shell. The moisture content was measured from a subsample twice each row using an electrical conductivity moisture meter. The mean of the two moisture readings was used as the moisture content from the plot. Cob weights from shelled ears were recorded to determine the grain/cob mass ratio. This ratio was used to project the grain weight for the remaining harvested rows. Duncan’s grain yield model and Russell’s biomass model were curve fitted to the data for areas of 0.00040 hectares at the p < 0.05 significance level or greater in all population density plots. Individual plant grain masses were curve fitted to Duncan’s model with p < 0.05 significance in 3 out of 15 plots. Grain mass was negatively correlated (R < 0) with standard deviation of within row spacing in 14 of 15 plots. A linear fit to this trend was significant in only 2 of 15 plots. The Duncan yield curve and the Russell aboveground biomass model fit all 6 genotype by environment interactions for 2007 and 2008 to the α = 0.05 level of confidence when evaluated over a 5.3 meter length on 76.2 cm wide rows. Individual plants fit linearly at α = 0.05 in 9 out of 15 plots. Individual plants fit the Duncan yield curve at α = 0.05 in 4 out of 15 plots. Standard deviation of within row spacing fit grain yield loss significantly at &#; = 0.05 in two of 15 plots. The individual plant spacing and local population density collectively fit nine plots significantly at α = 0.05 or better.
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Kean, J. M. "Metapopulation theory in practice." Lincoln University, 1999. http://hdl.handle.net/10182/1372.

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A metapopulation is defined as a set of potential local populations among which dispersal may occur. Metapopulation theory has grown rapidly in recent years, but much has focused on the mathematical properties of metapopulations rather than their relevance to real systems. Indeed, barring some notable exceptions, metapopulation theory remains largely untested in the field. This thesis investigates the importance of metapopulation structure in the ‘real world’, firstly by building additional realism into metapopulation models, and secondly through a 3-year field study of a real metapopulation system. The modelling analyses include discrete-and continuous-time models, and cover single species, host-parasitoid, and disease-host systems, with and without stochasticity. In all cases, metapopulation structure enhanced species persistence in time, and often allowed long-term continuance of otherwise non-persistent interactions. Spatial heterogeneity and patterning was evident whenever local populations were stochastic or deterministically unstable in isolation. In metapopulations, the latter case often gave rise to self-organising spatial patterns. These were composed of spiral wave fronts (or ‘arcs of infection’ in disease models) of different sizes, and were related to the stability characteristics of local populations as well as the dispersal rates. There was no evidence for self-organising spatial patterns in the host-parasitoid system studied in the field (the weevil Sitona discoideus and its braconid parasitoid Microctonus aethiopoides), and a new model for the interaction suggested that this is probably due to the strong host density-dependence and stabilising parasitism acting on local populations. Dispersal may be important because of very high mortality in dispersing weevils, which may be related to the scarcity of their host plant in the landscape. If this is the case, the model suggested that local weevil density may be sensitive to the area of crop grown. Stochastic models showed that species in suitably large metapopulations may persist for very long times at relatively low overall density and with very low incidence of density-dependence. This suggests that metapopulation processes may explain a general inability to detect density-dependence in many real populations, and may also play an important part in the persistence of rare species. For host-parasitoid metapopulation models, persistence often depended on the way in which they were initialised. Initial conditions corresponding to a biological control release were the least likely to persist, and the maximum host suppression observed in this case was 84%, as compared with 60% for the corresponding non-spatial models and >90% often observed in the field. Metapopulation structure also allowed persistence of ‘boom-bust’ disease models, although the dynamics of these were particularly dependent on assumptions about what happens to disease classes at very low densities. Models assuming infinitely divisible units of density, models incorporating a non-zero extinction threshold, and individual-based models all gave differing results in terms of disease persistence and rate of spatial spread. Fitting models to overall metapopulation dynamics often gave misleading results in terms of underlying local dynamics, emphasising the need to sample real populations at an appropriate scale when seeking to understand their behaviour.
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10

Aston, Christopher Eric. "Statistical models for multilocus structures." Phd thesis, 1985. http://hdl.handle.net/1885/141088.

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Books on the topic "Plant population genetics Mathematical models"

1

IUFRO Working Party "Ecological and Population Genetics". Meeting. Population genetics in forestry: Proceedings of the meeting of the IUFRO Working Party "Ecological and Population Genetics" held in Göttingen, August 21-24, 1984. Berlin: Springer-Verlag, 1985.

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I, Li͡ubich I͡U. Mathematical structures in population genetics. Berlin: Springer-Verlag, 1992.

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Etheridge, Alison. Some Mathematical Models from Population Genetics. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-16632-7.

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Edwards, A. W. F. Foundations of mathematical genetics. 2nd ed. Cambridge, U.K: Cambridge University Press, 2000.

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Introduction to theoretical population genetics. Berlin: Springer-Verlag, 1992.

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Dynamic population models. Dordrecht: Springer, 2006.

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Population genetics of multiple loci. Chichester: Wiley, 2000.

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Bürger, R. The mathematical theory of selection, recombination, and mutation. Chichester: Wiley, 2000.

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Bürger, Reinhard. The mathematical theory of selection, recombination, and mutation. Chichester: John Wiley, 2000.

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M. C. M. de Gunst. A random model for plant cell population growth. [Amsterdam, the Netherlands]: Centrum voor Wiskunde en Informatica, 1989.

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Book chapters on the topic "Plant population genetics Mathematical models"

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Ewens, Warren J. "Discrete Stochastic Models." In Mathematical Population Genetics, 92–135. New York, NY: Springer New York, 2004. http://dx.doi.org/10.1007/978-0-387-21822-9_3.

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Lyubich, Yuri I., and Ethan Akin. "Elementary Models." In Mathematical Structures in Population Genetics, 23–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-76211-6_2.

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Neuhauser, C. "Mathematical Models in Population Genetics." In Handbook of Statistical Genetics, 753–80. Chichester, UK: John Wiley & Sons, Ltd, 2008. http://dx.doi.org/10.1002/9780470061619.ch22.

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Etheridge, Alison. "Introduction." In Some Mathematical Models from Population Genetics, 1–3. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16632-7_1.

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Etheridge, Alison. "Mutation and Random Genetic Drift." In Some Mathematical Models from Population Genetics, 5–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16632-7_2.

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Etheridge, Alison. "One Dimensional Diffusions." In Some Mathematical Models from Population Genetics, 33–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16632-7_3.

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Etheridge, Alison. "More than Two Types." In Some Mathematical Models from Population Genetics, 53–64. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16632-7_4.

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Etheridge, Alison. "Selection." In Some Mathematical Models from Population Genetics, 65–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16632-7_5.

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Etheridge, Alison. "Spatial Structure." In Some Mathematical Models from Population Genetics, 89–107. Berlin, Heidelberg: Springer Berlin Heidelberg, 2010. http://dx.doi.org/10.1007/978-3-642-16632-7_6.

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Neuhauser, C. "Mathematical Models in Population Genetics." In Handbook of Statistical Genetics. Chichester: John Wiley & Sons, Ltd, 2004. http://dx.doi.org/10.1002/0470022620.bbc20.

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