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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Leclerc, Melen, Julie A. J. Clément, Didier Andrivon, and Frédéric M. Hamelin. "Assessing the effects of quantitative host resistance on the life-history traits of sporulating parasites with growing lesions." Proceedings of the Royal Society B: Biological Sciences 286, no. 1912 (October 2, 2019): 20191244. http://dx.doi.org/10.1098/rspb.2019.1244.
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Assessing life-history traits of parasites on resistant hosts is crucial in evolutionary ecology. In the particular case of sporulating pathogens with growing lesions, phenotyping is difficult because one needs to disentangle properly pathogen spread from sporulation. By considering Phytophthora infestans on potato, we use mathematical modelling to tackle this issue and refine the assessment of pathogen response to quantitative host resistance. We elaborate a parsimonious leaf-scale model by convolving a lesion growth model and a sporulation function, after a latency period. This model is fitted to data obtained on two isolates inoculated on three cultivars with contrasted resistance level. Our results confirm a significant host–pathogen interaction on the various estimated traits, and a reduction of both pathogen spread and spore production, induced by host resistance. Most interestingly, we highlight that quantitative resistance also changes the sporulation function, the mode of which is significantly time-lagged. This alteration of the infectious period distribution on resistant hosts may have strong impacts on the dynamics of parasite populations, and should be considered when assessing the durability of disease control tactics based on plant resistance management. This inter-disciplinary work also supports the relevance of mechanistic models for analysing phenotypic data of plant–pathogen interactions.
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Njoroge, Martin W., Sarah Rylance, Rebecca Nightingale, Stephen Gordon, Kevin Mortimer, Peter Burney, Jamie Rylance, Angela Obasi, Louis Niessen, and Graham Devereux. "Cohort profile: The Chikwawa lung health cohort; a population-based observational non-communicable respiratory disease study of adults in Malawi." PLOS ONE 15, no. 11 (November 12, 2020): e0242226. http://dx.doi.org/10.1371/journal.pone.0242226.
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Purpose The aim of this article is to provide a detailed description of the Chikwawa lung health cohort which was established in rural Malawi to prospectively determine the prevalence and causes of lung disease amongst the general population of adults living in a low-income rural setting in Sub-Saharan Africa. Participants A total of 1481 participants were randomly identified and recruited in 2014 for the baseline study. We collected data on demographic, socio-economic status, respiratory symptoms and potentially relevant exposures such as smoking, household fuels, environmental exposures, occupational history/exposures, dietary intake, healthcare utilization, cost (medication, outpatient visits and inpatient admissions) and productivity losses. Spirometry was performed to assess lung function. At baseline, 56.9% of the participants were female, mean age was 43.8 (SD:17.8) and mean body mass index (BMI) was 21.6 Kg/m2 (SD: 3.46) Findings to date The cohort has reported the prevalence of chronic respiratory symptoms (13.6%, 95% confidence interval [CI], 11.9–15.4), spirometric obstruction (8.7%, 95% CI, 7.0–10.7), and spirometric restriction (34.8%, 95% CI, 31.7–38.0). Additionally, an annual decline in forced expiratory volume in one second [FEV1] of 30.9mL/year (95% CI: 21.6 to 40.1) and forced vital capacity [FVC] by 38.3 mL/year (95% CI: 28.5 to 48.1) has been reported. Future plans The ongoing phases of follow-up will determine the annual rate of decline in lung function as measured through spirometry and the development of airflow obstruction and restriction, and relate these to morbidity, mortality and economic cost of airflow obstruction and restriction. Population-based mathematical models will be developed driven by the empirical data from the cohort and national population data for Malawi to assess the effects of interventions and programmes to address the lung burden in Malawi. The present follow-up study started in 2019.
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Gonzalez-Rodriguez, Sara, and Maria Luisa Fernandez-Marcos. "Phosphate sorption and desorption by two contrasting volcanic soils of equatorial Africa." PeerJ 6 (October 23, 2018): e5820. http://dx.doi.org/10.7717/peerj.5820.
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Volcanic soils cover 1% of the Earth’s surface but support 10% of the world’s population. They are among the most fertile soils in the world, due to their excellent physical properties and richness in available nutrients. The major limiting factor for plant growth in volcanic soils is phosphate fixation, which is mainly attributable to active species of aluminium and iron. The sorption and desorption of phosphate is studied on the surface horizons of two African agricultural soils, a silandic Andosol (Rwanda) and a vitric Andosol (São Tomé and Principe). Both soils are slightly acid. The silandic Andosol is rich in active aluminium forms, while the vitric Andosol has high amounts of crystalline iron and aluminium oxides. Sorption isotherms were determined by equilibrating at 293K soil samples with phosphate solutions of concentrations between 0 and 100 mg P L−1 in NaNO3; phosphate was determined by visible spectrophotometry in the equilibrium solution. To study desorption, the soil samples from the sorption experiment were equilibrated with 0.02 M NaNO3. The isotherms were adjusted to mathematical models. In almost all the concentration range, the adsorption of phosphate by the silandic Andosol was greater than 90% of the amount added, being lower in the vitric Andosol but always higher than 65%. The high sorption by the silandic Andosol is attributed to its richness in non-crystalline Fe and Al, while in the vitric Andosol crystalline iron species seem to play a relevant role in the adsorption. The sorption isotherms of both soils fitted to the Temkin model, the adjustment to the Langmuir or Freundlich models being unsatisfactory; throughout the range studied, the sorption increases with increasing phosphorus concentration, a maximum sorption is not predictable (as occurs when the sorption is adjusted to the Langmuir model). For an added P concentration of 100 mg L−1 (3.2 mmol L−1), the sorption is 47.7 µmol P g−1 in the silandic Andosol and 41.6 µmol P g−1 in the vitric Andosol. The desorption is low and the comparison of the sorption and desorption isotherms reveals a pronounced hysteresis, that is, the irreversibility of the sorption. The high phosphate sorption and its irreversibility are comparable to those published for other volcanic soils with high contents of allophane, active aluminium and free iron. The strong phosphate adsorption is a serious limiting factor for plant growth, which requires a careful management of phosphorus fertilization.
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Borer, Benedict, and Dani Or. "Bacterial age distribution in soil – Generational gaps in adjacent hot and cold spots." PLOS Computational Biology 18, no. 2 (February 25, 2022): e1009857. http://dx.doi.org/10.1371/journal.pcbi.1009857.
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Resource patchiness and aqueous phase fragmentation in soil may induce large differences local growth conditions at submillimeter scales. These are translated to vast differences in bacterial age from cells dividing every thirty minutes in close proximity to plant roots to very old cells experiencing negligible growth in adjacent nutrient poor patches. In this study, we link bacterial population demographics with localized soil and hydration conditions to predict emerging generation time distributions and estimate mean bacterial cell ages using mechanistic and heuristic models of bacterial life in soil. Results show heavy-tailed distributions of generation times that resemble a power law for certain conditions, suggesting that we may find bacterial cells of vastly different ages living side by side within small soil volumes. Our results imply that individual bacteria may exist concurrently with all of their ancestors, resulting in an archive of bacterial cells with traits that have been gained (and lost) throughout time–a feature unique to microbial life. This reservoir of bacterial strains and the potential for the reemergence of rare strains with specific functions may be critical for ecosystem stability and function.
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Gil, Marie-Eve, Francois Hamel, Guillaume Martin, and Lionel Roques. "Mathematical Properties of a Class of Integro-differential Models from Population Genetics." SIAM Journal on Applied Mathematics 77, no. 4 (January 2017): 1536–61. http://dx.doi.org/10.1137/16m1108224.
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Pettersson, Susanne, and Martin Nilsson Jacobi. "Spatial heterogeneity enhance robustness of large multi-species ecosystems." PLOS Computational Biology 17, no. 10 (October 27, 2021): e1008899. http://dx.doi.org/10.1371/journal.pcbi.1008899.
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Understanding ecosystem stability and functioning is a long-standing goal in theoretical ecology, with one of the main tools being dynamical modelling of species abundances. With the help of spatially unresolved (well-mixed) population models and equilibrium dynamics, limits to stability and regions of various ecosystem robustness have been extensively mapped in terms of diversity (number of species), types of interactions, interaction strengths, varying interaction networks (for example plant-pollinator, food-web) and varying structures of these networks. Although many insights have been gained, the impact of spatial extension is not included in this body of knowledge. Recent studies of spatially explicit modelling on the other hand have shown that stability limits can be crossed and diversity increased for systems with spatial heterogeneity in species interactions and/or chaotic dynamics. Here we show that such crossing and diversity increase can appear under less strict conditions. We find that the mere possibility of varying species abundances at different spatial locations make possible the preservation or increase in diversity across previous boundaries thought to mark catastrophic transitions. In addition, we introduce and make explicit a multitude of different dynamics a spatially extended complex system can use to stabilise. This expanded stabilising repertoire of dynamics is largest at intermediate levels of dispersal. Thus we find that spatially extended systems with intermediate dispersal are more robust, in general have higher diversity and can stabilise beyond previous stability boundaries, in contrast to well-mixed systems.
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Provorov, Nikolay A., and Nikolay I. Vorobyov. "Evolution of micro-symbionts of cultured plants: experimental and mathematical models." Ecological genetics 9, no. 3 (September 15, 2011): 20–22. http://dx.doi.org/10.17816/ecogen9320-22.
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Formation of the cultured flora resulted in a decrease of plant symbiotic potential based on interactions with beneficial microorganisms. This decrease leads to transformation of plant micro-symbionts into the non-adaptive forms caused by: а) blocking the selection in favor of mutualistic strains; б) horizontal gene transfer in the microbial communities resulted in formation of virulent “symbiotic cheaters”. Mathematical simulation suggests that these tendencies may be overcome by formation of the optimal population structures in symbiotic system which should possess a high integrity and specificity of partners’ interactions as well as by a tolerance to the invasions of non-active aboriginal strains from the local soil populations.
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Wei, Hui, Craig A. Atkins, and David B. Layzell. "Adenylate Gradients and Ar:O2 Effects on Legume Nodules: I. Mathematical Models." Plant Physiology 134, no. 2 (January 22, 2004): 801–12. http://dx.doi.org/10.1104/pp.103.032318.
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Zhang, X. S., and J. Holt. "Mathematical Models of Cross Protection in the Epidemiology of Plant-Virus Diseases." Phytopathology® 91, no. 10 (October 2001): 924–34. http://dx.doi.org/10.1094/phyto.2001.91.10.924.
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Mathematical models of plant-virus disease epidemics were developed where cross protection occurs between viruses or virus strains. Such cross protection can occur both naturally and through artificial intervention. Examples of diseases with continuous and discontinuous crop-host availability were considered: citrus tristeza and barley yellow dwarf, respectively. Analyses showed that, in a single host population without artificial intervention, the two categories of host plants, infected with a protecting virus alone and infected with a challenging virus, could not coexist in the long term. For disease systems with continuous host availability, the virus (strain) with the higher basic reproductive number (R0) always excluded the other eventually; whereas, for discontinuous systems, R0 is undefined and the virus (strain) with the larger natural transmission rate was the one that persisted in the model formulation. With a proportion of hosts artificially inoculated with a protecting mild virus, the disease caused by a virulent virus could be depressed or eliminated, depending on the proportion. Artificial inoculation may be constant or adjusted in response to changes in disease incidence. The importance of maintaining a constant level of managed cross protection even when the disease incidence dropped was illustrated. Investigations of both pathosystem types showed the same qualitative result: that managed cross protection need not be 100% to eliminate the virulent virus (strain). In the process of replacement of one virus (strain) by another over time, the strongest competition occurred when the incidence of both viruses or virus strains was similar. Discontinuous crop-host availability provided a greater opportunity for viruses or virus strains to replace each other than did the more stable continuous cropping system. The process by which one Barley yellow dwarf virus replaced another in New York State was illustrated.
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Jungck, John R., Holly Gaff, and Anton E. Weisstein. "Mathematical Manipulative Models: In Defense of “Beanbag Biology”." CBE—Life Sciences Education 9, no. 3 (September 2010): 201–11. http://dx.doi.org/10.1187/cbe.10-03-0040.
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Mathematical manipulative models have had a long history of influence in biological research and in secondary school education, but they are frequently neglected in undergraduate biology education. By linking mathematical manipulative models in a four-step process—1) use of physical manipulatives, 2) interactive exploration of computer simulations, 3) derivation of mathematical relationships from core principles, and 4) analysis of real data sets—we demonstrate a process that we have shared in biological faculty development workshops led by staff from the BioQUEST Curriculum Consortium over the past 24 yr. We built this approach based upon a broad survey of literature in mathematical educational research that has convincingly demonstrated the utility of multiple models that involve physical, kinesthetic learning to actual data and interactive simulations. Two projects that use this approach are introduced: The Biological Excel Simulations and Tools in Exploratory, Experiential Mathematics (ESTEEM) Project ( http://bioquest.org/esteem ) and Numerical Undergraduate Mathematical Biology Education (NUMB3R5 COUNT; http://bioquest.org/numberscount ). Examples here emphasize genetics, ecology, population biology, photosynthesis, cancer, and epidemiology. Mathematical manipulative models help learners break through prior fears to develop an appreciation for how mathematical reasoning informs problem solving, inference, and precise communication in biology and enhance the diversity of quantitative biology education.
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van den Bosch, F., N. McRoberts, F. van den Berg, and L. V. Madden. "The Basic Reproduction Number of Plant Pathogens: Matrix Approaches to Complex Dynamics." Phytopathology® 98, no. 2 (February 2008): 239–49. http://dx.doi.org/10.1094/phyto-98-2-0239.
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The basic reproduction number, R0, is defined as the total number of infections arising from one newly infected individual introduced into a healthy (disease-free) host population. R0 is widely used in ecology and animal and human epidemiology, but has received far less attention in the plant pathology literature. Although the calculation of R0 in simple systems is straightforward, the calculation in complex situations is challenging. A very generic framework exists in the mathematical and biomathematical literature, which is difficult to interpret and apply in specific cases. In this paper we describe a special case of this general framework involving the use of matrix population models. Leading by example, we explain the existing mathematical literature on this subject in such a way that plant pathologists can apply the method for a wide range of pathosystems.
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Brown, David. "Linking Molecular and Population Processes in Mathematical Models of Quorum Sensing." Bulletin of Mathematical Biology 75, no. 10 (July 27, 2013): 1813–39. http://dx.doi.org/10.1007/s11538-013-9870-1.
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Novák, Libor, Luis Larrea, and Jiri Wanner. "Mathematical model for soluble carbonaceous substrate biosorption." Water Science and Technology 31, no. 2 (January 1, 1995): 67–77. http://dx.doi.org/10.2166/wst.1995.0075.
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An activated sludge mathematical model for soluble carbonaceous substrate biosorption has been developed. The model allows the soluble COD fractions in biological reactors of a wastewater treatment plant and/or in batch cultivations to be predicted more precisely than by using conventional models. Special attention was paid to interactions between the biokinetic model structure and population dynamics of microorganisms in activated sludge. The model was developed using observations made on a synthetic wastewater which was dosed to a lab-scale, continuously operated plant with the D-R-D-N configuration. The development of the model advanced through several biokinetic models which resulted in a final version of the biosorption model. The model is constructed on a matrix structure. Adsorption, desorption and hydrolysis kinetics are incorporated into the model. Experimental results from batch cultivations carried out under anoxic and oxic conditions as well as some dynamic tests carried out with the continuously operated system served for the model calibration. Simulations of a wide diversity of kinetic tests demonstrate that the model is able to accurately predict the soluble COD under different cultivation conditions.
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Araújo Júnior, Carlos Alberto, Renato Vinícius Oliveira Castro, João Batista Mendes, and Helio Garcia Leite. "CAN LINEAR PROGRAMMING ASSIST METAHEURISTICS IN FOREST PRODUCTION PLANNING PROBLEM?" FLORESTA 51, no. 3 (June 22, 2021): 751. http://dx.doi.org/10.5380/rf.v51i3.72612.
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The planning of forest production requires the adoption of mathematical models to optimize the utilization of available resources. Hence, studies involving the improvement of decision-making processes must be performed. Herein, we evaluate an alternative method for improving the performance of metaheuristics when they are applied for identifying solutions to problems in forest production planning. The inclusion of a solution obtained by rounding the optimal solution of linear programming to a relaxed problem is investigated. Such a solution is included in the initial population of the clonal selection algorithm, genetic algorithm, simulated annealing, and variable neighborhood search metaheuristics when it is used to generate harvest and planting plans in an area measuring 4,210 ha comprising 120 management units with ages varying between 1 and 6 years. The same algorithms are executed without including the solutions mentioned in the initial population. Results show that the performance of the clonal selection algorithm, genetic algorithm, and variable neighborhood search algorithms improved significantly. Positive effects on the performance of the simulated annealing metaheuristic are not indicated. Hence, it is concluded that rounding off the solution to a relaxed problem is a good alternative for generating an initial solution for metaheuristics.
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Hughes, G. "Validating mathematical models of plant-disease progress in space and time." Mathematical Medicine and Biology 14, no. 2 (June 1, 1997): 85–112. http://dx.doi.org/10.1093/imammb/14.2.85.
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Frisman, E. Ya, O. L. Zhdanova, M. P. Kulakov, G. P. Neverova, and O. L. Revutskaya. "Mathematical Modeling of Population Dynamics Based on Recurrent Equations: Results and Prospects. Part I." Biology Bulletin 48, no. 1 (January 2021): 1–15. http://dx.doi.org/10.1134/s1062359021010064.
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Abstract Approaches to modeling population dynamics using discrete-time models are described in this two-part review. The development of the scientific ideas of discrete time models, from the Malthus model to modern population models that take into account many factors affecting the structure and dynamics, is presented. The most important and interesting results of recurrent equation application to biological system analysis obtained by the authors are given. In the first part of this review, the population dynamic effects that result from density-dependent regulation of population, the age and sex structures, and the influence of external factors are considered.
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Westcott, M. P., and N. W. Callan. "Modeling Plant Population and Rectangularity Effects on Broccoli Head Weights and Yield." Journal of the American Society for Horticultural Science 115, no. 6 (November 1990): 893–97. http://dx.doi.org/10.21273/jashs.115.6.893.
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Broccoli (Brassica oleracea L. var. italica) head weights and yields are highly sensitive to plant densities (P) and rectangularity. Broccoli cultivars were grown at four plant spacings (2.2 to 8.6 plants/m2) and four N rates (O to 336 kg N/ha) in 1986 and 1987. In 1988, plug spacings, as above, were factorially combined with treatments of one, two, or three plants per plug. Head weight (w) data were fitted to the reciprocal model: 1/w = a + bp and the exponential model: w = AKP, where a, b, A, and K are constants. Nitrogen rate did not interact with p. In 1986 and 1987, both the reciprocal and exponential models fit the w data (expressed as w relative to wmax for each cultivar) with highly significant R2 values of 0.525 to 0.605. Yield equations derived from these models were asymptotic. In 1988, clumping (multiple plants per plug) reduced head weights but interacted with plant density. Only the exponential model could account for the assumption that clumping effects diminish as plant densities increase; the reciprocal model predicted the opposite effect. The exponential model was expanded to the form: w = CAKP, where C is proportionate reduction of w due to clumping. Derived yield models were asymptotic for the reciprocal model and parabolic for the exponential model.
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Spencer, Hamish G., and Janine A. Barnett. "Mutation-Selection Balance at a Modifier-of-Imprinting Locus." Genetics 144, no. 1 (September 1, 1996): 361–67. http://dx.doi.org/10.1093/genetics/144.1.361.
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Abstract We propose a pair of population genetic models for a modifier-of-imprinting locus for which different genotypes imprint different proportions of an imprintable target locus in their gametes. The two models examine the situations in which imprinting is advantageous or disadvantageous, and we discuss three cases for which the modifier is respectively partially dominant, dominant, or recessive. The models predict the stable equilibrium frequencies of the mutant modifier and functionally diploid individuals in a large population in terms of up to four parameters: the mutation rate at the modifier locus, v; the selection coefficient against the disadvantageous phenotype, s; the proportion of unimprinted eggs produced by homozygotes for the mutant modifier, 8, and, in the partially dominant models, the dominance parameter, k. The equilibrium frequency of the mutant phenotypes is shown to be approximately twice that of standard Mendelian models: 2v/s or 4v/s when the modifier is recessive or dominant, respectively. Mathematical equivalences between these and nonimprinting models are noted.
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Eldon, Bjarki. "Evolutionary Genomics of High Fecundity." Annual Review of Genetics 54, no. 1 (November 23, 2020): 213–36. http://dx.doi.org/10.1146/annurev-genet-021920-095932.
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Natural highly fecund populations abound. These range from viruses to gadids. Many highly fecund populations are economically important. Highly fecund populations provide an important contrast to the low-fecundity organisms that have traditionally been applied in evolutionary studies. A key question regarding high fecundity is whether large numbers of offspring are produced on a regular basis, by few individuals each time, in a sweepstakes mode of reproduction. Such reproduction characteristics are not incorporated into the classical Wright–Fisher model, the standard reference model of population genetics, or similar types of models, in which each individual can produce only small numbers of offspring relative to the population size. The expected genomic footprints of population genetic models of sweepstakes reproduction are very different from those of the Wright–Fisher model. A key, immediate issue involves identifying the footprints of sweepstakes reproduction in genomic data. Whole-genome sequencing data can be used to distinguish the patterns made by sweepstakes reproduction from the patterns made by population growth in a population evolving according to the Wright–Fisher model (or similar models). If the hypothesis of sweepstakes reproduction cannot be rejected, then models of sweepstakes reproduction and associated multiple-merger coalescents will become at least as relevant as the Wright–Fisher model (or similar models) and the Kingman coalescent, the cornerstones of mathematical population genetics, in further discussions of evolutionary genomics of highly fecund populations.
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Niklas, Karl J. "Modeling fossil plant form-function relationships: A critique." Paleobiology 26, S4 (2000): 289–304. http://dx.doi.org/10.1017/s009483730002697x.
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Attempts to model form-function relationships for fossil plants rely on the facts that the physiological and structural requirements for plant growth, survival, and reproductive success are remarkably similar for the majority of extant and extinct species regardless of phyletic affiliation and that most of these requirements can be quantified by means of comparatively simple mathematical expressions drawn directly from the physical and engineering sciences. Owing in part to the advent and rapid expansion of computer technologies, the number of fossil plant form-function models has burgeoned in the last two decades and encompasses every level of biological organization ranging from molecular self-assembly to ecological and evolutionary dynamics. This recent and expansive interest in modeling fossil plant form-function relationships is discussed in the context of the general philosophy of modeling past biological systems and how the reliability of models can be examined (i.e., direct experimental manipulation or observation of the system being modeled). This philosophy is illustrated and methods of validating models are critiqued in terms of four models drawn from the author's work (the quantification of wind-induced stem bending stresses, wind pollination efficiency of early Paleozoic ovulate reproductive structures, population dynamics and species extinction in monotypic and “mixed” communities, and the adaptive radiation of early vascular land plants). The assumptions and logical (mathematical) consequences (predictions) of each model are broadly outlined, and, in each case, the model is shown to be overly simplistic despite its ability to predict the general or particular behavior or operation of the system modeled. Nonetheless, these four models, which illustrate some of pros and cons of modeling fossil form-function relationships, are argued to be pedagogically useful because, like all models, they expose the internal logical consistency of our basic assumptions about how organic form and function interrelate.
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Britton, Nicholas F., Iulia Martina Bulai, Stéphanie Saussure, Niels Holst, and Ezio Venturino. "Can aphids be controlled by fungus? A mathematical model." Applied Mathematics and Nonlinear Sciences 4, no. 1 (June 21, 2019): 79–92. http://dx.doi.org/10.2478/amns.2019.1.00009.
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AbstractThe control of insect pests in agriculture is essential for food security. Chemical controls typically damage the environment and harm beneficial insects such as pollinators, so it is advantageous to identify targetted biological controls. Since predators are often generalists, pathogens or parasitoids are more likely to serve the purpose. Here, we model a fungal pathogen of aphids as a potential means to control of these important pests in cereal crops. Typical plant herbivore pathogen models are set up on two trophic levels, with dynamic variables the plant biomass and the uninfected and infected herbivore populations. Our model is unusual in that (i) it has to be set up on three trophic levels to take account of fungal spores in the environment, but (ii) the aphid feeding mechanism leads to the plant biomass equation becoming uncoupled from the system. The dynamical variables are therefore the uninfected and infected aphid population and the environmental fungal concentration. We carry out an analysis of the dynamics of the system. Assuming that the aphid population can survive in the absence of disease, the fungus can only persist (and control is only possible) if (i) the host grows sufficiently strongly in the absence of infection, and (ii) the pathogen transmission parameters are sufficiently large. If it does persist the fungus does not drive the aphid population to extinction, but controls it below its disease-free steady state value, either at a new coexistence steady state or through oscillations. Whether this control is sufficient for agricultural purposes will depend on the detailed parameter values for the system.
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Rousseau, Elsa, Mélanie Bonneault, Frédéric Fabre, Benoît Moury, Ludovic Mailleret, and Frédéric Grognard. "Virus epidemics, plant-controlled population bottlenecks and the durability of plant resistance." Philosophical Transactions of the Royal Society B: Biological Sciences 374, no. 1775 (May 6, 2019): 20180263. http://dx.doi.org/10.1098/rstb.2018.0263.
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Plant qualitative resistances to viruses are natural exhaustible resources that can be impaired by the emergence of resistance-breaking (RB) virus variants. Mathematical modelling can help determine optimal strategies for resistance durability by a rational deployment of resistance in agroecosystems. Here, we propose an innovative approach, built up from our previous empirical studies, based on plant cultivars combining qualitative resistance with quantitative resistance narrowing population bottlenecks exerted on viruses during host-to-host transmission and/or within-host infection. Narrow bottlenecks are expected to slow down virus adaptation to plant qualitative resistance. To study the effect of bottleneck size on yield, we developed a stochastic epidemic model with mixtures of susceptible and resistant plants, relying on continuous-time Markov chain processes. Overall, narrow bottlenecks are beneficial when the fitness cost of RB virus variants in susceptible plants is intermediate. In such cases, they could provide up to 95 additional percentage points of yield compared with deploying a qualitative resistance alone. As we have shown in previous works that virus population bottlenecks are at least partly heritable plant traits, our results suggest that breeding and deploying plant varieties exposing virus populations to narrowed bottlenecks will increase yield and delay the emergence of RB variants. 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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Innan, Hideki. "Population genetic models of duplicated genes." Genetica 137, no. 1 (March 6, 2009): 19–37. http://dx.doi.org/10.1007/s10709-009-9355-1.
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Otto, S. P., and A. C. Gerstein. "Why have sex? The population genetics of sex and recombination." Biochemical Society Transactions 34, no. 4 (July 21, 2006): 519–22. http://dx.doi.org/10.1042/bst0340519.
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One of the greatest puzzles in evolutionary biology is the high frequency of sexual reproduction and recombination. Given that individuals surviving to reproductive age have genomes that function in their current environment, why should they risk shuffling their genes with those of another individual? Mathematical models are especially important in developing predictions about when sex and recombination can evolve, because it is difficult to intuit the outcome of evolution with several interacting genes. Interestingly, theoretical analyses have shown that it is often quite difficult to identify conditions that favour the evolution of high rates of sex and recombination. For example, fitness interactions among genes (epistasis) can favour sex and recombination but only if such interactions are negative, relatively weak and not highly variable. One reason why an answer to the paradox of sex has been so elusive is that our models have focused unduly on populations that are infinite in size, unstructured and isolated from other species. Yet most verbal theories for sex and recombination consider a finite number of genotypes evolving in a biologically and/or physically complex world. Here, we review various hypotheses for why sex and recombination are so prevalent and discuss theoretical results indicating which of these hypotheses is most promising.
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Gomulkiewicz, Richard, and Ruth G. Shaw. "Evolutionary rescue beyond the models." Philosophical Transactions of the Royal Society B: Biological Sciences 368, no. 1610 (January 19, 2013): 20120093. http://dx.doi.org/10.1098/rstb.2012.0093.
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Laboratory model systems and mathematical models have shed considerable light on the fundamental properties and processes of evolutionary rescue. But it remains to determine the extent to which these model-based findings can help biologists predict when evolution will fail or succeed in rescuing natural populations that are facing novel conditions that threaten their persistence. In this article, we present a prospectus for transferring our basic understanding of evolutionary rescue to wild and other non-laboratory populations. Current experimental and theoretical results emphasize how the interplay between inheritance processes and absolute fitness in changed environments drive population dynamics and determine prospects of extinction. We discuss the challenge of inferring these elements of the evolutionary rescue process in field and natural settings. Addressing this challenge will contribute to a more comprehensive understanding of population persistence that combines processes of evolutionary rescue with developmental and ecological mechanisms.
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Sugg, D. W., and R. K. Chesser. "Effective population sizes with multiple paternity." Genetics 137, no. 4 (August 1, 1994): 1147–55. http://dx.doi.org/10.1093/genetics/137.4.1147.
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Abstract While the concept of effective population size is of obvious applicability to many questions in population genetics and conservation biology, its utility has suffered due to a lack of agreement among its various formulations. Often, mathematical formulations for effective sizes apply restrictive assumptions that limit their applicability. Herein, expressions for effective sizes of populations that account for mating tactics, biases in sex ratios, and differential dispersal rates (among other parameters) are developed. Of primary interest is the influence of multiple paternity on the maintenance of genetic variation in a population. In addition to the standard inbreeding and variance effective sizes, intragroup (coancestral) and intergroup effective sizes also are developed. Expressions for effective sizes are developed for the beginning of nonrandom gene exchanges (initial effective sizes), the transition of gene correlations (instantaneous effective sizes), and the steady-state (asymptotic effective size). Results indicate that systems of mating that incorporate more than one male mate per female increase all effective sizes above those expected from polygyny and monogamy. Instantaneous and asymptotic sizes can be expressed relative to the fixation indices. The parameters presented herein can be utilized in models of effective sizes for the study of evolutionary biology and conservation genetics.
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Schoen, Daniel J., and Michael T. Clegg. "MONTE CARLO STUDIES OF PLANT MATING SYSTEM ESTIMATION MODELS: THE ONE-POLLEN PARENT AND MIXED MATING MODELS." Genetics 112, no. 4 (April 1, 1986): 927–45. http://dx.doi.org/10.1093/genetics/112.4.927.
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ABSTRACT Estimation of mating system parameters in plant populations typically employs family-structured samples of progeny genotypes. These estimation models postulate a mixture of self-fertilization and random outcrossing. One assumption of such models concerns the distribution of pollen genotypes among eggs within single maternal families. Previous applications of the mixed mating model to mating system estimation have assumed that pollen genotypes are sampled randomly from the total population in forming outcrossed progeny within families. In contrast, the one-pollen parent model assumes that outcrossed progeny within a family share a single-pollen parent genotype. Monte Carlo simulations of family-structured sampling were carried out to examine the consequences of violations of the different assumptions of the two models regarding the distribution of pollen genotypes among eggs. When these assumptions are violated, estimates of mating system parameters may be significantly different from their true values and may exhibit distributions which depart from normality. Monte Carlo methods were also used to examine the utility of the bootstrap resampling algorithm for estimating the variances of mating system parameters. The bootstrap method gives variance estimates that approximate empirically determined values. When applied to data from two plant populations which differ in pollen genotype distributions within families, the two estimation procedures exhibit the same behavior as that seen with the simulated data.
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Jovanović, Ivana, and Igor Miljanović. "Modelling Of Flotation Processes By Classical Mathematical Methods – A Review." Archives of Mining Sciences 60, no. 4 (December 1, 2015): 905–19. http://dx.doi.org/10.1515/amsc-2015-0059.
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Abstract Flotation process modelling is not a simple task, mostly because of the process complexity, i.e. the presence of a large number of variables that (to a lesser or a greater extent) affect the final outcome of the mineral particles separation based on the differences in their surface properties. The attempts toward the development of the quantitative predictive model that would fully describe the operation of an industrial flotation plant started in the middle of past century and it lasts to this day. This paper gives a review of published research activities directed toward the development of flotation models based on the classical mathematical rules. The description and systematization of classical flotation models were performed according to the available references, with emphasize exclusively given to the flotation process modelling, regardless of the model application in a certain control system. In accordance with the contemporary considerations, models were classified as the empirical, probabilistic, kinetic and population balance types. Each model type is presented through the aspects of flotation modelling at the macro and micro process levels.
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Smieja, Jaroslaw, Andrzej Swierniak, and Zdzislaw Duda. "Gradient Method for Finding Optimal Scheduling in Infinite Dimensional Models of Chemotherapy." Journal of Theoretical Medicine 3, no. 1 (2000): 25–36. http://dx.doi.org/10.1080/10273660008833062.
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One of the major obstacles against succesful chemotherapy of cancer is the emergence of resistance of cancer cells to cytotoxic agents. Applying optimal control theory to mathematical models of cell cycle dynamics can be a very efficient method to understand and, eventually, overcome this problem. Results that have been hitherto obtained have already helped to explain some observed phenomena, concerning dynamical properties of cancer populations. Because of recent progress in understanding the way in which chemotherapy affects cancer cells, new insights and more precise mathematical formulation of control problem, in the meaning of finding optimal chemotherapy, became possible. This, together with a progress in mathematical tools, has renewed hopes for improving chemotherapy protocols. In this paper we consider a population of neoplastic cells stratified into subpopulations of cells of different types. Due to the mutational event a sensitive cell can acquire a copy of the gene that makes it resistant to the agent. Likewise, the division of resistant cells can result in the change of the number of gene copies. We convert the model in the form of an infinite dimensional system of ordinary differential state equations discussed in our previous publications (see e.g. Swierniak etal., 1996b; Polariski etal., 1997; Swierniak etaL, 1998c), into the integro-differential form. It enables application of the necessary conditions of optimality given by the appropriate version of Pontryagin's maximum principle, e.g. (Gabasov and Kirilowa, 1971). The performance index which should be minimized combines the negative cumulated cytotoxic effect of the drug and the terminal population of both sensitive and resistant neoplastic cells. The linear form of the cost function and the bilinear form of the state equation result in a bang-bang optimal control law. To find the switching times we propose to use a special gradient algorithm developed similarly to the one applied in our previous papers to finite dimensional problems (Duda 1994; 1997).
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Pochukalin, A. Ye. "COMPARING THE VALUES OF CONSOLIDATION AND DISCRETION BY SELECTIVE OBSERVATIONS AND THEIR COMPLEXES IN RIGIONAL FAMILIES OF VOLINIAN BEEF." Animal Breeding and Genetics 54 (November 29, 2017): 91–97. http://dx.doi.org/10.31073/abg.54.11.
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Factory families today have not lost their influence on the formation of the desired genotype of offspring with high performance. This is contributed to the forgotten but active biological role of the maternal effect. The reduced attention in the breeding process with the work of factory families is reduced to two factors, namely the reduction of the length of productive use of cows and a small number of offspring. But in scientific publications, especially in dairy cattle breeding, there are constantly reported on the number, characteristics of breeding grounds or the evaluation of plant families in mathematical models based on population genetic parameters. In meat cattle, the importance of families has not become widespread, although the duration of productive use of cows of meat production has advantages over diary. The aim of the research was to evaluate the factory families of Volinian meat breed for using different coefficients of consolidation of the main breeding grounds. Materials and methods of research. The research was carried out in the conditions of the breeding farm of LLC "Zorya" of Kovel district of Volyn region. The object of research was the cows of the Volinian meat breed. According to the breeding records, 18 regional families were formed, which belong to six lines with a total population of 160 heads. In order to assess the stability (restriction of phenotypic variability) of plant families in practical selection, we have tested the methods of determining the degree of consolidation by certain characteristics of Yu. P. Polupan and the degree of discreteness of families V. V. Seromolot, S. I. Svyatchenko. The average level of consolidation by Yu. P. Polupan was calculated from the mean-square values. The methodical suitability of these methods was evaluated in two (dairy animals after the first calving and live weight in 210 days) and four (live weight at the age of 210 days, 12, 15 months and breast milk) by the studied characteristics. In the long-term selection process in families, the process of consolidation with a constant level of quantitative attributes, which are consistently inherited in generations while simultaneously narrowing genotype and phenotypic variability, is achieved. The mentioned process in the studied factory families has a significant variability according to the selection criteria. In studying the consolidation of live weight in different age periods, there are variables in ten families. The families of Akula 102, Arpha 599 and Wisla 1016 for live weight were unconsolidated at all ages, and their average rate was -0.148. Among the five, the consolidated families have an average value of 210 days, 0.244, in the 12 and 15 months, respectively, 0.375 and 0.268. The greatest value are the families of Verbi 1536, Galky 37 and Veselky 444 and Bistroi 1124, whose consolidation coefficient ranges from 0.260 to 0.430. These families, in our opinion, should be considered valuable, since, in addition to the reduced group volatility, they have high actual mean values for live weight, and therefore extensions of these families should have an advantage over the selection of repair young animals. The lowest level of consolidation is with the families of Arpha 599, Bulana 943 and Wisla 1016. Selection work with them should be aimed at selecting the breeding stock of prey bulls of high tribal value. The significant difference (1,136) between the threshold levels of the coefficient of family consolidation for the milk yield of cows after the first calving indicates a high variability. The average of nine consolidated families is 0.175, which is only 0.088 above the average for the general group. The highest coefficient values were obtained in the families of Garna 536, Galka 421 and Rosetka 1313. With a decrease in the number of economic indicators considered useful in both methods, there is a decrease in unconsolidated families to six. The average values in discrete families are 0.336, consolidated at 0.178. The most consolidated were the families of Galka 421, Rosetka 1313 and Garna 536, and the discrete families of Galka 421, Corona 2382 and Rosetka 1313, the average value of which is respectively 0.630 and 0.367. The use of the coefficients of phenotypic consolidation and discreteness in the complex of breeding grounds in the factory families showed the advantage of consolidation by the leveling of the results obtained and the lower the dependence on the number of accounted signs. The index of discreteness for an increase of two to four characteristics taken into account on a modulus increases on average by 1.54 times.
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Gilligan, Christopher A., and Adam Kleczkowski. "Population dynamics of botanical epidemics involving primary and secondary infection." Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences 352, no. 1353 (May 29, 1997): 591–608. http://dx.doi.org/10.1098/rstb.1997.0040.
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In this paper we study the dynamical properties of models for botanical epidemics, especially for soil–borne fungal infection. The models develop several new concepts, involving dual sources of infection, host and inoculum dynamics. Epidemics are modelled with respect to the infection status of whole plants and plant organs (the G model) or to lesion density and size (the SW model). The infection can originate in two sources, either from the initial inoculum (primary infection) or by a direct transmission between plant tissue (secondary infection). The first term corresponds to the transmission through the free–living stages of macroparasites or an external source of infection in certain medical models, whereas the second term is equivalent to direct transmission between the hosts in microparasitic infections. The models allow for dynamics of host growth and inoculum decay. We show that the two models for root and lesion dynamics can be derived as special cases of a single generic model. Analytical and numerical methods are used to analyse the behaviour of the models for static, unlimited (exponential) and asymptotically limited host growth with and without secondary infection, and with and without decay of initial inoculum. The models are shown to exhibit a range of epidemic behaviour within single seasons that extends from simple monotonic increase with saturation of the host population, through temporary plateaux as the system switches from primary to secondary infection, to effective elimination of the pathogen by the host outgrowing the fungal infection. For certain conditions, the equilibrium values are shown to depend on initial conditions. These results have important consequences for the control of plant disease. They can be applied beyond soil–borne plant pathogens to mycorrhizal fungi and aerial pathogens while the principles of primary and secondary infection with host and inoculum dynamics may be used to link classical models for both microparasitic and macroparasitic infections.
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Przulj, Novo, and Vojislava Momcilovic. "Characterization of vegetative and grain filling periods of winter wheat by stepwise regression procedure: I. Vegetative period." Genetika 43, no. 2 (2011): 349–59. http://dx.doi.org/10.2298/gensr1102349p.
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Modeling plant growth by mathematical functions is important for understanding plant development and growth. Most of the models of dry matter accumulation in small cereals simulated the period of grain filling while small attention has been devoted to mathematical simulation of vegetative period till anthesis. The aim of this research was to determine the most appropriate polynomial non-linear regression for dry matter accumulation till anthesis in winter wheat. Pobeda, a medium early variety, was used as model genotype for this research. A 5-year field data were analyzed by the forward procedure of stepwise regression. Although the procedure requires the maximum power of the polynomial regression to be used, we suggest using a lower power since it is easier for understanding and explanation and it is taking into account literature sources and biological laws. It can be accepted that quadratic regression model appropriately fits the process of dry matter accumulation till anthesis in winter wheat.
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Hu, Xin-Sheng, and Richard A. Ennos. "Impacts of Seed and Pollen Flow on Population Genetic Structure for Plant Genomes With Three Contrasting Modes of Inheritance." Genetics 152, no. 1 (May 1, 1999): 441–50. http://dx.doi.org/10.1093/genetics/152.1.441.
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Abstract The classical island and one-dimensional stepping-stone models of population genetic structure developed for animal populations are extended to hermaphrodite plant populations to study the behavior of biparentally inherited nuclear genes and organelle genes with paternal and maternal inheritance. By substituting appropriate values for effective population sizes and migration rates of the genes concerned into the classical models, expressions for genetic differentiation and correlation in gene frequency between populations can be derived. For both models, differentiation for maternally inherited genes at migration-drift equilibrium is greater than that for paternally inherited genes, which in turn is greater than that for biparentally inherited nuclear genes. In the stepping-stone model, the change of genetic correlation with distance is influenced by the mode of inheritance of the gene and the relative values of long- and short-distance migration by seed and pollen. In situations where it is possible to measure simultaneously Fst for genes with all three types of inheritance, estimates of the relative rates of pollen to seed flow can be made for both the short- and long-distance components of migration in the stepping-stone model.
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Elgazzar, Ahmed S. "Simple mathematical models for controlling COVID-19 transmission through social distancing and community awareness." Zeitschrift für Naturforschung C 76, no. 9-10 (April 19, 2021): 393–400. http://dx.doi.org/10.1515/znc-2021-0004.
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Abstract The novel COVID-19 pandemic is a current, major global health threat. Up till now, there is no fully approved pharmacological treatment or a vaccine. Also, its origin is still mysterious. In this study, simple mathematical models were employed to examine the dynamics of transmission and control of COVID-19 taking into consideration social distancing and community awareness. Both situations of homogeneous and nonhomogeneous population were considered. Based on the calculations, a sufficient degree of social distancing based on its reproductive ratio is found to be effective in controlling COVID-19, even in the absence of a vaccine. With a vaccine, social distancing minimizes the sufficient vaccination rate to control the disease. Community awareness also has a great impact in eradicating the virus transmission. The model is simulated on small-world networks and the role of social distancing in controlling the infection is explained.
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Tokuda, Isao T., Ozgur E. Akman, and James C. W. Locke. "Reducing the complexity of mathematical models for the plant circadian clock by distributed delays." Journal of Theoretical Biology 463 (February 2019): 155–66. http://dx.doi.org/10.1016/j.jtbi.2018.12.014.
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Shahtahmasebi, Said. "The Good Life: A Holistic Approach to the Health of the Population." Scientific World JOURNAL 6 (2006): 2117–32. http://dx.doi.org/10.1100/tsw.2006.341.
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The idea of a holistic approach towards public health planning presented itself through a food-related and trivial curiosity. It is, however, emphasized that food and nutrition are only one aspect of public health. The aim is to reintroduce a holistic approach to achieve sustainable public health with emphasis on the interpretation of the term “holistic”. Holistic decision making is not a new phenomenon and has historical basis. In line with shifts in social norms, decision making has evolved. In particular, various complex models for public health have been proposed to respond to ever-increasing health issues. The advancement in mathematical sciences and technology has led to the quantification of health models. However, mathematical representations pose a major limitation on the holistic approach. Due to its evolutionary nature, human health is dynamically related to social, environmental, and other processes. With the current knowledge, it is difficult to quantify the evolution and feedback effects in holistic models. In this paper, the individual's and public's health is viewed as a dynamic process, but not independent of other dynamic processes (e.g., agriculture, economy, politics) that are all part of a much bigger process. Furthermore, it is argued that it is not merely sufficient to account for all known factors to be holistic. In this paper, the holistic conceptual model is illustrated, using public health as the central issue. The application of the conceptual model is also discussed using two practical examples.
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Paenke, Ingo, Tadeusz J. Kawecki, and Bernhard Sendhoff. "The Influence of Learning on Evolution: A Mathematical Framework." Artificial Life 15, no. 2 (April 2009): 227–45. http://dx.doi.org/10.1162/artl.2009.15.2.15204.
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The Baldwin effect can be observed if phenotypic learning influences the evolutionary fitness of individuals, which can in turn accelerate or decelerate evolutionary change. Evidence for both learning-induced acceleration and deceleration can be found in the literature. Although the results for both outcomes were supported by specific mathematical or simulation models, no general predictions have been achieved so far. Here we propose a general framework to predict whether evolution benefits from learning or not. It is formulated in terms of the gain function, which quantifies the proportional change of fitness due to learning depending on the genotype value. With an inductive proof we show that a positive gain-function derivative implies that learning accelerates evolution, and a negative one implies deceleration under the condition that the population is distributed on a monotonic part of the fitness landscape. We show that the gain-function framework explains the results of several specific simulation models. We also use the gain-function framework to shed some light on the results of a recent biological experiment with fruit flies.
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Cai, Xiaodian, Jinyan Teng, Duanyang Ren, Hao Zhang, Jiaqi Li, and Zhe Zhang. "Model Comparison of Heritability Enrichment Analysis in Livestock Population." Genes 13, no. 9 (September 13, 2022): 1644. http://dx.doi.org/10.3390/genes13091644.
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Heritability enrichment analysis is an important means of exploring the genetic architecture of complex traits in human genetics. Heritability enrichment is typically defined as the proportion of an SNP subset explained heritability, divided by the proportion of SNPs. Heritability enrichment enables better study of underlying complex traits, such as functional variant/gene subsets, biological networks and metabolic pathways detected through integrating explosively increased omics data. This would be beneficial for genomic prediction of disease risk in humans and genetic values estimation of important economical traits in livestock and plant species. However, in livestock, factors affecting the heritability enrichment estimation of complex traits have not been examined. Previous studies on humans reported that the frequencies, effect sizes, and levels of linkage disequilibrium (LD) of underlying causal variants (CVs) would affect the heritability enrichment estimation. Therefore, the distribution of heritability across the genome should be fully considered to obtain the unbiased estimation of heritability enrichment. To explore the performance of different heritability enrichment models in livestock populations, we used the VanRaden, GCTA and α models, assuming different α values, and the LDAK model, considering LD weight. We simulated three types of phenotypes, with CVs from various minor allele frequency (MAF) ranges: genome-wide (0.005 ≤ MAF ≤ 0.5), common (0.05 ≤ MAF ≤ 0.5), and uncommon (0.01 ≤ MAF < 0.05). The performances of the models with two different subsets (one of which contained known CVs and the other consisting of randomly selected markers) were compared to verify the accuracy of heritability enrichment estimation of functional variant sets. Our results showed that models with known CV subsets provided more robust enrichment estimation. Models with different α values tended to provide stable and accurate estimates for common and genome-wide CVs (relative deviation 0.5–2.2%), while tending to underestimate the enrichment of uncommon CVs. As the α value increased, enrichments from 15.73% higher than true value (i.e., 3.00) to 48.93% lower than true value for uncommon CVs were observed. In addition, the long-range LD windows (e.g., 5000 kb) led to large bias of the enrichment estimations for both common and uncommon CVs. Overall, heritability enrichment estimations were sensitive for the α value assumption and LD weight consideration of different models. Accuracy would be greatly improved by using a suitable model. This study would be helpful in understanding the genetic architecture of complex traits and provides a reference for genetic analysis in the livestock population.
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Steiner, Margaret C., and John Novembre. "Population genetic models for the spatial spread of adaptive variants: A review in light of SARS-CoV-2 evolution." PLOS Genetics 18, no. 9 (September 22, 2022): e1010391. http://dx.doi.org/10.1371/journal.pgen.1010391.
Full textAbstract:
Theoretical population genetics has long studied the arrival and geographic spread of adaptive variants through the analysis of mathematical models of dispersal and natural selection. These models take on a renewed interest in the context of the COVID-19 pandemic, especially given the consequences that novel adaptive variants have had on the course of the pandemic as they have spread through global populations. Here, we review theoretical models for the spatial spread of adaptive variants and identify areas to be improved in future work, toward a better understanding of variants of concern in Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) evolution and other contemporary applications. As we describe, characteristics of pandemics such as COVID-19—such as the impact of long-distance travel patterns and the overdispersion of lineages due to superspreading events—suggest new directions for improving upon existing population genetic models.
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Villafaina, Santos, Clarissa Biehl-Printes, José A. Parraca, Fabiane de Oliveira Brauner, and Pablo Tomas-Carus. "What Mathematical Models Are Accurate for Prescribing Aerobic Exercise in Women with Fibromyalgia?" Biology 11, no. 5 (May 4, 2022): 704. http://dx.doi.org/10.3390/biology11050704.
Full textAbstract:
Objectives: This article aims to verify the agreement between the standard method to determine the heart rate achieved in the ventilatory threshold 1 in the cardiopulmonary exercise testing (VT1) and the mathematical models with exercise intensities suggested by the literature in order to check the most precise for fibromyalgia (FM) patients. Methods: Seventeen women with FM were included in this study. The VT1 was used as the standard method to compare four mathematical models applied in the literature to calculate the exercise intensity in FM patients: the well-known “220 − age” at 76%, Tanaka predictive equation “208 − 0.7 × age” at 76%, the FM model HRMax “209 – 0.85 × age” at 76%, and Karvonen Formula at 60%. Bland–Altman analysis and correlation analyses were used to explore agreement and correlation between the standard method and the mathematical models. Results: Significant correlations between the heart rate at the VT1 and the four mathematical estimation models were observed. However, the Bland-Altman analysis only showed agreement between VT1 and “220 − age” (bias = −114.83 + 0.868 × x; 95% LOA = −114.83 + 0.868 × x + 1.96 × 7.46 to −114.83 + 0.868 × x − 1.96 × 7.46, where x is the average between the heart rate obtained in the CPET at VT1 and “220 − age”, in this case 129.15; p = 0.519) and “209 − 0.85 × age”(bias = −129.58 + 1.024 × x; 95% LOA = −129.58 + 1.024 × x + 1.96 × 6.619 to −129.58 + 1.024 × x − 1.96 × 6.619, where x is the average between the heart rate obtained in the CPET at VT1 and “209 − 0.85 × age”, in this case 127.30; p = 0.403). Conclusions: The well-known predictive equation “220 − age” and the FM model HRMax (“209 − 0.85 × age”) showed agreement with the standard method (VT1), revealing that it is a precise model to calculate the exercise intensity in sedentary FM patients. However, proportional bias has been detected in all the mathematical models, with a higher heart rate obtained in CPET than obtained in the mathematical model. The chronotropic incompetence observed in people with FM (inability to increase heart rate with increasing exercise intensities) could explain why methods that tend to underestimate the HRmax in the general population fit better in this population.