九州大学数理生物学研究室

セミナー情報

ME Seminar


The Mathematical Biology Laboratory of Kyushu University holds informal seminars.
Anyone who has interest in them is welcome!


Access:  Kyushu University - Ito campus (West Zone 1)


Coordinator:  Shoya Iwanami
Graduate School of Systems Life Sciences, Kyushu University,
Fukuoka 819-0395, Japan
tel +81-92-802-4299

Moving beyond classical genome-wide association studies – complex traits and extended models

Eriko Sasaki

Gregor Mendel Institute of Molecular Plant Biology

2018/10/17, 16:30-, at W1-C-909



Abstract

     Many traits of individuals are controlled by genetic basis, as well as by the environment. Despite intense research over the last several decades, genotype-phenotype relationships remain largely unclear. However, with the accumulation of large numbers of individual genome sequences due to the rapid development of sequencing technology, this is beginning to change. A Genome-Wide Association Study (GWAS) is a method for identifying the genetic basis of quantitative traits by exploring associations between SNPs and phenotypic variations within a population. Extension of GWAS models makes it possible to flexibly estimate the effects of genetics, the environment, and their interaction. Using these extended GWAS models and natural populations of the model plant Arabidopsis thaliana, we are exploring the genetic architectures underlying complex quantitative traits. In this seminar, I will introduce two examples of GWAS applications from our previous studies. The first example concerns the genetic and environmental interactions (G x E) that control a life-history trait, flowering time (Sasaki et al., 2015). Although the environmental response is a major factor of adaptation, the genetic basis of this response is largely unknown. Using GWAS, we screened for environment-dependent genetic effects on flowering time phenotypes and identified small fractions of the genome that explained almost all the flowering time variation. The second example concerns the genetic control of an epigenetic mark, DNA methylation variation (Kawakatsu et al., 2016). DNA methylation plays an important role in various biological systems, including silencing of transposons and imprinting, and large natural variation in methylation has been reported. In this study, we identified major alleles controlling this phenotypic variation in two key DNA methylation pathways and found the geographic cline.

References
Sasaki, E. et al., "Missing" G x E Variation Controls Flowering Time in Arabidopsis thaliana. PLoS Genet., 11(10):e1005597 (2015)
Kawakatsu T., et al., Epigenetic Diversity in a Global Collection of Arabidopsis thaliana Accessions. Cell, 166:492-505 (2016)

TCR signaling in a pool of low affinity ligands

Koichi Saeki

Utrecht University

2018/10/16, 13:30-, at W1-C-909



Abstract

     T cells scan the surface of antigen presenting cells (APCs) to detect foreign peptides on major histocompatibility complex (MHC). Recognition takes place via the binding of T cell receptor (TCR) to peptide-MHC (pMHC) and the transduction of downstream signaling cascades. To induce a proper immune response, it is essential that T cells are activated when they bind to foreign peptides and not when confronted with self-peptides. Although T cells that have high affinity to self-peptides are deleted during development in the thymus, T cells in the periphery should still discriminate foreign peptides with high affinity to its TCR from the many and abundant low affinity self peptides. Failures in this discrimination result in either infection or autoimmune diseases.
     Many models have been suggested to explain this, however, it is not clear that how peptide discrimination by TCRs is disturbed in the background of many low affinity self-peptides that could antagonize signaling. Here we simulate the TCR signaling model developed by Francois et al. 2013 with low affinity ligands, and quantify the ability of ligand discrimination using mutual information. The mutual information indicates the maximum number of input signal values that a signaling pathway can reliably resolve. The results show that ligand discrimination works only in the presence of antagonists with very low affinity, which suggests that negative selection of immature T cells should be very strict. We will also discuss how the selection of immature T cells with different strength of TCR signaling results in different T cell differentiation.

Understanding the Dynamics of Biodiversity Loss.

John M. Halley

Department of Biological Applications and Technology, University of Ioannina, Greece

2018/8/10, 13:30-, at W1-C-909



Abstract

     If habitats contract or get fragmented, these reduced habitats cannot continue to support the same biodiversity as they did before, so they must lose species. While some species will be lost immediately, others can persist for a long time before going extinct. Indeed, areas recently protected may continue to lose species long after habitat loss has stopped. So, just because we don’t observe extinctions right away does not mean that everything is going to be OK. This phenomenon, often called “extinction debt”, also has implications for how ecosystems respond to climate change and to ecological invasions. A major scientific challenge is to understand the dynamics of this effect: how long before the extinctions are complete and which parameters drive it? Answering these depends to a large extent not only on having good empirical results but also on having a sound theoretical model of the community. I will be reviewing our current state of knowledge in this area and what case studies and larger meta-analyses have revealed. I will also discuss research on various models of the process and how our theoretical results can be used to design improved protected areas.

Evolution of mutation rate considering the trade-off between replication speed and fidelity and effects of genome size: analyses by simulations.

Yuta Aoyagi

Graduate School of Life Science, Tohoku University

2018/8/9, 13:30-, at W1-C-909



Abstract

     Mutation rates are diversified within a species and across species. Why has the diversity of mutation rates evolved? What factors select high and low mutation rates? In this research, to elucidate the evolution of the diversity of the mutation rates and conditions selecting high and low mutation rates, we constructed a simulation model considering genes governing faithful DNA replication and growth rate.
     We considered a population consisted of monoploid unicellular asexual organisms. Each individual has two groups of genes: the repair genes and the competition genes. The repair genes govern DNA repair and replication speed. Here, we considered the trade-off between replication speed and fidelity; it is necessary to repair faithfully to suppress mutations, but it takes more time to repair faithfully. Thus, the higher fidelity, the lower replication speed is. The individuals with faster replication speed divides faster. The competition genes govern the competitive ability between individuals for survival. In DNA replication, replication errors occur in these two groups of genes and are partially repaired. The repairing probability of errors is determined by the repair genes and both of beneficial and deleterious replication errors are repaired at the same probability without discrimination. After that, individuals compete for survival. This process repeats until a stationary state. We analyzed the effects of genome size (the total size of the repair genes and the competition genes), probability of occurring beneficial and deleterious mutations, population size and others, on the evolution of mutation rate.
     In a population consisted of individuals with a large genome size, a high repair rate (consequently, a low mutation rate), a slow replication speed, and a large competitive ability evolved. Such a result may be because larger genome sizes potentially lead to large numbers of replication errors. Thus, to prevent considerable decrease in competitive ability by the large amount of deleterious mutations, even though the replication speed becomes late, a high repair rate and a consequent low mutation rate evolved. Furthermore, the lower mutation rate was, the larger competitive ability was; i.e., advantageous traits evolve when mutation rates are low. This result can be intuitively understood. If mutation rates are high, many mutations simultaneously occur in single individuals. Then, if beneficial mutations occur rarely, the fitnesses of these individuals should decrease due to the overall effects of mutations, and rare beneficial mutations cannot spread. On the other hand, if mutation rates are low, it is possible that individuals having only a beneficial mutation emerge in the population, though most other individuals should have low numbers of disadvantageous mutations. Then, the individuals having beneficial mutations are superior in the survival, spreading beneficial mutations to the population.
     Low mutation rate evolves in small genome size, and high mutation rate evolves in large genome size. Furthermore, high mutation rate evolves when high growth rate is advantageous, and low mutation rate evolve when individuals need to acquire beneficial mutations.

Harmonising Creative Destruction and the Natural Economy using a Macro-economic Game and Pasinetti’s Vertically Integrated Analysis.

Koji Akimoto

Faculty of Economics, Kurume University

2018/6/25, 16:30-, at W1-C-909



Abstract

     This paper studies a proposition. That is, can a natural economy operate in the violent structural changes caused by creative destruction? A fundamental awareness of problem is that a fundamental cause of economic crises is a deviation from natural economy. To analyse this proposition, we demonstrate that the macro-economic game in Akimoto (2016)* is continuous to the Pasinetti’s vertically integrated model at natural economy.
     Akimoto (2016) demonstrated a natural economy could operate in the macro-economy and obtained an important result that a Nash equilibrium which brought about natural economy was played in the macro-economic game. The production sectors in Akimoto (2016) are constructed by two-sector-model and their technical coefficients are fixed. However, the real economy has the complicated production sectors which can be modelled by the input-output model. In addition, the structure of the input-output model is always violently destroyed by creative destruction. Therefore, the problem is whether a natural economy can operate in the creative destruction.
     This paper tries to link the macro-economic game at natural economy with Pasinetti’s vertically integrated model which can analyse creative destruction and to demonstrate how natural economy can be operated in creative destruction.

*Akimoto, K. (2016), “Can a Natural Economy Operate in Macroeconomy? A Caution for Deviation from Natural Economy,” Italian Economic Journal, Vol.2, pp.123-142.

Evolution and learning of behavioral response to unknown signals.

Shinsuke Satoi

Kyushu University

2018/1/24, 13:30-, at W1-C-909



Abstract

     All organisms receive signals from environment and perform appropriate behavior. The evolution of optimal behavior for signals have been discussed in signal detection theory and decision theory (Willey 1994). However many organisms can remember and learn signals and they can change their behavior to the same signals. Some mathematical model about signal learning are also reported (Sherratt 2011), but there are no discussion about the relationship between evolution and learning. In this presentation, I talk about the model which explains behavior against repeated signals including both evolution and learning. I compare the results with past models and discuss the relationships between evolutionary models and learning models.

Estimation of divergence times when evolutionary rate varies.

Koichiro Tamura

Department of Biological Sciences, Tokyo Metropolitan University

2017/12/19, 15:30-17:00, at W1-D-1025



Abstract

     Inference of divergence times among macro molecules is one of the major subjects in molecular phylogenetic analyses to elucidate evolutionary histories of genes, genomes and species. Inference of divergence times requires either an assumption of constant rate throughout the tree (a molecular clock) or a statistical distribution to model the variation of evolutionary rates among lineages. Widely used Bayesian methods use a probability distribution of evolutionary rates in the tree (e.g., lognormal distribution) and whether the rates among lineages are correlated or independent. In contrast, our newly developed approach (RelTime) does not require such a probability distribution but estimates relative rates throughout the tree to generate relative node ages that can transformed into absolute dates by using temporal constrains for one or more nodes. RelTime has performed well in timetree analysis of many large empirical datasets, and it shows high accuracy in computer simulations. In this seminar, I would like introduce current state of the molecular clock applications as well as our RelTime approach.

Dissemination of multidrug resistance via conjugative plasmid.

Yoshiharu Yamaichi

Institute for Integrative Biology of the Cell (I2BC), CNRS-Gif-sur-Yvette, FRANCE

2017/11/06, 13:30-, at W1-D-923



Abstract

     Wide-spreading of antibiotic resistance is one of the most important issues in not only public health but also a huge economic burden. Dissemination of multidrug resistance (MDR) gene(s) resulted in emergence of MDR bacteria, or casually called “superbugs”. These transmissions were often carried out by conjugative plasmids that also encode genes sufficient for a means of horizontal gene transfer, namely conjugation which is carried out by cell-to-cell contact. We are interested in dynamics of dissemination of MDR conjugative plasmid, using pESBL as our model plasmid. This plasmid was originally identified in Escherichia coli O104 outbreak strain in Germany in 2011, and participated the severity of outbreak as it provided MDR phenotype to the host cells.
     Taking advantage of Transposon insertion site sequencing (Tnseq), a recently developed technique which allows the high-throughput quantitative fitness assessment of individual genomic loci, we identified genes involved in the conjugative transfer of pESBL. Surprisingly, Tnseq also unveiled a small regulatory region in pESBL: mutations in this region result in highly elevated transfer efficiency of the plasmid. This and other lines of evidence indicate that single mutations can create plasmids with substantially increased ability to spread, threatening emergence of ’superspreader’ mutants.
     Transferred plasmid molecule has to be established in the recipient cell for the completion of the conjugative DNA transfer. I will also discuss our recent studies on various factors involved in this establishment, such as plasmid partitioning and a system counteracting host immunity.

The genomic landscape at the later stages of speciation: insights from Japanese sticklebacks.

Mark Ravinet

CEES, University of Oslo, Norway

2017/10/18, 15:00-, at W1-D-208



Abstract

      Speciation is a continuous process and analysis of species pairs at, "different stages of divergence provides insight into how it unfolds. Spanning the speciation continuum stickleback species pairs are ideal for investigating how genomic divergence builds up during speciation. However attention has largely focused on young postglacial species pairs with little known of the genomic signatures of divergence and introgression in older systems. The Japanese stickleback species pair Gasterosteus aculeatusG. nipponicus which co-occur in the Japanese islands is at a late stage of speciation. Here we use coalescent analyses and Approximate Bayesian computation to show that the two species split approximately 0.68-1 million years ago but that they have continued to hybridise at a low rate throughout divergence. Population genomic data revealed that high levels of genomic differentiation are maintained across the majority of the genome when gene flow occurs. However despite this we identified multiple small regions of introgression strongly correlated with recombination rate. Our results demonstrate that a high level of genome-wide divergence can establish in the face of persistent introgression and that gene flow can be localized to small genomic regions at the later stages of speciation with gene flow, composed of the Pacific Ocean three-spined stickleback and the Japan Sea stickleback.

Linking biodiversity, ecosystems, and people across scales: challenges for ecology and sustainability.

Michel Loreau

Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, UMR 5321 CNRS and Paul Sabatier University, France

2017/10/18, 15:00-, at W1-D-208



Abstract

      People are now driving the sixth mass extinction in Earth’s history, and yet biodiversity enhances many of nature’s benefits to people. The influence and dependence of people on biodiversity have mainly been studied separately and at contrasting scales of space and time but new ecological theory is beginning to link these relationships across scales. This theory shows that biodiversity loss substantially diminishes many ecosystem services by altering ecosystem functioning and stability especially at the large temporal and spatial scales that are most relevant for policy and conservation. The influence and dependence of people on biodiversity also generate an important if poorly understood feedback loop between humans and nature. New models of social-ecological systems emphasize the role of feedbacks and scales in human-nature interactions and the importance of foresight for the sustainability of human societies. They call for the development of integrative management approaches that account for the coupled dynamics of human populations biodiversity and ecosystems across multiple spatial and temporal scales.

Eco-evolutionary feedback between size and strategy; alternative migratory tactics in salmonid.

Junnosuke Horita1 and Yuuya Tachiki1,2

1Kyushu University
2Department of Animal and Plant Sciences, The University of Sheffield, UK

2017/10/03, 13:30-, at W1-C-909



Abstract

     In salmonids, some juveniles migrate to the ocean and come back to their natal river (migrant tactic), whereas others mature in the river without migration (resident tactic). There is a trend that larger one becomes a resident. This trend is explained by the status-dependent-strategy model(SDS), in which fitness functions of both tactics are functions of status, and the status where both fitness functions intersect is a threshold at which tactic changes. A density dependence of growth is documented. We incorporate the growth suppression of juveniles into the SDS, and explore how it affects the dynamics of alternative tactics. In this talk, we demonstrate that the negative feedback between resident density and juvenile body size can cause an instability of size distribution of juvenile, resulting in a fluctuation of the population density of migrant type as well as stream population. We also consider the effect of climate change on the average body size of juvenile, and investigate the ecological and evolutionary response to it. As a result, change in the average size can cause phase transition from stable to unstable and vice versa. Evolutionary response to the change can recover the state of population to the same state before environmental change, but various type of dynamics emerged during evolutionary response.

Advantage of sexual reproduction resulting from sibling diversity: the effects of selection intensity, environmental variance, and reduced genetic diversity.

Makoto Douge1 and Yoh Iwasa1

1Kyushu University

2017/09/26, 13:30-, at W1-C-909



Abstract

     The reason of why sexual reproduction has been maintained is a big question. About forty years ago Maynard Smith presented a concept of "two-fold cost of sex. Since then many hypotheses have been submitted. However the general answer has not been found yet. One of the hypotheses showed that the diversity of siblings was the cause (Lottery Hypothesis, Williams). Maynard Smith investigated it by computer simulation called "sib-competition model". He resulted that in the model the diversity of siblings was not able to overtake the two-fold cost of sex. Currently it is almost neglected. We revised the sib-competition model to shows the force that surpasses the two-fold cost. Further, we added the following three factors in the model to get closer to the reality: [1] milder selection, [2] environmental variance (VE), [3] reduced number of phenotypes. The result showed the advantage of sexual reproduction in some probable conditions. We think that the diversity of siblings may have the important roll for the big question.

Mathematical modeling of oncolytic virotherapy in combination with chemotherapy.

Kwang Su Kim1, Jungmin Lee1, Sangil Kim2,* and Il Hyo Jung1

1Department of Mathematics, Pusan National University, Busan, 609-735, South Korea
2WISE Institute, Hankuk University of Foreign Studies, 156-849, South Korea

2017/7/25, 13:30-, at W1-C-909



Abstract

      Over the past few years, several studies have been made on cancer viral therapy. One of the major advantages of oncolytic virotherapy over standard cytotoxic chemotherapeutic agents is that tumor cell selectivity can potentially target and eliminate cancer cells without affecting normal cells. Therefore studies of the virus dynamics are needed for the purpose of cancer treatment, not the virus as the cause of the disease.
     We introduce a deterministic and stochastic model of tumor-viral dynamics. For finding conditions of virotherapy failure, the local asymptotic stability and the global asymptotic stability of a virotherapy failure equilibrium are studied. By using the basic reproductive ratio, we investigate its sensitivity to the parameter values characterizing viruses. We also derive a system of stochastic differential equations that based on the deterministic model and explore the probability of uninfected tumor and infected tumor extinction. The analysis suggests that an oncolytic virus is desired with a high infection rate and optimal cytotoxicity for effective treatment. Recent investigators showed that the combination of viral therapy with chemotherapy may lead to synergistic mechanisms for eliminating cancer not achievable by either therapy alone. So our main problems are “Which combination therapy should we take for more effective treatment?” and “How can we measure and predict the quantity of synergy effect?”. Koizumi and Iwami suggested the estimation methods of the optimal dose point that is calculated from the difference between the effects of the combined drugs obtained by modeling the dynamics and the additive effects by Loewe additivity. Based on their ideas, we investigate a synergistic effect between oncolytic virus therapy and chemotherapy. Extended synergy concepts for combination therapy are discussed.

自殖の進化の新仮説:送粉をめぐる種間競争が先行自家受粉の進化を促進する(日本語)

勝原光希, 丑丸敦史

神戸大・人間発達環境学

2017/7/4, 13:30-, at W1-C-909



Abstract

      顕花植物における配偶システムは、完全他殖から完全自殖まで、また中間的な自殖率を持つ種など、驚くべき多様性を持っている。自殖を行う種の両性花においては、能動的に自家花粉を柱頭に付着する自動自家受粉を行う種が多く知られている。近交弱勢や多様化の可能性の減少といったネガティブな効果の存在にも関わらず、自動自家受粉が進化してきた要因については、これまで不安定or予測不可能な送粉環境に対する繁殖保証として自殖が機能するという文脈によって説明されてきた。
      自動自家受粉は、開花時に行う先行自家受粉と、閉花時に行う遅延自家受粉に大別される。これまで、送粉者による授粉が十分でない(送粉者制限が存在する)場合に遅延自家受粉が進化すること、先行自家受粉を専門的に行う花が相対的にローコストで生産できる場合に先行自家受粉も進化する可能性があること、が先行研究において明らかにされてきた。
      発表者は、同所的に分布する在来一年生草本2品種、ツユクサCommelina communisとケツユクサC. communis f. cliataにおいて、非対称的な繁殖干渉が発生していること(ツユクサがケツユクサより繁殖干渉において優位)、その非対称性がツユクサがケツユクサよりも高い先行自家受粉率を持っていることによって説明されること、を明らかにしてきた。それらの結果から、通常先行自家受粉が進化しない(送粉者制限がない・遅延自家受粉ができる)場合でも、送粉者を介した種間競争が存在する場合には先行自家受粉が進化するという仮説を立て、個体ベースモデルシミュレーションを用いて検証を行ったので、その結果について紹介する。

Allergen immunotherapy as a treatment of pollen allergy, and possible coupling with intestinal microbe community dynamics.

Akane Hara and Yoh Iwasa

Kyushu University

2017/6/27, 13:30-, at W1-C-909



Abstract

      Allergen immunotherapy is a treatment method for Japanese cedar pollen allergy (JCPA). Patients suffer symptoms such as runny noses and itchy eyes in pollen season often early spring in Japan. In the therapy, patients take in a small amount of pollen extract dose for several years and their allergic symptoms are suppressed when exposed to large amount of environmental pollen. However, the therapy is not always effective for all the patients of JCPA.
      To reveal conditions in which the therapy is effective, we developed simple mathematical model of allergen immunotherapy describing the differentiation process of Th2 cells (type 2 helper T cells; trigger of allergy) and Treg cells (regulatory T cells; suppressor of allergy). We found conditions for therapeutic success as follows: [1] Treg cells must have a low decay rate in order to achieve accumulation during therapy phase, and [2] therapy schedule with a longer "induction phase" in which patients have gradually increasing pollen dose with time is more effective in suppressing allergy by exposure to environmental pollen without symptoms caused by the therapy itself.
      Recently, close relation between human immune system and intestinal microbes has been known, and the effect of a particular group of bacteria on avoiding development of allergy has been reported. In this seminar, I will discuss a possible extension of the allergen immunotherapy model to a coupled immune-enterobacteria dynamics.

Number of infection events per cell during HIV-1 cell-free infection.

Yusuke Ito

Kyushu University

2017/2/14, 13:30-, at W1-C-909



Abstract

      Human Immunodeficiency Virus type 1 (HIV-1) accumulates changes in its genome through both recombination and mutation during the course of infection. For recombination to occur, a single cell must be infected by two HIV strains. These coinfection events were experimentally demonstrated to occur more frequently than would be expected for independent infection events and do not follow a random distribution. Although the heterogeneity of target cell susceptibility was proposed as a possible mechanism for the non-randomness, the quantitative evaluation of its impact on coinfection frequency is lacking, especially for cell-free infection in vitro.
     Here, we developed a novel mathematical model considering the heterogeneity of target cells and analysed datasets of cell-free HIV-1 single and double infection experiments in cell culture. Interestingly, we showed that the number of infection events per cell during cell-free HIV-1 infection follows a negative-binomial distribution, and our novel model reproduces these datasets. Furthermore, our quantitative analyses reveal that the average number of infection events increases from 1.02 to 1.65 as the amount of inoculated HIV-1 increases, and the multiple infection frequency increases to 17%. These findings demonstrate that cell-free HIV-1 infection has an important role in driving virus recombination. Therefore, spatially separated HIV-1 variants from different organs might be able to recombine within patients via cell-free infection.

Mathematical model of hematopoietic system with myeloid bypass.

Shoya Iwanami

Kyushu University

2017/2/7, 13:30-, at W1-C-909



Abstract

      The conventional model of hematopoiesis has hierarchical structure and it is considered that all blood cells produced through multi-potent progenitors (MPPs). Recently, many researches about hematopoietic stem cells (HSCs) implied the differentiation of HSC incline to produce myeloid cells. Furthermore, Yamamoto et al (2013) showed the existence of some cells producing only myeloid cells in HSC fraction and proposed a new model of hematopoiesis which has the bypass which produce myeloid cells from the stage of the stem cell.
      In our study, we developed the mathematical model based on myeloid bypass model and analyzed the data from an experiment of single cell transplantation using mice. From result of analysis, we discuss the existence and the significance of the myeloid bypass.

Evolution of density-dependent wing determination that is regulated by juvenile hormone level.

Takahiro Kamioka

Kyushu University

2017/1/31, 13:30-, at W1-C-909



Abstract

      We studied the evolution of juvenile hormone (JH) regulation in wing-polymorphic insects. We considered an asexual species that undergo larval and adult stages living in many patches. The rate of larval growth depends on within-patch resources which can be depleted by larvae. Dispersal-type adults migrate out of the natal patch just before reproductive stage; reproductive-type adults have a greater fertility than those of dispersal-type adults but no dispersal ability. The wing type was determined by the juvenile hormone (JH) level in a critical period if the larval stage. The carrying capacity of resources fluctuates between high and low values. The JH level follows a normal distribution. Evolution modifies the mean and the variance of JH level. The mean of JH level is determined by the basal JH level and density dependent degradation. The variance of JH level is constant.
      First, we calculated when the mean and the variance of the JH level were evolved separately. In the evolution of mean of JH level, both of the basal JH level and density response affected the dispersal type production. In the evolution of variance of JH level, the variance evolved smaller when the environmental fluctuation was large. In both cases, the production of dispersal type was small if the density was low, and it increased rapidly if the density was large. The production of dispersal type was larger when the environmental fluctuation was larger. The growth rate and mortality of insects, and recovery of resources also affected the dispersal type production. Second, we calculated when the mean and the variance of the JH level were evolved simultaneously. When the environmental fluctuation was large, the variance was converged into minimum value. When the environmental fluctuation was small, all of these values affected the wing determination.

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