Agriculture, Forestry and Fisheries 2013, 2(2): 6-101
Algorithmsfor control of genetic-breeding improvementof economically valuabletraits ofself-pollinatedplants
Mikhailenko I.M.1, Dragavtsev V.A.2
1Scientific deputy director, head of lab of infornatic-measuring systems,Agrophysical institute of RAAS, Saint-Petersburg, 195220, Grazhdansky prospect 14, Russia
2Main scientist of plant ecologic physiology lab, Agrophysical institute of RAAS, Saint-Petersburg, 195220, Grazhdansky prospect 14, Russia
E-mail address:
(Mikhailenko I. M.), (Dragavtsev V. A.)
To cite this article:
Mikhailenko I. M., Dragavtsev V. A.. Algorithms for Control of Genetic-Breeding Improvement of Economically Valuable Traits of Self-Pollinated Plants, Agriculture, Forestry and Fisheries. Vol. 2, No. 2, 2013, pp. 6-10. doi: 10.11648/j.aff.20130202.12
Abstract: Thenew approachesto solving problems of selection parent’s pairs(varieties)for crossingand forecast of eco-geneticportrait ofthe future new variety.Paper supplementsthe two previous publications onthe formalizationof the quantitative theoryof eco-geneticprocesses [1,2].
Keywords: Eco-Genetic Portrait, Genetic-Physiological Systems, Selection,MathematicalModelOf "Genotype-Environment Interaction”, Management By EnvironmentalFactors.
Agriculture, Forestry and Fisheries 2013, 2(2): 6-101
1. Introduction
Fromquantitative geneticsis known [3] that the phenotypicvariabilityof any quantitativetrait (it is visible bythe nakedeye inasegregatingpopulation)-is:
(1)
where: - thephenotypicvariance, -genotypic variance, - environmentalvariancecaused byvariationsof micro-environmental conditionsforindividual plants ofpopulations.
Breederdesire to know the genotypic variance of productivity trait, because selection of the best genotypic deviationsand their subsequent cloning (for example potatoes or fruit trees) leads to increase productivity, improvement of stability and quality of new clones.Now it is known the next principles for rapid estimation of genotypical variance (without raising progeny):
1.The principleof artificiallevelingbackgroundof growinga segregatingpopulation [4].
2.The principleof measurement standards(comparisonof phenotypic variationin wild or segregating population () withthe variabilityin clonesorpure lines,the obtainedfrom this population() [3].
3.Shrikhandeprinciple[5,6,7].
4.The principleof backgroundcharacters [8,9,10,11,12,13], which from fourprinciples showed oneself the most accurate andreliable. [14].
For grainself-pollinated cropscanevaluategenotypicvarianceby calculation ofthe varianceof character’s averages on the plotswith different varietiesin collection of anybreedingcenter.
Duringthe calculation ofthe averagecharacteristics of the varietyin the plotall the noiseseliminated, and the averagemeaningin the plot- isgenotypicvalue of the character, and the variance of averages of plot is . However, the crops do not propagate byclones or by grafting,soto predictpossible geneticimprovement ofcropproductivity and yield the breeder shouldknowthe additivegeneticvariance.
It is known [3] that
(2)
where - theadditivevariance(caused bya variety ofadditive effectsof polygenes), - the dominantvariancecaused bythe effectsof dominance and Vi - the variance of epistaticeffects.
Until recently inquantitativegeneticswas only one principle for estimation of additive variance -on the correlation of"parent-offspring"- , or on the correlationof relatives (half-sibs) [15].
This principle requiresthe change of generations, so it cannot workin the populations ofF2.Until now,breedersvisuallyselectthe bestphenotypes in theF2,but not the bestgenotypes, and certainly not the bestadditivegenotypes (transgressions).This selectionhas a verylow efficiency.Litunwrites: "Thesolvability of themodern technological schemesof selections- 0.01% [16].Using the principleof backgroundcharacters whetherwe brought theefficiency of selectionof barleyup to 15%”(that is increased the efficiency ofidentification of individualgenotypes in1500 times).
In 1979 wascreatedan expressmethod ofevaluation of additive variance (without raising progeny)forquantitative traits using similyaritytheir responsesinenvironmental gradient[17].
In1998 wascreatedan expressmethod ofevaluation for eachof the sevengenetic-physiological systemsthat contribute to theproductivityof individuals and theyield perunit areaphytocenosis[18, pp. 33 -35].This methodformed the basisof mathematical models of"genotype-environment interaction” and algorithms of identification of genotype by phenotype, whichwere presented in [1,2].
These tasks are thestagesof the general problem- controlgenetic-breedingprocess.Inthis paper we considerthe followingproblem: the selection of the parentalcouplesto ensurethe desired resultof crossing, and the prediction result of crossing parentalpairs (Fig. 1).
Fig. 1.Block diagram ofthe interactionof management tasks by genetic-breedingprocess.
Main body
Eco-genetic portraits
The starting point forthese tasksis to set thedesiredcombinationof breeding characters(BC),whichmust be obtainedin the second(segregated) progeny ofthe results ofcross-breeding.Information andalgorithmicfoundation of theseproblems isthe concept of "eco-genetic portrait", formulated in [2]. It representsa combinationof positive feedback, or shiftsBCderivedfrom the contributions of7genetic-physiological systems ina module of finalproducts. This combination canbe representedas a vectorof these responsesΔFT= [Δφ1, Δφ2, Δφ3, Δφ4, Δφ5, Δφ6, Δφ7],ora graphical diagram(Fig. 2).
Fig. 2.Eco-genetic portraitof the variety (genotype) on the outputmodule of crop.
In fact, sucheco-genetic portraitis more complex,has several levels,and includesjoint ventures andchangesin other modulesof quantitative traits. However, mostbreederseffortsaimed at gettingthe desired combination ofBCisthe levelsof productivity andyield.In addition, thisportrait isincomplete, as in theother modules,priorto the end, not shownthe effectofa 7-genetic-physiological systems.Inparticular the systems ofattractions andmicro -distributionappear onlyin the last stagesofontogenesis in the final product.
Δφ1-contribution ofattractions, Δφ2 - contribution of themicro-distribution, Δφ3 - contributionsystemsadaptation (resilience to climate protectionand chemicalstressors), Δφ4 - polygeniccontributionofimmunityto the agents ofplant diseases, the development of plantdefense mechanisms, Δφ5-contribution systemof "payment" limiting theproductivityof soil nutritionelements, Δφ6 - contributionof tolerance to density, Δφ7 - contributionvariabilityperiodsof ontogenesis(the possibilityof a selection"withdrawal"critical phaseof ontogenesisfrom hits ofthe stressor).
The general scheme ofsolving task selectionthe optimalparental pair
We start from demonstration ofthe initial situation in whichthe problem is solved. At the disposalof the breederhas a setBCof the final product(output module) - X*(T), which must be obtainedfrom a cross, and there is data onthe dynamicsofthe limiting factorsfor the placeof cultivationofhybrid - F (t). In addition, the breeder hasthe original basevariety or hybrid, the BC of which must be improved, as well as a databaseof mathematical models ofpotential parents,by whichfor a givenenvironmental conditions andusing technologycan be predictedoutcome -, where T -the timesince the end ofvegetation.
The basic variety was obtained as a result of previous acts of breeding, and for it, except the mathematical model of "genotype-environment", at the disposal of the breeder has itseco-genetic portrait - ΔF0T = [Δφ10, Δφ20, Δφ30, Δφ40, Δφ50, Δφ60, Δφ70] obtained for optimal growing conditions. Availability of models and eco-genetic portraitgive possibility to predict the final result and estimatethe contribution of all genetic-physiological systems. Therefore, modelling its growth and development, we can at a negativeeffects of environmental factors to assess negative changes or failures in all the required joint venture BCand in addition to forecast eco-genetic portrait for the given growth conditions. Then, using the principle of estimationof the additive genetic-physiological systems [18], we fill the "holes" in the eco-genetic portrait, and we haveforecast eco-genetic portrait oftop transgressions in generation F2 -, entering this information into a mathematical model of the "genotype-environment" possible to predict the expected results for a given BC- . By comparing it with the required values X*(T), we can decide to stop the process and go to the next possible crossings. Consistently going through all the available options for the crossing, we'll do the final selection on the option that provides the greatest proximity to the required values BC- X*(T).
We reviewedthe general schemeof selectionof parental pairsforthe finalmoduleof products.However, oftenthe problemis complicated bythe need toselecta substantialimpactof thegenetic-physiologicalsystems, and thestate of someof intermediatemodules, such asthe module, "the number of grains per plant," multiplied by the"weightof onegrain," as well "grainweightper plant". Result expressedonthis moduledetermines theproductivity ofindividual.
Algorithm forthe selection ofoptimalparental pair
Let us considerin more detailthe algorithmofoptimal selectionof parentalpairs forgrainself-pollinated cropsin consideringmodulegrain productivity. Assume thatin Fig. 2shows theeco-geneticportrait of the initialgenotypes(variety), which we want to improveresistance tostress andto "pay" byproductivity the lim-factorof soil nutrition. As can be seenin theeco-geneticportraitof these indicatorsarethe "holes" because the responsesappropriategenetic-physiological systemsarezero - Δφ3 =0, Δφ5 = 0.
Fromthe breeder’s data bankof potential parents we choose the optionforeco-genetic portraitwhich these"holes"are filled (see Fig. 3).
Fig. 3.Eco-genetic portraitof the variety (genotype) with the required BC foradaptabilityand "payment" of lim-factor of soil nutrition(dotted line shows thecontributions of othergenetic-physiological systems).
In caseif thegenetic-physiological systemsare additive,we have the rightto combineeco-geneticportraits ofparents, and get the forecasteco-genetic portrait of the future newvariety:
Fig. 4.Predictedeco-genetic portrait of variety.
We introduce responses of genetic-physiologicalsystems. Theyare components of thepredictedeco-geneticportraitin the outputmoduleof the mathematicalmodel of "genotype-environment" [2]:
(3)
wherethe following notation: x1 - grainweightper eari-thindividual, x2 - mass ofchaffin the ear, x3 - strawweight, u- controlof nitrogen nutrition; f1 - luminousefficiencyfactor, f2-temperature factorproductivity, f3 - moisture,as a factor ofproductivity; φ1 ... φ7 - influenceof genetic-physiological systems; ξ1, ξ2, ξ3 - random disturbances, reflecting the informational uncertainty ofthemodel; akj, bk, ckj, dkj - the dynamic parametersof the model.
Model (3)is more convenientto consideramore compactvector-matrix form
(4)
where allvariables and parameters arecombined inthe respectivevectors and matrices.
The resultingmodelBC- Xj(T), we will compare with the requiredvaluesX*(T),thenwe needa stopping criterionprocedures
,(5)
whereδ-specified threshold numberit’s above leads to the needto continueprocess of selection ofthe parental pairby selectingfrom the databasefollowing options for thecrossing.
In thecase when breeder has no of eco-geneticportraitsof potentialparents,use a staticversion of themodel "ecological disturbance- the reaction ofgenetic-physiological systems” of the parents, as indicated inour previous paper [2]
.(6)
Management of environmentalfactors in process of breeding
Theidea of controlling thegenetic-breeding process is basedon the theory ofeco-genetic organizationof quantitative traitsand simulationofthe system interaction of "genotype-environment." According to themit follows,that environmentalfactors oftenmake a significantcontribution to thejoint venture BC of generations, as the level of productivityof any characteris the result ofthe interaction of "genotype-environment”. Therefore, intermsof thebreedingprocess in thephytotrons, the most important factor in increasing thereliability is managementbyenvironmental factorsofbreeding.Thisallows to makethe breeding processfrom a passiveprocedure of consistentcomparisonof parentalpairs, in activecontrolled process of quick searchthe best optionswhilemaking maximum useof their geneticpotential.Furthermore, the presenceof control by environmental factorswill significantly improvethe identificationof genotypestophenotypes,and thusto speed upthe release of newvarieties.
Combinemodeloutput module(4) withthe state modelof genetic-physiological systems (3):
,(7)
andtoget managedthesystemof environmental factors, where P(t) -vectorof parameterscontrolenvironmental factors.
Now thetask of achieving thedesiredBCina selectablegenerationlooksas follows
(8)
and consists infinding the bestpair forcrossingand optimization ofenvironmentaleffects inthe breeding process.
Note thatin the presence of control by environmental factorsof breeding,response of thegenetic-physiological systemsare not analyzedseparately, but are onlyintermediate variablessearch procedure, whichis formedwhen stoppingforecasteco-genetic portrait and the correspondingforecast valuesBC.
The algorithmis implementedentirelyon a virtuallevel, butnatureis carried onlya singleoptionfor the crossing, which resulted from a population ofF2thenselecta singlegenotypethat meets the givenrequirements (incase of theimprovements of commercial variety). In thisrealizeda significant accelerationofthe breeding process.
2. Conclusions
The algorithmcontrols by the breeding processbased on themathematical model of"genotype-environment" interaction, is a logicalchoiceof variantsof complementaryeco-geneticportraits ofpotential parentsandthe resultingquantitativepredictionof breedingcharacters.At the same timethe choiceof optionsis carried outto the requireddegree of agreement betweenpredicted andexperimental breedingcharacters.In the presenceof controlenvironmental factorssuch anoptionis supplemented byoptimizingparameters of the environment, which ensures the maximum use ofeco-genetic potential of theparents.
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