The use of genetic maps is a useful tool in genetic research. The association between map distance andrecombination frequency is expressed by a genetic mapping function. However, several of these functions do not presupposethe joint recombination percentage. In other words, they are not multilocus probabilities. This work aimed to compare,through simulations, the efficiency in the use of different mapping functions with and without multilocus analysis as a tool inthe construction of genetic maps. A genome constituted of three linkage groups (50, 100 and 200 cM) was simulated for acomparative study. Four mapping populations were simulated, F2, with 50, 100, 200 and 400 individuals, with 10 replicaseach. It was verified, after the analyses, that the multilocus analysis was not efficient to rescue the size of the connectiongroups, concluding that the non use of the multilocus analysis would be viable

Cosme Damião Cruz

Edmar Soares de Vasconcelos

Leonardo Lopes Bhering

Márcio Fernando Ribeiro de Resende Junior

Tatiana Barbosa Rosado

Willian Silva Barros

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308                                                                                                        Crop Breeding and Applied Biotechnology 9: 308-312, 2009LL Bhering et al.Crop Breeding and Applied Biotechnology 9: 308-312, 2009Brazilian Society of Plant Breeding. Printed in BrazilReceived 24 November 2008Accepted 05 August 2009Efficiency of the multilocus analysis for the constructionof genetic mapsLeonardo Lopes Bhering1*, Cosme Damião Cruz2, Edmar Soares de Vasconcelos2, Márcio Fernando Ribeiro de Resende Junior2,Willian Silva Barros2, and Tatiana Barbosa Rosado2ABSTRACT- The use of genetic maps is a useful tool in genetic research. The association between map distance andrecombination frequency is expressed by a genetic mapping function. However, several of these functions do not presupposethe joint recombination percentage. In other words, they are not multilocus probabilities. This work aimed to compare,through simulations, the efficiency in the use of different mapping functions with and without multilocus analysis as a tool inthe construction of genetic maps. A genome constituted of three linkage groups (50, 100 and 200 cM) was simulated for acomparative study. Four mapping populations were simulated, F2, with 50, 100, 200 and 400 individuals, with 10 replicaseach. It was verified, after the analyses, that the multilocus analysis was not efficient to rescue the size of the connectiongroups, concluding that the non use of the multilocus analysis would be viable.Key words: Statistical genomics, simulation, mapping.1 Embrapa Agroenergia, Av. W3 Norte, (Pq EB), s/n, 70770-901, Brasília, DF, Brazil. *E-mail: leonardo.bhering@embrapa.br2 Universidade Federal de Viçosa (UFV), Departamento de Biologia Geral, 36570-000, Viçosa, MG, BrazilINTRODUCTIONGenetic maps are useful tools in various fields ofgenetic research. The map distance between two markersis defined as a significant number of recombinationevents in each meiosis, expressed in centimorgans(cM).  The relationship between map distance andrecombination frequency is expressed by a mappingfunction. Different mapping functions correspond todifferent degrees of interference in crossing over (Stam1993).  However, various mapping functions fail to yieldproper joint recombination probabilities for more thanthree loci, which mean they are not multilocusprobabilities (Goldstein et al. 1995).Models for multilocus analysis are different frommodels for two loci analysis because it considers allthe information of the intervals between pairs of loci ina linkage group (Schuster and Cruz 2004).According to Liu (1998), there are a few obstaclesto the implementation of the multilocus analysis ingenetic linkage studies and in the construction of maps.Some of those obstacles are the complexity of themultilocus likelihood function, the large number ofparameters when high levels of interference occurs andthe loss of part of the data necessary to construct amultilocus model. In addition there is still demand forintensive computational time for the construction ofgenetic maps in this multilocus model.When the multilocus analysis is used, theappropriateness of the mapping functions depends onwhether what is assumed about the existence andmagnitude of interference is true or false.  The choiceCrop Breeding and Applied Biotechnology 9: 308-312, 2009  309Efficiency of the multilocus analysis for the construction of genetic mapsof the mapping function is very important to the resultobtained since the adoption of one, between thedifferent mapping functions, depends on assumptionsabout the distribution of the crossing over, degree ofinterference and length of the chromosome segment inquestion (Schuster and Cruz 2004).The objective of this study is to compare, throughsimulations, the efficiency in the use of differentmapping functions with and without multilocus analysisas a tool in the construction of genetic maps.MATERIAL  AND METHODSA genome with three linkage groups wassimulated. The first linkage group had 50 centimorgans(cM), the second and third had 100 cM and 200 cMrespectively.  Each group had 11 molecular markers, co-dominant, and equally spaced, so that each linkagegroup had the saturation of 5, 10 and 20 cM respectively.Homozygous and contrasting parents were used. Parent1 was dominant and parent 2 was recessive.  Wesimulated four F 2 mapping populations with 10 replicaseach. The size of each population was 50, 100, 200 and400 individuals respectively.After these simulations the distance matrices weregenerated using the different mapping functions andmultilocus analysis, resulting in five treatments. Thefirst treatment had the distance unit expressed inrecombination frequency. This was used as a controltreatment since it did not use any multilocus analysis.The second treatment had the distance expressed inHaldane function and multilocus analysis based on themaximum likelihood method.  The third treatment hadthe distance expressed in Haldane´s function andanalysis based on multilocus method of least squares.Treatment four had the distance expressed in Kosambi´sfunction and multilocus analysis based on the maximumlikelihood method.  Treatment five had the distanceexpressed in Kosambi´s function and analysis basedon multilocus method of least squares.All simulations and comparisons of the genomeswere accomplished using the software GQMOL (Cruzand Schuster 2001)After estimating the distances between the marksan analysis of variance (Anova) was performed for thetotal length of each linkage group. To compare themeans of each treatment studied, a Tukey test wasperformed using the software Genes (Cruz 2006).RESULTS AND DISCUSSIONIn the population with 50 individuals it was observed,through the analysis of variance, statistical significanceonly between treatments in the first linkage group withlength of 50 cM (GL1). Treatments for the secondlinkage group (100cM) did not show statisticalsignificance (Table 1). In this population, the treatmentsfor the third linkage group (200cM) were not analyzedbecause during the mapping procedure, in 70% of the times(7 replicas), the markers located in this linkage group weremapped in more than one group. This event shows thatpopulation's sizes below 50 individuals are not sufficientto recover the information during the mapping procedurewhen a low level of saturation, such as 20cM, is used. Inthis case, larger populations or higher saturation levelsshould be used (Bhering and Cruz 2008).The treatments where multilocus analysis wasperformed based on least square (treatments 3 and 5)showed worse distance estimations in relation to valuesobtained by the method of maximum likelihood(treatments 2 and 4 ), although this was not a statisticallysignificant difference (Table 2). In this case the closerto 50 cM indicates that is the best methodology torecover the information originally set out in simulations.Table 1. Analysis of variance of the two linkage groups for the population of 50 individuals GL1(50cM) and GL2 (100cM)Lenght (GL1) Lenght (GL2)Source of variation df MS F MS FTreatments 4 207.4724** 4.6085 1527.1603 0.0785Residue 45 45.0197 1945.0596Total 49Mean 47.1706 102.2828CV(%) 14.2242 43.1185** Significant at a statistical significance level of 1% by F test310                                                                                                        Crop Breeding and Applied Biotechnology 9: 308-312, 2009LL Bhering et al.It was also observed that the distances estimations(42,395 and 41,975) were more distant from the expectedsize of the linkage group when the Kosambi functionwas used (treatments 4 and 5 respectively).In the population of 100 individuals it wasobserved that the linkage groups 1 and 2 (GL1 and GL2)had significant differences at 1%, between theirtreatments. Only the GL3 was not statistically differentfor the treatments tested (Table 3). All the treatmentssucceeded in mapping the simulation informationshowing that by increasing the population size of theoriginal information can be correctly estimated.Table 4 shows the result obtained by the Tukeytest performed for the first and second linkage group(GL1 and GL2) since the third linkage group was notstatistically significant. The treatments 1, 2 and 3 didnot differ among themselves, and have their valuescloser to what was set initially (50 cM for GL1 and 100cM for GL2).  Once again it was observed that when theKosambi function is used, the distances are moredivergent than desirable. It was also observed thatdistance estimates for treatment 1 (where the multilocusanalysis was not used) were closer to the values initiallyset (50 cM for GL1 and 100 cM for GL2) although thisresult was not statistically different.The treatments of population of 200 individualsshowed significant differences for all 3 sizes of thelinkage group tested as can be seen in the Table 5 ofanalysis of variance.The Tukey test was performed on the populationof 200 individuals (Table 6). It was observed that forthe GL1, treatments 1, 2 and 3 did not differ amongthemselves, and the distance values were the closestto the original 50 cM.  For GL2, Treatment 1, which didnot use multilocus analysis, showed the closestestimation of the expected distance of 100 cM. Similarresults were observed for GL3, but in this case treatments1, 2 and 3 did not differ statistically.  This indicates thatthe multilocus analysis was not an effectivemethodology for this type of analysis.Treatment Length (GL1)3 50.667 a*1 50.44 ab2 50.376 ab4 42.395 ab5 41.975 bDMS 8.5296* Averages followed by the same letter do not differ statistically at5% levelTable 2. Tukey test performed on the population of 50 individualsat the significance level of 5%Length (GL 1) Length (GL 2) Length (GL 3)Source of variation df MS F MS F MS FTreatments 4 234.864** 5.802 1472.068** 21.506 28515.367 2.061Residue 45 40.474 68.447 13830.765Total 49Mean 47.865 98.377 261.575CV(%) 13.291 8.409 44.960** Significant at a statistical significance level of 1% by F testTable 3. Analysis of variance of the three linkage groups for the population of 100 individualsTreatment Length (GL1) Treatment Length (GL2)2 52.928   a * 3 109.95   a *3 51.17 a 2 109.668 a1 49.83 ab 1 100.86 a4 42.975 b 4 85.937 b5 42.423 b 5 85.474 bDMS 8.0875 DMS 10.5173* Averages followed by the same letter do not differ statistically at 5% levelTable 4. Tukey test performed on the population of 100 individuals at a significance level of 5%Crop Breeding and Applied Biotechnology 9: 308-312, 2009  311Efficiency of the multilocus analysis for the construction of genetic maps  The Haldane´s function is more effective forsmaller linkage groups (50 cM) than the Kosambi´sfunction. When the size of the linkage group isincreased, distances in Kosambi´s function becomesmore effective. Considering the same unit of distance(Haldane or Kosambi) there was not any statisticaldifference between the two methods of multilocusanalysis (Maximum Likelihood and Least Squares).The analysis of variance of the linkage group lengthfor the population size of 400 is shown in Table 7. Notethat it was observed, for all three linkage groups,significant differences between the treatments. Thetukey test, shown in table 8, demonstrated similar resultsthan the ones obtained in table 6 (population of 200Length (GL 1) Length (GL 2) Length (GL 3)Source of variation df MS F MS F MS FTreatments 4 230.5899** 9.512 1607.9652** 31.407 17556.8225** 9.193Residue 45 24.2221 51.1974 1909.7841Total 49Mean 47.7306 104.7128 253.6142CV(%) 10.3112 6.8332 17.2313** Significant at a statistical significance level of 1% by F testTable 5. Analysis of variance of the three linkage groups for the population size of 200Treatment Length (GL1) Treatment Length (GL2) Treatment Length (GL3)1 51.56 a 3 118.114 a 3 311.159 a2 51.365 a 2 116.912 a 2 273.571 ab3 50.754 a 1 104.19 b 5 253.961 bc4 42.827 b 4 92.343 c 4 226.58 bc5 42.147 b 5 92.005 c 1 202.8 cDMS 6.2565 DMS 9.096 DMS 55.5544Table 6. Tukey test performed on the population of 200 individuals at the significance level of 5%individuals). Treatments 1, 2 and 3,  did not differ amongthemselves. Treatment 1, without multilocus analysisstatistically differed from the others For the linkagegroups  2 and 3 (GL2 and GL3). The linkage group´slengths of treatment 1 were the closest among alltreatments to the desired size ( 100 cM gor GL2 and  200cM for GL3).In possession of all the results, it could beobserved that multilocus analysis was not efficient torecover the linkage group´s size of this simulation.  Inall cases the treatment which the distance estimationwas expressed in recombination frequency (Morgan),obtained the best distance estimate, since their valueswere always the closest to the values initially set.Length (GL 1) Length (GL 2) Length (GL 3)Source of variation df MS F MS F MS FTreatments 4 226.138** 17.152 1690.948** 51.151 15024.993** 8.486Residue 45 13.184 33.057 1770.502Total 49Mean 50.410 103.056 245.251CV(%) 7.202 5.579 17.156** Significant at a statistical significance level of 1% by F test.Table 7. Analysis of variance of the three linkage groups for the population size of 400312                                                                                                        Crop Breeding and Applied Biotechnology 9: 308-312, 2009LL Bhering et al.Another important fact that we can infer is thatHaldane’s function was more efficient when smallerlinkage groups (50 cM) were used. In both casessignificant differences between the two multilocusmethodologies tested could not be observed (MaximumLikelihood and Least Squares). Therefore the superiorityof either strategy for multilocus analysis cannot beinferred.When the population’s size was increased, largerdifferences between treatments were observed. In thepopulation of 50 individuals only linkage group 1showed statistic difference and GL3 was unable toreproduce the original linkage group. All the otherpopulations' sizes reproduced the original linkage groupand  all the groups were statistically significant in thesizes of 200 and 400.With the results obtained it could be observedthat:The multilocus analysis was not efficient in anycase for the construction of genetic maps and was notuseful to improve the efficiency of the distanceestimates.It was not possible to infer the efficiency of thetwo multilocus methodologies tested since we couldnot detect statistically significant differences betweenthem.Distances expressed in Kosambi´s function weremore efficient thant Haldane´s function for larger linkagegroups.The simulation study was better accomplishedwith larger population sizes since in those sizes thedifferences between treatments could be observed.Eficiência da análise multiloco para a construção demapas genéticosRESUMO - Na pesquisa genética, a utilização de mapas genéticos se torna uma ferramenta muito útil, sendo que a relaçãoentre distância de mapa e freqüência de recombinação é expressa por uma função de mapeamento genético. Porém, váriasdestas funções não pressupõem a porcentagem de recombinação conjunta, ou seja, não são probabilidades de multilocos. Oobjetivo deste trabalho foi comparar, através de simulações, a eficiência na utilização de diferentes funções de mapeamentocom e sem análise multiloco como ferramenta na construção de mapas genéticos. Para estudo comparativo foi simulado umgenoma constituído de três grupos de ligação (50, 100 e 200 cM). Foram simuladas quatro populações de mapeamento, F2,com 50, 100, 200 e 400 indivíduos, e com 10 réplicas cada. Após análises dos resultados verificou-se que a análise multiloconão foi eficiente para resgatar o tamanho dos grupos de ligação, concluindo que a não utilização da análise multiloco seriamais viável.Palavras-chave: Estatística genômica, simulação, mapeamento.REFERENCESBhering LL and Cruz CD (2008) Tamanho de população idealpara mapeamento genético em famílias de irmãos completos.Pesquisa Agropecuária Brasileira  43: 379-385.Cruz  CD and Schuster I (2001) Programa GQMOL: Programapara análise de genética quantitativa e molecular v:2006.9.1.Cruz CD (2006) Programa Genes: Estatística experimentale matrizes. Editora UFV, Viçosa, 285p.Goldstein DR,  Zhao H and Speed TP (1995) Relative efficienciesof c2 models of recombination for exclusion mapping andgene ordering. Genomics 27: 265-273.Liu (1998) Statistical genomics: linkage, mapping, andQTL analysis. CRC Press, Boca Raton, 611p.Schuster I and Cruz CD (2004) Estatística genômica aplicadaa populações derivadas de cruzamentos controlados.Editora UFV, Viçosa, 568p.Stam P (1993) Construction of integrated genetic linkage mapsby means of a new computer package: JoinMap. The PlantJournal 3: 793-744.

Efficiency of the multilocus analysis for the construction of genetic maps

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