Crop Science Illumina
HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
QUICK SEARCH:   [advanced]


     

Published online 1 March 2007
Published in Crop Sci 47:537-546 (2007)
© 2007 Crop Science Society of America
677 S. Segoe Rd., Madison, WI 53711 USA
This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Ishii, T.
Right arrow Articles by Yonezawa, K.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Ishii, T.
Right arrow Articles by Yonezawa, K.
Agricola
Right arrow Articles by Ishii, T.
Right arrow Articles by Yonezawa, K.
Related Collections
Right arrow Biometrics
Right arrow Stochastic Processes
Right arrow Crop Genetics

CROP BREEDING & GENETICS

Optimization of the Marker-Based Procedures for Pyramiding Genes from Multiple Donor Lines: I. Schedule of Crossing between the Donor Lines

T. Ishiia and K. Yonezawab,*

a Marker-assisted Rice Breeding Research Team, National Institute of Crop Science, Tsukuba 305-8518, Japan
b Dep. of Biotechnology, Kyoto Sangyo Univ., Kyoto 603-8555, Japan

* Corresponding author (yonezaw{at}cc.kyoto-su.ac.jp).


   ABSTRACT
TOP
 ABSTRACT
INTRODUCTION
 DEFINITIONS OF CROSSING...
 COMPARISON OF THE SCHEDULES
 RESULTS AND DISCUSSION
 REFERENCES
 
Recent exploitation of DNA markers of desirable trait genes facilitates construction of high-degree, gene-pyramided lines via assembling markers from multiple donor lines. In such a program, a plant that has all the target markers in a heterozygous state must be produced first. Efficient procedures for that are discussed. When pyramiding the genes onto the genetic background of a particular recipient line, the backcross should be performed separately for each donor before the crossing between the donors. The plants produced through the backcross should be crossed in a schedule with structure and disposition of the plants as symmetric as possible. When four such plants (A, B, C, and D) are produced, for instance, they should be crossed in a schedule like (A x B) x (C x D) in which the number of target markers of A plus B should be as similar as possible to that of C plus D. Ideal-type schedules in the presence of four to eight donors are presented. A contrastingly different guideline applies when the donors themselves are crossed without the backcross; they should be crossed in a schedule with completely tandem structure in which donors with fewer target markers enter the schedule in earlier stages. The disposition of donors in the schedule should be modified in the presence of linked or redundant markers. Donors should be disposed in a pattern to minimize the occurrence of repulsion linkages. Formulae for the modification under a high redundancy are presented.

Abbreviations: ANP, the average number of plants tested per generation of selection • BF, BL, and NB, the schedules of crossing in which the backcross with a recipient line is performed first (before crossing between the donors), last (after the crossing), and not performed, respectively • CRO, the total number of crossings performed in a crossing schedule • ETN, the expected total number of plants tested in a crossing schedule • GEN, the number of generations used for a crossing schedule • S, T, and ST, the crossing schedules with symmetric, tandem, and mixed structures, respectively • SEL, the total number of generations of selection performed in a crossing schedule.


   INTRODUCTION
TOP
 ABSTRACT
 INTRODUCTION
DEFINITIONS OF CROSSING...
 COMPARISON OF THE SCHEDULES
 RESULTS AND DISCUSSION
 REFERENCES
 
MANY DNA MARKERS linked with useful trait genes have been detected in recent years in various crop species (Fujino and Sekiguchi, 2005; Mano et al., 2005; Guo et al., 2006; Sakata et al., 2006; Wight et al., 2006). DNA markers, once validated via appropriately designed experiments (Li et al., 2001; Zhou et al., 2003; Glover et al., 2004; Landi et al., 2005), could be effectively used for accumulating into single genotypes useful genes that have been detected separately in different plant lines (Liu et al., 2000; Singh et al., 2001; Datta et al., 2002; Castro et al., 2003; Jiang et al., 2004). Multigene pyramided lines thus produced will be of high practical use as a parent for a new inbred as well as hybrid market cultivar. With a wide variety of gene-pyramided lines becoming available, it will become possible to breed superior market cultivars solely by marker-based selection without phenotypic test, just by assembling markers from a number of gene-pyramided stock lines, as actually planned by Bonnett et al. (2005) for wheat breeding.

The marker-based gene accumulation will be rather straightforward when two or three donor lines are involved; procedures practicable with a minimum resource expense could be easily found in such a case. When accumulating many genes from four or more donor lines, however, some guideline principles are needed to find the best procedures. To our knowledge, procedures for marker-based gene accumulation from multiple donor lines have been little discussed, although studies have been made in detail for the marker-assisted backcross strategy for gene introgression (Tanksley, 1983; Hospital et al., 1992; Tanksley and Nelson, 1996; Frisch, 2004) as well as the marker-assisted selection strategies in which the detection of markers and selection assisted by the detected markers are performed for biparentally initiated populations in outcrossing crops (Lande and Thompson, 1990; Whittaker et al., 1995; Moreau et al., 1998; Hospital et al., 2000; Liu et al., 2003) and self-fertilizing crops (van Berloo and Stam, 1998; Charmet et al., 1999; Liu et al., 2004). With more and more markers of useful trait genes becoming available every year, it will be important to establish strategies for utilizing these markers to produce high-degree, gene-pyramided lines.

Procedures in a marker-based gene accumulation program proceed in two steps. First, all target markers in the donor lines are assembled into the genome of a single plant in a heterozygous state, and second, a plant that has all the markers in a homozygous state is selected from among the progeny of the heterozygous plant produced in the first step. Different parameters determine the efficiency of the two steps; the schedule (pattern and order) of crossing between donor lines is important in the first step, and the scheme of selection, in the second step. The purpose of this paper is to propose some guidelines for optimizing the procedures of the first step.


   DEFINITIONS OF CROSSING SCHEDULES AND EFFICIENCY INDICATORS
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS OF CROSSING...
COMPARISON OF THE SCHEDULES
 RESULTS AND DISCUSSION
 REFERENCES
 
We discuss the cases in which useful genes are pyramided onto the genetic background of a recipient inbred line V from k (≥4) donor inbred lines in a monoecious diploid plant species. Donor line Mi (i = 1 ~ k) has mi (≥1) target markers (Fig. 1 ), each of the markers being perfectly linked with a desirable gene for a qualitative or quantitative trait. The recipient inbred line V may also carry some markers to be accumulated which, however, are irrelevant for comparing the relative efficiencies of different crossing schedules and are ignored in the present discussion. The target markers are assumed to be codominant or dominant, being independently inherited. Selection in any generation is performed on the basis of the markers. To obtain a plant that carries all the target genes in a homozygous state in the genetic background of line V, a plant genotype that has all target markers in a heterozygous state must be produced in the first step (Step I in Fig. 1), followed by selection for obtaining the objective plant that has all the markers in a homozygous state (Step II). Here, we describe the optimum procedures for Step I. Several generations of backcrosses are used in Step I for recovery of the genetic background of V but are not used in the absence of any particular recipient line. We discuss both two cases. The guideline principles derived herein will apply not only to autogamous plant species but also to allogamous species when the recipient line V and donor lines Mis are inbred.


Figure 1
View larger version (22K):
[in this window]
[in a new window]

  		Figure 1. Procedural flow of marker-based gene pyramiding from k donor lines.

 
The efficiency of Step I depends on the schedule of crossing between plants. Guidelines for the best schedule are derived via comparing the efficiencies of some typical crossing schedules described in Fig. 2 (a) and (b) , where schedules are named on the basis of the stage of backcross [backcross first (BF) versus backcross last (BL)], the number of donor lines (k), and the structure of crossing schedule [symmetric (S), tandem (T), and mixed (ST)]. The schedule is either symmetric or tandem when k = 4. A schedule with completely symmetric structure cannot be constructed when k = 5. Among different schedules with mixed structures, one in which a tandem structure occurs in an earlier stage has a more symmetric structure as a whole. In this sense, BF-5ST1 and BL-5ST1 are more symmetric than BF-5ST2 and BL-5ST2, respectively. In all schedules in categories BF and BL, five generations (n = 5) of crossing with recipient line V (one generation for the initial crossing and four subsequent generations of backcrossing with V) are completed unless otherwise stated. From each genetically segregating population, a plant (designated by a "

Formula

" in Fig. 2) that has the target markers of the parents in heterozygous state is selected to be used as a parent for the next generation. The background selection for facilitating the recovery of the recipient genetic background (Tanksley et al., 1989; Reyes-Valdes, 2000; Bouchez et al., 2002; Frisch, 2004) is not used. The backcross is not necessary when there is no particular recipient line or the genes are assembled from a set of isogenic lines (carrying the markers in the same genetic background). Crossing schedules without backcross are designated as NB (no backcrossing), which are not described in Fig. 2 because they are the same as schedules in category BL with the process of backcross having been eliminated. For the purpose of minimizing the time expenditure, no generations for the advancement of homozygosity are employed in any schedule; a plant heterozygous for the markers is selected and crossed with a donor plant to raise a population for the next generation selection.


Figure 2A
View larger version (16K):
[in this window]
[in a new window]

  		Figure 2a. Crossing schedules discussed in this paper. The mark "{circ}" designates an F1 plant produced via crossing between a donor and recipient line (in the schedules of category BF) or two donor lines (in the schedules of category BL), and "Figure 2A" designates a selected plant that has the targeted markers in heterozygous state.

 

Figure 2B
View larger version (12K):
[in this window]
[in a new window]

  		Figure 2b.
 
The efficiency of a schedule can be indicated by the following five indicators, i.e., the minimum sufficient number of generations required to accomplish the schedule (GEN), the total number of crossings between plants completed in the schedule (CRO), the total number of generations in which selection is performed (SEL) and the expected total number of plants tested in the schedule (ETN), as well as the number of tested plants per generation in which selection is performed (ANP), which is ETN/SEL. A schedule with smaller values of these indicators can be regarded as more efficient. However, a schedule that is efficient with respect to any one indicator is not necessarily efficient with respect to the others. Of the five indicators, GEN (indicative of the minimum required time) and ETN (indicative of the total cost for marker genotyping) will be the most important in most projects of gene pyramiding. With the same number of donor lines (k), GEN is almost the same in all schedules within each of the categories, i.e., BF, BL, and NB. Therefore, superiority among the schedules within the same category could be discussed on the basis of ETN.

For each genetically segregating population, the marker test ends when a plant with the target marker genotype ("

Formula

" in Fig. 2) is detected. The expected number of plants tested in this selection is represented by the reverse of segregation proportion of the plant with the target marker genotype, i.e., 1/p [because the probability of x plants being tested until finding the target plant is (1 – p)x – 1p, the expected number of tested plants equals pFormulax(1–p)x–1 , p being the segregation pro-

portion of the target plant]. The expected total number of tested plants, ETN, is calculated as the sum of the expected plant numbers across all generations in which the marker

selection is performed, i.e., Formula(1/pj), where pj stands for the segregation proportion of the target genotype in generation j. In schedule NB-4T, as the most convenient example, a plant having all target markers of donors M1, M2, and M3 in a heterozygous state occurs in a proportion of 1/2m1 + m2 in the first genetically segregating generation [Generation 3 in Fig. 2(a)], and one having all markers of M1 to M4 occurs in a proportion of 1/2m1 + m2 + m3 in the next generation and 1/2m1 + m2 + m3 + m4 in all (n) subsequent generations, giving a total expected plant number of 2m1 + m2 + 2m1 + m2 + m3 + n x 2m1 + m2 + m3 + m4 (mi stands for the number of markers possessed by donor Mi). For brevity, formulae of ETN as well as the other indicators are presented in the supplements of the tables that appear in the next section.


   COMPARISON OF THE SCHEDULES
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS OF CROSSING...
 COMPARISON OF THE SCHEDULES
RESULTS AND DISCUSSION
 REFERENCES
 
Comparison in the Absence of Redundant Markers
Our discussion is directed first to the cases in which the donor lines have no markers in common. Table 1 (a) and (b) contain the calculations of the five efficiency indicators for cases of k = 4 and 5. In Table 1(a), schedules in category BL require more plants (greater ETN and ANP) than those in BF in any set of mis assumed, while no difference exists in the number of generations (GEN) required for the accomplishment of the gene-pyramiding project. This trend gets much more pronounced with increasing numbers of donors (k) and markers (mi) (data not presented), substantiating the superiority of schedules in category BF over those in BL. An additional advantage exists with BF; the linkage drag surrounding the target genes will more easily be reduced when the backcross is performed separately for each donor line. Schedules in BL, therefore, will be of little practical use and are not taken up in the following discussion. Because of the absence of the backcross, the indicators of schedules in NB take much smaller values than those in BF.


View this table:
[in this window]
[in a new window]

  		Table 1. Calculations of the five efficiency indicators for the various schedules of crossing defined in Fig. 2.

 
With the same set of donor lines, ETN and ANP depend on the structure of crossing schedule and the disposition with which the k plants (BC4F1 plants) obtained through the backcross (in schedules in BF) or the k donor lines (in schedules in NB) are taken into the schedule. Formulae of ETN of Table 1(a) show that the superiority between BF-4S and BF-4T depends on the magnitude of 2m3 + m4 relative to 2m1 + m2 + m3, simply, m4 relative to m1 + m2. Therefore, as seen from the calculations in Table 1(a), BF-4S is always superior to BF-4T when all of the donors have the same number of markers (m1 = m2 = m3 = m4). The superiority of BF-4S also holds with unequal numbers of markers; in the range of dispositions from (1, 2, 3, 4) to (4, 3, 2, 1) [Table 1(a)], schedule BF-4S with disposition (1, 4, 2, 3) gives the smallest value of ETN, i.e., 1208. In this schedule, the crossing is made in two pairs in the first stage [cf., Fig. 2(a)], with the same total number of markers being disposed to each pair (m1 + m2 = m3 + m4).

A contrastingly different trend is observed regarding superiority between schedules in category NB; a schedule with tandem structure (NB-4T) is superior to that with symmetric structure (NB-4S) in any sets of mis calculated. Generality of this trend is substantiated by the formulae of Table 1(a); NB-4T is superior to NB-4S when 2m1 + m2 + 2m1 + m2 + m3 < 2m1 + m2 + m3 + m4, simply, 1 + 2m3 < 2m3 + m4, which always holds. With the same set of donors, a disposition directed as m1 ≤ m2 ≤ m3 ≤ m4 is most efficient [Table 1(a)]. Screening is not necessary for the markers of a donor (M4) that is used in the last stage in a tandem schedule (NB-4T). This explains how NB-4T is superior to NB-4S.

When k = 5, schedules with mixed structure, BF-5ST1 and BF-5ST2, are superior to that with fully tandem structure, BF-5T, in any cases calculated [Table 1(b)]; the conditions for BF-5ST1 and BF-5ST2 to be superior to BF-5T are derived as 2m4 + m5 < 2m1 + m2 + m3 + m4 and 2m3 + m4 < 2m1 + m2 + m3, being simplified to m5 < m1 + m2 + m3 and m4 < m1 + m2, respectively. Of the two schedules BF-5ST1 and BF-5ST2, the former is superior in all cases calculated, indicating that when a tandem structure is unavoidable within a schedule, it should be used in the earliest possible stage. By the formulae given in the supplement of Table 1(b), BF-5ST1 is superior to BF-5ST2 when 2m1 + m2 + m3 + 2m4 + m5 < 2m3 + m4 + 2m1 + m2 + m3 + m4, which always holds when m5 ≤ m3. In the range of dispositions of (1, 2, 2, 3, 4) to (4, 3, 2, 2, 1), ETN is minimized (taking a value of 4368) in BF-5ST1 with disposition (1, 2, 3, 2, 4) in which the crossing is performed in two clusters, i.e., a triplet composed of M1, M2, and M3 and a pair of M4 and M5, with the same total number of markers being disposed to each cluster, i.e., 6 (1 + 2 + 3 and 2 + 4). This result coincides with the one obtained in case of k = 4 that ETN in BF-4S is minimized when each of the two pairs, i.e., M1 and M2 versus M3 and M4, is disposed with the same total number of markers, i.e., 5 (1 + 4 and 2 + 3). Of the two dispositions (1, 2, 3, 2, 4) and (1, 3, 2, 2, 4) in BF-5ST1, the former requires a fewer ETN, indicating that two plants with fewest markers should be crossed first within a triplet cluster.

The superiority among schedules in NB is contrastingly different from that among schedules in BF. In Table 1(b), the superiority occurs in the order of NB-5T > NB-5ST2 > NB-5ST1 in all cases calculated; from the formulae attached to this table, the superiority conditions for NB-5T over NB-5ST2 and for NB-5ST2 over NB-5ST1 are derived as 2m1 + m2 + 2m1 + m2 + m3 < 2m1 + m2 + m3 + m4 (simply, 1 + 2m3 < 2m3 + m4) and 2 x 2m1 + m2 + m3 + m4 < 2m1 + m2 + 2m1 + m2 + m3 + m4 + m5 (simply, 21 + m3 + m4 < 1 + 2m3 + m4 + m5), both of which hold with any sets of mis. NB-5T with disposition m1 ≤ m2 ≤ m3 ≤ m4 ≤ m5 is the best, as is confirmed with the calculations of Table 1(b).

In short, a crossing schedule with more symmetric structure as well as disposition of the donor plants is superior when heterozygous plants obtained via backcrossing with a recipient line are used as donors. Ideal-type schedules with four to eight donors are presented in Table 2 for breeder's convenience. By contrast, a schedule with tandem structure and asymmetric disposition directed as m1 ≤ m2 ≤ ··· ≤ mk is superior when the inbred (homozygous) donors themselves are crossed without the backcross.


View this table:
[in this window]
[in a new window]

  		Table 2. Ideal-type schedule of crossing between plants obtained through the backcross with a recipient line.

 
Comparison in the Presence of Redundant Markers
Some markers may be present in two or more donor lines. Redundancy in the markers causes no complications in finding out efficient schedules in BF, because the redundancy can be excluded in the process of backcross, with each marker being screened in only one among k courses of the backcross. Exclusion of the redundancy greatly facilitates the progress of backcross as well as simplifies the schedule of crossing that follows.

Complications may occur in schedules of category NB. From the formulae of ETN of NB-4S and NB-4T presented in the supplement of Table 3, the condition for NB-4T to be superior to NB-4S is derived approximately as m12 < m40 + 0.42x(m14 + m24) [derived from the inequality 2m10 + m20 + 2m10 + m20 + m30 + m12 x (4/3)m13 + m23 < 2m10 + m20 + m30 + m40 x (4/3)m13 + m14 + m23 + m24, which can be approximated to m12 < m40 + (2 – ln3/ln2)x(m14 + m24)]. This condition indicates that, as confirmable with the calculations in Table 3, NB-4T is superior when the two donors carrying fewer redundant markers (m12) than intrinsic markers of the fourth donor M4 (m40) are crossed in the first stage. On the other hand, comparison of the dispositions of intrinsic markers of (1, 2, 3, 4) to (4, 3, 2, 1) shows that, with the same configuration of redundancy, ETN of NB-4T is minimized with disposition (1, 2, 3, 4). These two trends lead to a guideline that a tandem crossing schedule should be used in which two donors with the fewest intrinsic (m10 and m20) as well as redundant (m12) markers are crossed in the first stage and a donor with the greatest number of intrinsic (m40) as well as redundant (m14 and m24) markers being crossed in the last stage. Such a schedule may not be constructed when donors with the fewest intrinsic markers have relatively many redundant markers. The best schedule in such a case should be based on the calculations using the formulae. Doubly redundant markers (m34) as well as trebly and quadruply redundant markers (mijks and m1234) are irrelevant to the superiority when k = 4 because all of the plants obtained through the last crossing have these markers.


View this table:
[in this window]
[in a new window]

  		Table 3. Calculations of the expected total number of tested plants (ETN){dagger} in the presence of redundant markers with four donors involved (k = 4).

 
When k = 5, ETN is formulated as 2m10 + m20 + m14 + m24 + (m15 + m25 + m145 + m245) + 2m10 + m20 + m30 + m12 + (m15 + m25 + m35 + m125) x (4/3)m13 + m23 + (m135 + m235) + 2m10 + m20 + m30 + m40 + m12 + m13 + m23 + m123 x (4/3)m14 + m24 + m34 + m124 x (8/7)m134 + m234 for NB-5T, 2m10 + m20 + m14 + m15 + m24 + m25 + m145 + m245 + 2m10 + m20 + m30 + m40 + m50 + m12 x (4/3)m14 + m15 + m24 + m25 + m34 + m35 + m124 + m125 for NB-5ST1, and 2m10 + m20 + m30 + m40 x (4/3)m13 + m14 + m23 + m24 + (m135 + m145 + m235 + m245) + 2m10 + m20 + m30 + m40 + m12 + m34 x (3/2)m13 + m14 + m23 + m24 x (4/3)m123 + m124 + m134 + m234 for NB-5ST2, where variables ms are defined the same as when k = 4 (cf., the supplement of Table 3), and those within parentheses are not necessary when selection for the markers redundant with the last donor M5 is performed only in the last generation. Quadruply and quintuply redundant markers (mijkls and m12345) are irrelevant for the same reason as mentioned when k = 4. Conditions for the superiority of the schemes are difficult to derive directly from these formulae. However, our calculations under some practically possible configurations of the redundancy (not presented here) revealed general superiority of a schedule with tandem structure over ones with symmetric or mixed structure; schedule NB-5T in which donors with fewer intrinsic markers are crossed in earlier stages is mostly superior to NB-5ST1 and NB-5ST2 unless doubly and trebly redundant markers, mij and mijk, are as many as or more than intrinsic markers (mi0) of any donor. Numerical calculations using formulae like ours are necessary in the presence of a high redundancy.

Influence of Linkage between the Markers
For markers located on the same homologous chromosomes of the same or different donors, linkage occurs in the genome of a plant selected in a stage. The crossing schedule should be duly modified in such a case. When compared with the case of independent inheritance, a linkage in the coupling phase produces a favorable effect; with the same number of targeted markers, the segregation proportion (pj) of the targeted genotype in the progeny raised via crossing the selected plant with a new donor plant increases in the presence of a coupling linkage, and, consequently, the number of tested plants decreases. By contrast, a linkage in the repulsion phase produces an unfavorable effect; more plants must be tested for the detection of a plant with the targeted marker genotype.

In the genome of a plant selected in each stage, markers that were newly incorporated via the latest crossing should be linked in the repulsion phase with markers that had been incorporated in any stages before the latest, whereas all markers incorporated in any stages before the latest should be linked in coupling phase. In the crossing schedules discussed in this paper, coupling linkages persist and accumulate with advance of the stages, whereas any repulsion linkage occurs in only one stage because it is converted to a coupling linkage after one round of marker selection. Although the occurrence of repulsion linkage cannot be avoided for the markers that are located on the same homologous chromosomes of different donors, its disadvantage could be minimized with a properly modified disposition of the donors.

In the presence of a repulsion linkage between two markers of a recombination value of r, the segregation portion of the targeted marker genotype decreases to 2r relative to that expected under independent inheritance of the two markers (r = 0.5) and, consequently, 1/(2r) times as many plants as tested under independent inheritance must be tested. The ratio 1/(2r) takes a value of 5.517, 3.033, and 2.216 with a map distance of 10, 20, and 30 cM, respectively, indicating that even a moderate repulsion linkage invokes a substantial disadvantage (increase in tested plants). More plants are tested in later stages because targeted markers increase with advance of stages. Therefore, when evaluated in the absolute number of tested plants instead of a ratio value as given above, a repulsion linkage with the same strength invokes a heavier disadvantage when it occurs in a later stage. On the other hand, a repulsion linkage, once converted to the coupling phase after one round of marker selection, contributes to reducing tested plants in all subsequent stages. Therefore, the disadvantage of a repulsion linkage can be minimized and best recovered when it occurs in an earliest possible stage, leading to a guideline that a crossing that invokes a strong repulsion linkage should be performed as early as possible. Markers located on the same homologous chromosome of the same donor cause no disadvantage because they are linked in the coupling phase in all stages. A pair or set of markers tightly linked in the coupling phase could be treated like a single marker.

Our calculations, though omitted here for brevity, also showed that a quite heavy disadvantage is invoked when repulsion linkages occur in duplicate in the genome of a selected plant, although the disadvantage is much mitigated when the repulsion linkages coexist with coupling ones. The occurrence of duplicate repulsion linkages can be managed via modifying the disposition of donors. A disposition with a minimum occurrence of duplicate repulsion linkages should be chosen.


   RESULTS AND DISCUSSION
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS OF CROSSING...
 COMPARISON OF THE SCHEDULES
 RESULTS AND DISCUSSION
REFERENCES
 
The trends we have pointed out lead to the following guidelines.

1. When pyramiding genes from four or more donor lines onto the genetic background of a particular recipient line (line V in Fig. 1 and 2), the backcross for the recovery of the genetic background should be performed separately for each donor line before, not posterior to, the crossing between the donor lines.
2. The plants obtained via the backcross should be crossed in a schedule with the most symmetric structure and disposition of the markers (mis) (cf., Table 2).
3. A contrastingly different guideline applies when inbred donors themselves are crossed without the backcrossing (absence of any particular recipient line). The donors should be crossed in a schedule with tandem structure in which donors carrying fewer markers are crossed in earlier stages.

The disposition of donors should be modified when some markers are possessed by two or more donors (redundant markers) or located on the same homologous chromosomes of the same or different donors (linked markers). Guidelines for the modification are as follows.

4. In schedules of category BF, the redundancy should be excluded via screening each of the target markers in only one among all courses of the backcross. In schedules of category NB, the guideline under nonredundancy may fail when markers of any class of redundancy, duplex to multiplex, are more than the intrinsic markers (mi0) of any donor. With such a high redundancy, numerical calculations of ETN will be needed to find the best schedule. Here we presented formulae of ETN in the presence of four and five donors. Stochastic rather than analytical calculations would be convenient for more donors.
5. In the presence of linked markers, the crossing schedule should be modified on a guideline that, with the number of targeted markers unchanged, a crossing that invokes a repulsion linkage should be performed in an earlier stage. It is important that donors should be disposed in a way to minimize the occurrence of repulsion linkages in duplicate in the genome of a selected plant.

Our discussion has been based on some assumptions for brevity. Modifications may occur if the assumptions are relaxed, some of which are as follows. The comparison among schedules in category BF was based on the assumption that five generations of crossing with a recipient line V (n = 5), i.e., one generation for the initial crossing between a donor line Mi and recipient line V and four subsequent generations of backcross, are used to recover the genetic background. Fewer generations of backcross may be sufficient when the recipient line V and donor lines Mis are relatively closely related. Calculations with fewer generations of the crossing showed that ETN does not noticeably decrease compared with those calculated before (data not presented), reflecting the fact that the number of plants tested in the course of backcross does not occupy a major part of ETN in schedules of BF. Therefore, our guidelines obtained with n = 5 need not be modified.

By selection for the background markers in the course of backcrossing (Tanksley et al., 1989; Bouchez et al., 2002; Frisch, 2004), we could save time. However, more plants need to be tested for detecting plants with minimum linkage drags as well as higher cost for genotyping many background marker loci. The advantage of background selection should depend on the circumstances. In any case, the superiority of the schedule will be the same whether or not the background selection is considered because the superiority is determined by the crossing schedule after the backcross.

ETN will be good to compare the efficiencies of different crossing schedules, but it does not necessarily indicate a sufficient number for the success of a gene-pyramiding project. The number of plants (x) tested in a generation of selection is subject to a high magnitude of chance fluctuation [x fluctuates with variance (1 ' p)/p2], and many more plants than the expected number E(x) (= 1/p) may be tested until finding a plant with the target marker genotype. Therefore, sufficiently more seeds (embryo plants) than 1/p should be taken to guarantee the success of selection in each generation, although not all of these seeds are actually used for the marker test. To ensure at least one seed carrying an embryo plant with the target marker genotype with a probability P, as many seeds as ln(1 – P)/ln(1 – p) must be taken; this is approximately –ln(1 – P) times as many as 1/p [note that ln(1 – p) can be approximated to 'p when p is sufficiently small]. In some plant species and/or inappropriate cultural conditions, sufficient seeds may not be obtained when only one plant is selected, and then, two or more plants with the target marker genotype must be selected. When selecting two such plants from a population, the expected number of tested plants is 2/p [because the probability of x plants being tested until finding two plants with the target marker genotype equals (x ' 1)(1 ' p)x – 2p2, the expectation of x is given by p2Formulax(x–1)(1–p)x–2, which equals 2/p], indicating

that ETN and ANP are two times as large as the values calculated before. However, the superiority of the schedule is the same whether based on 1/p or 2/p, and our guideline principles derived before hold without any modification.

A useful trait allele may be linked with a null marker (de Moraes et al., 2006). Because null markers cannot be screened in a heterozygous state, at least two generations are necessary for detecting a plant carrying the target allele, which requires a longer time and higher expenses. To minimize this disadvantage, a donor carrying an allele linked with a null marker should be taken into the crossing schedule in a latest possible stage.

The efficiency of marker-based gene-pyramiding will decrease substantially unless the markers are perfectly or tightly linked with useful trait genes. Association of a marker with a trait allele and consequently the reliability of the marker-based selection decreases with increasing cycles of meioses. Very simply, with a recombination value of r between a marker and trait allele, the probability of this linkage being maintained unbroken across s cycles of meiosis is equal to (1 – r)s. To keep this probability higher than a certain critical value, say P, s must not exceed lnP/ln(1 – r), suggesting that a phenotypic test should be performed every s generations of selection to confirm the persistence of the initial linkage. Or, to maintain this linkage across s generations with a probability higher than P, the recombination value r must be lower than 1 – P1/s. The critical linkage strength under some typical conditions of P and s is presented in Table 4 in relation to the map distance (in centimorgans) and recombination value (r), showing that a linkage as close as 1 cM can be maintained across five generations with a probability higher than 0.95, whereas the linkage must be extremely tight to be maintained with a probability higher than 0.99. The reliability of marker selection could be improved if flanking markers are considered (van Berloo and Stam, 1998; Frisch et al., 1999); this, however, requires more plants to be tested and higher cost per plant. It is imperative to explore markers that are tightly linked with useful trait genes.


View this table:
[in this window]
[in a new window]

  		Table 4. Critical strength of linkage (cM in the map distance and r in the recombination value) for the initial linkage between a marker and trait allele being maintained unbroken across s cycles of meiosis with a probability higher than P. cM was translated from r using the equation of Haldane (1919) and r was calculated using the relation r = 1 – P 1/s.

 
When three donors are involved, ETN is minimized when two donors with fewest target markers (intrinsic markers in the presence of redundancy) are crossed first. Redundant markers are irrelevant when finding the best schedule with three donors. Bonnett et al. (2005) planned gene pyramiding from three donor lines of wheat, HM14BS, Goldmark, and Sunstate, which have two, one, and three intrinsic markers, respectively. They adopted a right disposition (HM14BS x Goldmark) x Sunstate, with which ETN (2m10 + m20) takes a minimum value of 22 + 1 = 8.

Received for publication June 29, 2006.


   REFERENCES
TOP
 ABSTRACT
 INTRODUCTION
 DEFINITIONS OF CROSSING...
 COMPARISON OF THE SCHEDULES
 RESULTS AND DISCUSSION
 REFERENCES
 




This article has been cited by other articles:


Home page
 Crop Sci.Home page
T. Ishii, T. Hayashi, and K. Yonezawa
Optimization of the Marker-based Procedures for Pyramiding Genes from Multiple Donor Lines: III. Multiple-Gene Assemblage Using Background Marker Selection
Crop Sci., November 24, 2008; 48(6): 2123 - 2131.
[Abstract] [Full Text] [PDF]

Home page
 Crop Sci.Home page
T. Ishii and K. Yonezawa
Optimization of the Marker-Based Procedures for Pyramiding Genes from Multiple Donor Lines: II. Strategies for Selecting the Objective Homozygous Plant
Crop Sci., September 1, 2007; 47(5): 1878 - 1886.
[Abstract] [Full Text] [PDF]

This Article
Right arrow Abstract Freely available
Right arrow Figures Only
Right arrow Full Text (PDF) Free
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Download to citation manager
Right arrow reprints & permissions
Citing Articles
Right arrow Citing Articles via HighWire
Right arrow Citing Articles via Google Scholar
Google Scholar
Right arrow Articles by Ishii, T.
Right arrow Articles by Yonezawa, K.
Right arrow Search for Related Content
PubMed
Right arrow Articles by Ishii, T.
Right arrow Articles by Yonezawa, K.
Agricola
Right arrow Articles by Ishii, T.
Right arrow Articles by Yonezawa, K.
Related Collections
Right arrow Biometrics
Right arrow Stochastic Processes
Right arrow Crop Genetics

HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS
The SCI Journals Agronomy Journal Vadose Zone Journal
Journal of Natural Resources
and Life Sciences Education		 Soil Science Society of America Journal
Journal of Plant Registrations Journal of
Environmental Quality		 The Plant Genome