# Step 1: Computation of genotypic probabilities - Estimation of genetic values

Algorithms to compute the probabilities of IBD alleles transmission throughout generations of selection have been deployed and results are displayed via three tables (corresponding to tab_scores, tab_homo_hetero and tab_parents see previous section) and graphs (see below).

Figure 7: genetic value (molecular score) for each individual (all/each QTL)

Individuals are represented in lines followed by their pedigree, the cycle of selection and the group they belong to. Plants can be sorted regarding their value for any columns. For instance for the molecular score (column MS), which is the expected proportion of favorable allele at the QTL position(s), (click on the MS column) The genetic values (MS red column) vary between 0 and 1. A value of "1" indicates that the individual corresponds to the targeted ideotype (it is homozygous for the favorable allele(s) for this QTL or all the QTL).

In this maize example, MS varies between 0.27 (X: parental line at the bottom of the table, not presented in Fig. 7) and 0.83 (B8: individual presents at the top of the table, coming from the last cycle of selection). Note that the four inbred lines D (DE), F (F283), S (F810) and X (F9005) have a MS of 0.36, 0.36, 0.45 and 0.27 respectively.

More detailed genotypes can be displayed by double clicking on MS or QTL cells (see below). This view summarizes and aggregates the information presented in the two other tables (Homo/Hetero and Estimation of parental alleles probability).

Figure 8: detailed genotype in terms of parental alleles at QTL position

Fig. 8 shows that individual B8 has a molecular score of 0.8752 at QTL 4. It has a probability of 0.763260 to be homozygous for the favorable alleles s/f (i.e. Homo(+/+)). This score corresponds to the sum of the probabilities of the genotypes f:f=0.522327, s:f=0.225656 and s:s=0.015277). Its MS of 0.8752 corresponds to the expected proportion of favorable allele(s) (i.e. Homo(+/+) + 1/2 Hetero(+/-)). Founders (represented by d, f, s and x alleles) indicate the expected proportion of parental alleles. We notice that this individual is issued from three parental lines D, F, S and not X (see also pedigree in Fig. 20).

A colored view of the molecular score table can be displayed to identify more easily QTL for which a given individual is considered as fixed or not (see Fig. 9). Press Visualization > Color scheme... on the menu bar.

Figure 9: colored view of the molecular score table

A value of 0.75 (by default) is selected for the probability threshold to be considered as homozygous (un)favorable or heterozygous at the QTL positions. A color can be assigned to each of them. Genotypes which are not assigned to any of these categories are considered "uncertain genotypes (?)". When you apply a new set of parameters (cut-off / colors), the four corresponding columns (No.(+/+), No.(-/-), No(+/-), No.(?)) of the MS table are updated.

For example, in Fig. 9, individual B8 is considered as homozygous favorable for eight QTL (in blue, No.(+/+) = 8), homozygous unfavorable for only one QTL (in red, No.(-/-) = 1), it presents no heterozygous QTL (in grey, No.(+/-) = 0) and two QTL (in yellow, No.(?) = 2) are uncertain. Some MS at QTL positions are close to 1 (e.g. QTL3 = 0.9761) and some others are lower (e.g. QTL2 = 0.8598). This uncertainty can be due to (i) the fact that one marker flanking the QTL is heterozygous whereas the other one is homozygous favorable, which indicates that a recombination took place near the QTL position, or (ii) that there are missing data (see genotypes/pedigree file).

The results of the different tables can be visualized on graphs that are automatically generated by clicking on the Graphs tab (see below).

Figure 10: distribution of QTL MS, global genetic values and their evolution over the different cycles of selection

The graph on Fig. 10a indicates the frequency of favorable alleles at the different generations of selection (on average and for each QTL). Note that no genetic gain is expected for the last generation (C2, in blue) because individuals are not selected yet.

Fig. 10b and 10c show the distribution of the molecular score (for each QTL separately and on average for all QTL) whereas Fig. 10d displays the average of the MS for individuals classified according to another classification criterion (e.g. subprogrammes, families, etc). All the graphs can be exported (in png, svg or eps formats) by using the “Save…” button.

In the estimation of the Molecular Score (MS), OptiMAS attributes the same weight to all QTL declared in the map file. It is also possible to discard QTL and/or to attribute economical weights defined by the breeder, to compute a "Weight" index. Press the Weight button to open a dialog window (see below).

Figure 11: weighted molecular score give more or less importance to the different QTL

We noticed in this example that the favorable allele (x) at QTL1 may be lost because (i) the ten best individuals of the panel have a molecular score of 0 at QTL1 (see Fig. 9, cells in red) and (ii) graphs in Fig. 10a and 10b indicate the same decay. Thus, a weight of 3.0 has been attributed to the QTL 1. Assign QTL weights then press Apply. It will result in an update on the "Weight" column (in blue) and therefore produce a new classification of individuals.

In addition to the molecular score and the weight columns, OptiMAS estimates an "Utility Criterion" (UC, green column in Fig. 8) which evaluates the expected value of superior gametes of each individual by combining the molecular score with the expected variance of the MS of its gametes (see tab_scores section for more details).

Allelic effects of QTL for traits of interest can be provided by the user. Select File > Import Data... from the menu bar, browse the allelic effects file and click "proceed" (see section 5.1 figure 5).
Optimas then computes predicted molecular scores (PMS) for each trait documented with allelic effects and adds/replaces the corresponding columns (indicated by "PMS" prefix) on the right side of displayed table. Note that missing information "-" will be considered as zero.

Indexes can be defined by combining different sources of information (MS, MS_UC, QTL, PMS and quantitative trait information provided by the user). To do so, click on the Index button, define formula and click Apply (Figure 12 below). By default, the index column will be identified as "Index" but an alternative name can be chosen by the user by prepending the literal expression with this alternative name and the character '='. Note that formulas can be saved by clicking save (a file "saved_formulas.txt" is created in the working directory), and reused in the same or another Optimas session by clicking load.

Figure 12: the resulting index column is always located just before the MS column.

The "Find Id" dialog box can be used to search and locate a specific individual in the panel. Press “Find” button (see below).

Figure 13: find individual by name ("Find Id" dialog)

By default, research identifies individuals the name of which contains the declared string (“B124” in figure 13). Research is also possible via exact matching (check "Whole words only"). Enter the Id of the individual that you are looking for with the appropriate parameters into the search box and then press the "Find" button. Any matching results will move the main display to the exact position of the individual. It will also be graphically highlighted.

The Filter "Columns/Individuals rows" dialog is used to enable or disable the display of any columns (except Id column) and/or individuals rows on the MS table. Press the "View" button to display the filter dialog (see below).

Figure 14: Columns and Individuals rows filter dialog

The Fig. 14 presents two tables displaying (i) the list of the variables (left tab) and (ii) the list of all the individuals (right tab) in the display table. Individuals can be filtered by "Cycles" of selection, "Groups" or manually. Select and check columns and/or individuals rows to follow and press the "OK" button to apply the corresponding filter. This refreshes immediately the tables. This new view of the table can be useful if you are working with a large number of QTL and/or individuals and you want to focus on specific QTL/plants.