NESSI: a program for Numerical Estimations for Sporophytic Self-Incompatibility systems. ************************* Welcome in NESSI: Numerical Estimations for Sporophytic Self-Incompatibility. program written by Sylvain Billiard. see Billiard S, V. Castric and X. Vekemans 2007 Genetics for details. *************************

User’s Guide v0.2.3 1. What is it? Evolutionary biologists are still looking for evidence of selection in natural populations. One of the most famous examples is the self-incompatibility systems (SI) in plants, which allows the avoidance of self-fertilization as well as fertilization between genetically related individuals. As a consequence, it should decrease inbreeding depression. A particularity of interest of this mating system is that it is controlled by a single locus: the so-called S-locus. Two main types of SI are known in plants: Gametophytic SI (GSI) and Sporophytic SI (SSI). In GSI, only one of the homologous alleles at the S-locus is expressed in pollen and is implied in the recognition of self-pollen. In stigma, all homologous alleles are expressed, they are codominant. This case is relatively simple and many theoretical models and predictions have been done about the diversity at the S-locus in natural population. In SSI yet, all homologous alleles may be expressed in both pollen and stigma. The difficulty here is that there can be different dominance relationships between alleles in pollen and stigma, what makes the modelling and the predictions of the diversity at the S-locus more complex. As a consequence, it is difficult to identify the evolutionary processes involved in the diversity at the S-locus observed in natural populations. The main goal of this program is to provide a tool for evolutionary biologist interested in SSI to get estimations for different variables generally used by population geneticists in SI studies. The program can handle any kind of dominance relationships between alleles. One can use this program to perform estimations on a given population of a given species with given dominance relationships.

2. What can it do? Deterministic equilibrium frequencies: The program can provide the expected allelic and genotypic frequencies at deterministic equilibrium when only negative frequency-dependent selection (FDS) is involved. Allelic richness, allelic frequencies and genotypic frequencies distributions at driftmutation-FDS “equilibrium”: The program can provide an estimation of the distribution of the number of alleles, allelic frequencies and genotypic frequencies in an isolated panmictic population at equilibrium, with a given mutation rate (in a K-allele model), a given population size and a given sample size. Note that the initial genotypic frequencies are set to the deterministic equilibrium frequencies.

Distribution of the allelic and genotypic frequencies change in one generation: The program can provide the distribution of the genotypic and allelic frequencies after one generation from given initial genotypic frequencies. It is useful if one wishes to know if the observed frequencies change in a generation are concordant with the FDS hypothesis. You will choose what to compute after launching the executable NESSI.exe: *** Would you like to compute: (1) Deterministic genotypic and allelic equilibrium frequencies? (2) Distributions in finite populations? (3) Genotypic and Allelic frequencies change distributions in a generation?

3. Computations options Dominance relationships: The program can handle any kind of dominance relationships, especially specific dominance relationships determined from cross experiments. The program can handle as well classical kinds of dominance relationships (the so-called dom, domcod and cod models). *** Dominance relationships : (1) Simple: dom or domcod models? (2) Specific? Selection regime: The program can handle two types of selection regime, through male way only (the classical Wright’s model) or through both female and male ways (the so-called “fecundity selection” model). *** Frequency-dependent selection model through: (1) Male way only (Wright's model)? (2) Male and female ways (fecundity selection)? Mutation model: At this time, the single available model is the K-allele model (KAM). When a mutation occurs, an allele copy randomly chosen in the population is changed and becomes one the K-1 other possible alleles (without any limitation relied on the dominance class). K is fixed at the beginning by the user and is equal to the number of alleles given in dominance relationships input files (see further for details).

4. Input files: how to write them? See options summary below to know which informations are needed depending on which computations you want to perform. All input files MUST be in the same folder as NESSI.exe. __________________________________________________________________________

File containing the matrix of dominance relationships in pollen or pistil

One file for each matrix is needed. If there are K alleles, these files must contain K2 values, one for each allele pairwise. There must be 1 on the diagonal (for all {i,i} pairwise). The

element at row i and column j contains 1 if allele i is dominant over j, 0 if allele i is recessive relatively to j, and 0.5 if both are codominant. Note that this matrix is not symmetric since if element {i,j} is 1 then element {i, j} is 0. Example 1 (dom model): the file for the pollen and the pistil dominance relationships are the same : 1 0 0 0 0 0 1 1 0 0 0 0 1 1 1 0 0 0 1 1 1 1 0 0 1 1 1 1 1 0 1 1 1 1 1 1 Example 2 (not a classical model): 1 0 0 0 0 1 1 0.5 0.5 0 1 0.5 1 0.5 0 1 0.5 0.5 1 0.5 1 1 1 0.5 1 1 1 1 0.5 0.5

0 0 0 0.5 0.5 1

Note that partial dominance is not implemented in the program. Separation can be tabulations or space blanks. __________________________________________________________________________

File containing simple dominance relationships This file contains the type of classical dominance relationships as well as the number of alleles in each dominance class. The informations must be given in a single line with - the first number is at the beginning of the line refers to the dominance relationship (0=dom, 1= domcod, 2=coddom, 3=cod). - Following numbers refer to the number of alleles by class, from the most dominant to the most recessive. Example: 0 5 2 1 With this line in a file, computations will be performed with a dom model for dominance relationships, 3 different dominance classes, 5 allele in the most dominant class, 2 alleles in the intermediate class and 1 alleles in the most recessive class. Using this file can be convenient if one wishes to perform computations for several dominance relationships and allele number, one after the other. For this, just write all parameters set on different lines. Example: 0 1 0 1

5 5 2 2

2 2 2 2

1 1 1 1

Using this file will perform four computations: two under dom dominance model and two under domcod dominance model. The number of dominance classes is the same for the four computations but the total number of alleles is different as well as the number of alleles in the most dominant class. Note that this file can be used for deterministic or stochastic computations. Separation can be tabulations or space blanks. __________________________________________________________________________

Parameters of the simulations. user_parameters.txt: This file is the most important as it must be filled by the user with the parameters necessary for computation and is ALWAYS needed. The user must give in this file the parameter values and the name of the files containing the dominance relationships and optionally the initial genotypic frequencies. When a parameter or a file is not needed, just leave a blank (but keep a single line between all entries). The name of this parameters file can not be changed but all information it contains are reminded at the beginning of each output files. Explanation of each entry 1, 2 and 3 refer to the three computation options, respectively (1) Deterministic equilibrium, (2) Distributions in finite populations and (3) Frequency change in one generation. A number X at the end of each entry means that it is necessary for computation option X. A number between parentheses (X) means it is optional for computation option X. //*** Genotypic frequencies equilibrium criteria: 10e-x, x = ? (0