### Available estimators of sexual selection and isolation effects

The analyses implemented in JMATING focus on mating frequency data. The program admits complex tables with up to an indeterminate number of mating types (only limited by the computer memory and speed) and different choice designs: multiple choice, male choice, female choice or no choice designs. We provide two example data sets [Additional file 1]: Example 1 is from a descriptive study made in the wild [12], where two morphs of *Littorina saxatilis* (RB and SU) meet and hybridize on some micro-habitats from the rocky shore (Figure 1); Example 2 was obtained from a multiple choice experiment in the laboratory using two species of *Drosophila* (Table 2a in [6]).

We will use Example 1 to show some features of the analyses available in JMATING (Figure 1). Coloured rows and columns represent the number of specimens of the different types (mating types) used in the experiment. In Example 1 they represent morph frequencies sampled in the wild. For convenience rows always correspond to females (pink) and columns to males (blue). Numbers within the non-coloured cells represent the different mating pairs sampled in the wild (or obtained during the choice experiment, as in Example 2). Two different kinds of analyses are available: global and pairwise estimates.

The global analysis provides the best available estimators of sexual isolation (*I*_{
PSI
}, *Yule's V* and *YA*) [7] and sexual selection (W) [4]. The sexual isolation estimators can only be calculated, in principle, for each pair combination of types (in the example: T1 *versus* T2, T1 *versus* T3 and T2 *versus* T3; see Figure 2). The theoretical resampling standard deviation for each estimator is also provided following the formulae given by different authors [21]. The analysis also includes the calculation of the asymmetry of the deviations from random mating in homotypic and heterotypic pairs. For example, for the combination of T1 and T3, this index would be *PSI*_{
11
}/*PSI*_{
33
}and *PSI*_{
13
}/*PSI*_{
31
}for homotypic and heterotypic pairs, respectively (*PSI* estimates the deviations from random mating for each pair type; see below) [7]. Sexual selection estimates (W) are given for each mate type, in males and females separately, relative to the type with the highest sexual fitness [4] (Figure 2).

Additionally, the program estimates the global sexual isolation using a modification of the *I*_{
PSI
}estimator: the deviations from random mating in homotypic (∑(*PSI*_{
ii
})) and heterotypic (∑(*PSI*_{
ij
})) pairs are weighted by the number of mating clases.

\text{Total}{I}_{PSI}=\frac{\left((n-1)\times {\displaystyle \sum \left(PS{I}_{jj}\right)}\right)-{\displaystyle \sum \left(PS{I}_{ij}\right)}}{\left((n-1)\times {\displaystyle \sum \left(PS{I}_{jj}\right)}\right)+\left({\displaystyle \sum \left(PS{I}_{ij}\right)}\right)}

being *n* the number of different mating types used in the experiment and *PSI*_{
jj
}and *PSI*_{
ij
}are the sexual isolation estimates for homotypic and heterotypic pair combinations, respectively. To our knowledge, this is the first time that such estimator is proposed and has the advantage to present an overall estimation of sexual isolation when multiple mating types are being used.

The program also gives the pairwise estimates of total (*PTI*), sexual isolation (*PSI*) and sexual selection (*PSS*) effects from mating frequency data [described in [7]] (Figure 2). The *PSI* coefficients are the sexual isolation effects for each pair. The *PSS* coefficients represent the sexual fitness of each pair, and are an additive decomposition of the cross product estimator (W). The *PTI* coefficients, obtained from the product of *PSI* and *PSS* coefficients, represent the combined sexual selection and sexual isolation effects. All these coefficients can be calculated for the whole data set (all mating types) or comparing exclusively data from a given pair of mating types (Figure 3).

### Available statistical tests

Three different types of statistical tests can be accomplished with JMATING. First, a non-parametric *G* test is available to check for the whole data set if the sexual isolation and sexual selection effects (or both taken together) are significant. The *G* test has additive properties (Sokal and Rohlf, 1996), and thus it can be decomposed additively into the sexual selection (*G*_{
S
}) and sexual isolation (*G*_{
I
}) components. This decomposition was developed for laboratory experiments, like Example 2, but it can be used for wild data (like Example 1) if the estimates of the morphs in the population are based on large sample sizes (> 30 for each trait and sex). The program gives the value of *G*_{
S
}and *G*_{
I
}, and their degrees of freedom, as well as their combined effects (*G*_{
T
}= *G*_{
S
}+ *G*_{
I
}), and they can be compared with a χ^{2} distribution with their corresponding degrees of freedom. Second, JMATING also gives the theoretical sampling distribution for *I*_{
PSI
}, *YA* and *V* indexes, allowing the use of a t-test for classical parametric inference [26]. This approach, however, has a high false positive rate [21]. Third, JMATING also provides the bootstrap probability for rejecting the null hypothesis. This alternative is rather conservative [21], and so that we recommend not to use multitest corrections for the bootstrap probability values obtained with our program unless a great number of tests (> 10) are being performed.

JMATING resamples 10,000 times the observed values of mating pairs in order to estimate the bootstrap sampling distribution for the estimator (*I*_{
PSI
}, *YA* and *Yule's V*). Then the program calculates the bootstrap average and standard deviation as well as the two-tail probability of getting a sexual isolation estimate significantly different from zero (equivalent to random mating). JMATING can also calculate the bootstrap mean, standard deviation of the cross-product (W) estimators, as well as its (one tail) probability of getting values significantly smaller than 1 (in our case we consider values of W larger than 1 because we use the largest W as the reference value). Notice that the frequency of mating types in the population (in blue and pink cells) are not resampled, because we assume that they are the population frequencies in the experiment. This is only true in laboratory experimental data (Example 2). However, we allow the option to change this and to resample also non-mated data in the case of field experiments (like in Example 1).

Additionally, JMATING also calculates the bootstrap mean, standard deviation and probabilities for *PTI*, *PSI* and *PSS* coefficients. The program resamples 10,000 times the observed frequencies for getting *PTI* coefficients and the observed and the expected frequencies (assuming random mating) from mated data when estimating the *PSI* and *PSS* coefficients. This procedure is somewhat more conservative than resampling exclusively the observed mating pairs [12], but it allows getting independent bootstrapping for *PSI, PSS* and *PTI* coefficients. The latter is convenient if these coefficients are going to be analysed together.