Could someone please provide me with a clear and simple explanation of what tm (multilocus outcrossing rate) and ts (single-locus outcrossing rate) are and how to interpret them. As I currently understand, they are measures of the relative amount of gene exchange between different individuals (but I would like more specifics). Do they have an upper and lower limit (e.g. bound between 0 and 1)?
Hi Joshua,
you can consider tm and ts as the same parameter. They both denote the probability of outcrossing as the opposite to self-fertilisation. However, this definition requires that two types of mating can occur only: selfing and random mating. In other words, selfing is the only form of inbreeding in the model population. In the real world, however, mating patterns are not so simple and many different forms of inbreeding can occur. They can be referred to as mating between relatives, which leads to biparental inbreeding. Tm is far less sensitive to presence of biparental inbreeding than ts because it needs all loci to reflect self-fertilisation. Generally, the more loci are used the less sensitive it is. Thus we can say that tm refers exactly to non-self-fertilisation, so that all forms of outcrossing are included (both mating between relatives and unrelated). On the other hand, ts refers to non-inbreeding, so that outcrossing between unrelated individuals is included. This is the reason why ts is often smaller than tm in natural populations. Also, that's why the difference tm-ts is often used as an indicator of biparental inbreeding. Regarding the bound - if we use the definition based on probabilities, then outcrossing is between 0 and 1. Nonetheless, the estimator of tm and ts may not be limited to this values due to statistical reasons (it would suffer due to positive and negative bias near its extremes 0 and 1, respectively).
Best,
Igor
@Igor
Thanks for that excellent answer! Just one more quick question to round the it up: does the difference between tm - ts represent the estimated rate (/probability) of biparental inbreeding? e.g. if tm = 1.00, and ts = 0.98, the rate of biparental inbreeding is 0.02?
Joshua,
yes, the difference can be treated as the rate of biparental inbreeding. However, the term 'biparental inbreeding' is used here to denote mating between relatives and not a level of inbreeding within a population due to mating between relatives. Also, because robustness of tm depends on a number of loci, the rate of mating between relatives equals AT LEAST (tm-ts). Some interesting discussion on this topic can be found in Ritland 2002 (Heredity).
Igor
@Igor
I have generated binary data(1,0) of parent and their progeny and I want to analyse these data on MLTR software. Can you please guide the way to prepare a input file for MLTR based on the binary data.
@Chandan,
Sorry for late reply. If you still need any advice, could you describe in more details data you generated. MLTR requires progeny arrays, i.e. progenies grouped into families, with each family related through a mother. Offspring can be either after self-fertilization or outcross-fertilization. In your case, binary information means just selfed vs. outcrossed or something else?
@Igor,
Sorry for late reply. I have generated binary data of mother plants, progenies of this mother plant (seeds from its fruit) and the putative pollen donors, on the basis of presence or absence of bands. I have attached the excel file, can you please guide me how to prepare the file for mltr.
Abbreviations: PR: progeny, M: Mother plant of progenies, PD: Putative Pollen Donar
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