Hi. Theoretically, it is not necessary for some species to reach their mathematical limit of having unique facial structure/trait variations to start repeating the exact same faces. They could repeat the same faces at any moment. What you have to estimate is the probability of that happens and how large a population must be for it.
I believe the “easiest” way to estimate the amount of a population on which would be possible to observe two or more non-related individuals of the same specie sharing the exact same face traits all together, resulting in same faces at all, is to determinate all the possible combinations of all genome allelic variations of that specie. Or, the probability of two identical genomic sequences to appear independently in a population.
You would have to know all allelic frequencies and how the presence of one allele influences on the others (linkage disequilibrium).
Ok, the number would be astronomically large. But we would be able, until a certain point, to exclude many other parameters, making it easier to calculate.
If you pretend to approximate to the real number you can consider only the genes that influences on face traits. But you would had to know which are these exactly genes. Moreover, you would have to establish how these genes interact with each other and how environmental variables act to influence on gene expressions. At the end you would have a model with a limited power to estimate that probability, because you probably wouldn’t know all parameters necessary.
Most biological modeling problems reduce to an inverse problem, where parameters in the model must be estimated. Parameters are often estimated to fit models to experimental data, based on observed phenomenon. The model will be as good as one can predict which are the parameters and how they influence the trait variety.
For example, to any of those traits you asked, first you would had to observe how many variations exists, then you would had to estimate the parameters that may influence it, based on previously knowledge or other observations.
Some existing equations can estimate a “n” number of individuals you could randomly choose to observe all possible varieties of a specific trait to use as a sample on modeling studies. Most of these equations require previously knowledge on variables frequencies.
You must consider, at minimum, how many genes are involved in each trait, how many alleles exists to each of these genes, the frequencies of each allele, how those alleles interact in biochemical pathways, linkage disequilibrium, and the environmental variables that are influencing.
At the end you would have a group of models to each face trait. The hard work would be to put all these together in a unique master model, considering how the result of any equation influences the result of others.