The Gibbs Principle states that TSEs are inherently endemic and non-eradicatable, with all species of mammals contracting prionic spongiform encephalopathies through germline mutation and sporadic processes at a rate of roughly one per million per year. More broadly, the Gibbs Principle asserts that basically all human genetic diseases have TSE counterparts in basically all vertebrates.
In other words, scrapie can never be eradicated from sheep by breeding, "BSE-free country" is oxymoronic, and TSE will always be endemic everywhere, with all species from chickens to sharks to humans endogenously at risk. The best that can be done is reduce dietary amplification, use of pooled products, and lateral transmission, to asymptotically approach the basal de novo mutational level, rather than attaining eradication. Whatever steps are taken, there will always be a non-zero expectation value for the basal level of infectious prion titre arising from new mutations within the curent generation.
The rate is based on the incidence of sporadic and familial CJD in humans, experience with other genes, and general precepts from modern molecular biology. Overall, the Gibbs Principle is on solid ground, though accurate experimental estimation of the rate component could take years. The mutational rate in mammals is given in standard texts (Creighton, Proteins, 1993 2nd ed. pg.111) as one per 100 million nucleotides per generation, thus about 60 per round of replication. In the US, where there are conveniently 100 million cows, this says (ignoring hot spots) that essentially every one of the 750 nucleotides in the prion gene sees a germline or neuronal stemline mutational change every year. Some of these, unfortunately, cause TSE in cattle by the Gibbs Principle
Now this disease does not typically emerge in humans until age 60 or so; the question arises of whether the Gibbs Principle is applicable to shorter-lived mammals. Note first that the rate in humans is under-reported because most cases may be lost within Alzheimer's and other dementias. Secondly, it seems likely that the process of infectivity titre and neural death begins many years before symptoms are explicitly recognized; as with prostate cancer, many more die with CJD than from it. Disease onset may also be calibrated by basal metabolism rate and higher body temperatures in smaller mammals, compensating for shorter lifespan.
To what extent does transmissability recapitulates phylogeny? This notion seems imperfect experilmentally in two respects: adjacency and reciprocity. That is, transmission between two closely related species can be less efficient than to a more distant species, and efficiency from species A to species B need not be the same as from B to A (eg, mouse and hamster) In other words, the species barrier matrix is neither off-diagonally sparse nor symmetric, except perhaps in an overall statistical sense. In short, the species barrier is hard to predict.
Just as genes are organized into superfamilies by homology, so too are human genetic disorders ordered by paralogy. In other words, we might speak of paralogous anaemias associated with mutations in prothrombin and clotting facter X, or paralogous alpha and beta hemoglobinopathies, etc. The point of organizing disorders this way is to predict from the well-studied case that similar mechanistic opportunities may exist for disease in the paralogue case. Here we wish to bootstrap off our knowledge of mainstem prion disease.
For prion disease, the suite of paralogous diseases is predicted to include those arising from same normal to rogue conformational shift. This is because the 3d properties of proteins are 'the last thing to go' in evolutionary divergence, long after the original primary sequence appears as single copy in hybridization. If other proteins do exist with prionic properties, the paralogues are the first place to look for them.
In order to validate and broaden the idea of prionic diseases, there is interest in finding other diseases of this type in humans. A rational way to do this is as follows: push back the prion gene to the early vertebrates and beyond, until such time that the gene doubling is found that originally gave rise to the prion lineage. This requires determining prion homologues in ostriches, turtles, xenopus, zebrafish, dogfish, lamphries, amphioxus, tunicates, echinoderms, etc., until a gene divergence is found. There could be complications from gene fusion, unequal crossing over and the like, but we are 'certain' that the prion gene is not sui generis. Chicken 'prion' may be such a protein already.
Having found the paralogue, we then push it forward back to humans, using degenerate probe from the lower organism (or look in GenBank, etc.). In the best case scenario, the paralogue gene is known in humans with various disease states already assigned to it, but the local experts have not yet tested them for transmissibility, etc.