This question has a related issue that should be addressed first: what is a species? To some extent, if you want to understand how speciation can occur, then you have to consider how you are going to define a species. There is no species concept that applies to all species, past or present. The most widely applied concept is the biological species concept (Mayr 1942), which applies (imperfectly) to sexually reproducing species. Of course, Taenia does not always reproduce sexually. I think the discussion of species concepts is beyond this question but I encourage those that are interested to check out references [2-4] as well as a series of papers published in Systematic Zoology in the mid-70s. Here, I'll focus on genetic differentiation with a subtext of reproductive isolation.
Genetic differences can accumulate between populations$^1$ of Taenia in two different ways. The first is non-adaptive evolution via genetic drift. Drift is when allele frequencies change by random processes. For example, just by chance, tapeworms in a particular host may not live very long because the host was killed in a mudslide. Those tapeworms don't produce as many proglottids over their interrupted life so they don't leave as many copies of their alleles. Tapeworms in a host that lives a long time produces lots of proglottids and therefore produce many more copies of their alleles. The key point here is that the process of genetic drift is random. Allele frequency changes in one population of Taenia will be different from allele frequency changes in another population. Thus, over time, different populations of Taenia can become genetically different solely by chance. It's called non-adaptive evolution because natural selection is not evolved.
Adaptive evolution by natural selection can still occur on individuals that are asexually reproducing. Genetic differences will accumulate in a population over time to due mutations. Some mutations may be beneficial, some may not. Selection can increase the frequency of beneficial mutations and decrease the frequency of very mutations. Note that non-lethal but harmful mutations can accumulate in asexually reproducing species (see Muller's Ratchet) but I am assuming survivorship is decreased by harmful mutations for this example. If we assume that Taenia in different populations are subject to different selective pressures, then genetic differences can accumulate, leading to speciation. Note that drift will also affect the allele frequencies of both beneficial and harmful alleles because drift is random.
That brings us to the "mixed-up genes". I assume you mean the new genetic combinations that occur via sexual reproduction. Even if a host typically has only one individual of Taenia (not always the case), I suspect the opportunities for sexual reproduction in a population of Taenia are frequent, especially over evolutionary time. Consider places where tapeworm infestation of humans is high. Such places often have poor sanitary conditions so the opportunity for mixing of fecal material from different human hosts is high, and therefore the opportunity for mating among different individuals of Taenia is also high. If you have many humans living in squalor over long periods of time, then you have conditions very favorable for sexual reproduction of Taenia. Remember too that Taenia produce lots of proglottids, each with the chance for reproduction. Each reproductive opportunity creates new genetic combinations potentially subject to natural selection.
The final point to consider is population size. If the population size of Taenia is small (relatively few individuals) then genetic differences can accumulate fairly rapidly by genetic drift but the accumulation of beneficial mutations in the population will be low. If the population size is large then new mutations including beneficial ones can occur relatively often, increasing the rate of adaptive evolution among different populations.
Footnote
- I'm assuming some sexual reproduction among individuals of the same population and individuals from different populations do not interbreed. Without sexual reproduction, we have to think about the individual as the species and that makes my head hurt.
References
- Mayr, E. 1942. Systematics and the origin of speceis from the
viewpoint of a zoologist. Columbia University Press, New York, USA.
- Howard, D.J. and S.H. Berlocher (eds.). 1998. Endless forms:
Species and speciation. Oxford University Press, Oxford, England.
- Wheeler, Q.D. and Meier, R. (eds.). 2000. Species concepts and
phylogenetic theory: A debate. Columbia University Press, New
York, USA.
- Coyne, J.A. and H.A. Orr. 2004. Speciation. Sinauer Associates,
Inc., Sunderland, Massachusetts, USA.
