I am a Biology teacher.
The penis lecture is quite a good illustration of different evolutionary solutions to the problem of sperm transfer.
The major issue is that a penis that is constantly ready to provide the most effective method of putting sperm into the female will be so much in the way that it will reduce survival potential. This means that most mammals need a way of getting the thing out of the way except when it is needed.
There are three major ways of making the penis erect:
1. The os penis. Many mammals have a bone called the baculum in their penises. This provides instant rigidity but does mean that the penis has to be scabbarded in a sheath when not in use. The walrus is rather a champion in the os penis department with the Inuit occasionally using the things to make runners for their sledges.
2. The fibous (or fibro-elastic) penis. The bull penis is a good example of this. The penis is rigid all the time. Relaxation of a particular muscle enables the penis to swing free of the body and be ready for action. This large amount of fibrous material means that bulls’ penises can be used as whips when dried.
3. The hydraulic penis. This is the human type which relies for erection on blood being allowed into spongy tissue in the penis. Mammals with a fibrous penis or baculum have erectile tissue but the human relies entirely on blood pressure for reproductive readiness.
At this point, one can diverge into some particularly interesting examples such as the tapir (truly massive compared with the size of the already large animal) and the echidna (a four-headed penis resembling a shower attachment).
This lecture generally gets a remarkable level of attention and more than justifies the unusual choice of content to get the evolutionary message across.
Iceland has a phallological museum [1] which displays the members of a large number of species, although some are of elves and trolls. Interestingly, the elves and trolls themselves are invisible although it seems that the displayed parts aren’t.
[2]