There are no “laws” in evolutionary biology comparable to those in physics, except perhaps that “all species evolve”. But that’s not very exciting. What we have in my field are not unbreakable “laws,” but patterns or generalizations. When these become sufficiently general and impressive (i.e. 80-90% of species obey them, often across diverse taxa), then we have an area of research where explanations can be general. A lot of good evolutionary biology consists of case studies that don’t elucidate a previously understood pattern, and lots of those studies good, or even iconic —Peter and Rosemary Grants’ paper on the evolutionary increase in beak size of Geospiza fortis due to a drought is one example. It serves as an iconic example of natural selection, but doesn’t shed light on how natural selection works in other cases—and it’s no worse for that.

In my own work I’ve often tried to elucidate the genetic/evolutionary basis of these broad patterns, hoping that a simple and general explanation could at one stroke explain many “anecdotes.” I’ll simply describe below what I see as “laws of evolutionary biology”: those generalizations which hold sufficiently strongly that explaining them in one group might also give explanations for all groups. And I think we now know at least the partial biological basis for each of these “laws”?

1. If only one of the two sexes of a species is brightly colored, ornamented, or advertises itself to the other, that sex is usually the male. The explanation, first given by Darwin but subject to much recent work, is sexual selection, and we have a good understanding of how it works, but not necessarily why females in a population prefer one type of male over another. The evolutionary basis and mechanics of female preference is an active area of research.
2. If there is only one trait that can be used to distinguish members of different species, that trait is very often the shape or behavior of the male genitalia. This is the subject of William Eberhard’s excellent but underappreciated book, Sexual Selection and Male Genitalia, a must-read for evolutionary biologists. (It’s out of print now, I think, but you can get it from your library.) The answer appears to be sexual selection on those genitalia, implying that females can detect the differences in shapes as they evolve within a species—leading to differences between species. The fact that such characters are often diagnostic means that sexual selection on male genitals must be a potent and ongoing evolutionary force within species. (It’s interesting that in those groups where sperm is not transferred via the genitalia but by organs like spider pedipalps, it is the sperm transferring organs that are diagnostic, supporting the sexual-selection explanation.)
3. If in crosses between two closely-related species, only one sex among the hybrids is inviable or sterile, it is almost invariably the heterogametic sex (the one that has two unlike sex chromosomes). I spent much of my career working on this phenomenon, which holds widely: in insects, mammals, birds, worms, and so on. The generalization is called “Haldane’s rule” after its publication by the evolutionary geneticist J.B.S. Haldane in 1922. In the last 90 years the rule has been strengthened, holding widely across animals. And it holds regardless of which sex is heterogametic. In mammals and many insects, for instance, in which males are XY and females XX, the males are sterile or inviable in species crosses. But in birds and butterflies, in which females are heterogametic and males homogametic (having similar sex chromosomes), it is the females who are preferentially sterile or inviable in species crosses. This suggests that the cause of Haldane’s rule isn’t connected so much with one gender evolving faster than the other, but with the sex chromosomes themselves.
4. In crosses between species, the genetic cause of the preferential sterility/inviability of the heterogametic sex resides on the sex chromosomes. I worked a lot on this problem too, and it’s deeply connected with “law” #3. If genes for inviability or sterility act as recessives in hybrids, for instance, then every such gene in a hybrid’s heterogametic X chromosome will be expressed, and that individual will be sterile or inviable. (Males in XY species, for instance, will express every single gene on the X chromosome in hybrids: usually the Y has few genes. But females, being XX, will have every deleterious recessive masked by a dominant allele on the other sex chromosome, and so will be more fit.) This is called the “dominance theory,” and there’s a lot of evidence supporting it. Recessive genes that debilitate hybrids are also found on the autosomes, but are not expressed in first-generation species hybrids and so don’t cause Haldane’s rule. The other explanation for the “X-effect” is that the X chromosome evolves faster than the autosomes (non-sex chromosomes), and so deleterious interactions in hybrids will involve that chromosome more often. That, too, appears to play a role in Haldane’s rule, but probably not as large a role as the “dominance hypothesis.”

Readers are welcome to add to this list of evolutionary biology “laws,” for these are the only ones I can think of that hold so widely.