Monday, December 31, 2007

How to teach Hardy-Weinberg equilibrium

Over on the Gene Expression blog there's a discussion about how to explain Hardy-Weinberg equilibrium. Commentors are claiming that it's best explained mathematically rather than verbally. I'm posting a comment arguing that the best explanation is pictorial. Because I don't think I can put the picture in the comment I'm putting it here.

And here's the text of the comment I posted:
The best way to describe (and teach) Hardy-Weinberg Equilibrium is neither mathematically nor verbally but graphically, using a drawing that's like a Punnett Square with allele frequencies replacing the alleles. I've posted an example on my teaching blog.

Viewed this way, HWE is so obvious and so intuitive that there's no need for ps and qs at all. (And there never was any need for the apparent complication of q, as it's just 1-p.) The sides of the square are simply labeled with the actual allele frequencies, and the areas they create are the genotype frequencies in the next generation.

Of course math will be needed to deal with the deviations from HWE produced by selection and other factors, but starting with this graphical explanation helps beginning students see how simple and inevitable HWE is. (My freshman class on this is titled "The incredible tedium of Hardy-Weinberg equilibrium".)

Wednesday, December 26, 2007

Why biology is harder than physics

Beginning university students in the sciences usually consider biology to be much easier than physics or chemistry. From their experience in high school, physics has math and formulae that must be understood to be applied correctly, but the study of biology relies mainly on memorization. But in reality biology is much more complex than the physical sciences, and understanding it requires more, not less, brain work.

Biological processes of course are consequences of physics and chemistry, which is why we require our biology students to study the physical sciences. But organisms are also historical entities, and that's where the complexities arise. The facts of physics and chemistry are constant across time and space. Any one carbon atom is the same as any other, and today's carbon atoms are the same as those of a billion years ago. But each organism is different. That's not just a statement that fruit flies are different from house flies. Rather, each fruit fly is different from every other fruit fly alive today, and from every other fruit fly that ever lived, and it's the differences that make biology both thrilling and hard.

The differences have several causes and consequences. One cause is that biology depends on past history, because descendants are not identical to their ancestors. This is true at all scales, and the fundamental reason is that the process of genetic inheritance is not perfect. The DNA sequences we inherit from our parents are never identical copies of their DNA - instead they contain copying errors. So every copy is slightly different, even between two siblings. We are all mutants. These differences also accumulate over the generations, like in the party game Americans call "telephone" and the British call "Chinese whispers".

The second cause is natural selection, which shapes the accumulation of differences, favouring those that improve survival and reproduction and making it harder for disadvantageous differences to persist over the generations. And because most natural selection arises from interactions with other evolving organisms rather than with the relatively stable physical environment, the changes are rapid.

The result is that all biological systems are diverse at all levels. Even high school students are used to the idea of 'biodiversity', meaning the dramatic differences between different species of plants and animals. But the diversity is much more ubiquitous. Within each multicellular species, every individual is genetically different; every fruit fly is genetically different from every other fruit fly. The invisible bacteria turn out to be much more diverse than anyone would have thought. Bacteria isolated from natural environments are so different that even the individuals we would have considered the same species turn out to have about 10% of their genes from unrelated sources. In lab cultures, bacterial mutation rates are high enough that a single ml of culture will contain millions of different genotypes.

Even genetically identical cells are not functionally identical. When a cell divides its molecules are randomly distributed between the two daughters; because 'randomly' does not mean 'evenly', these daughters will have inherited different sets of the proteins and RNAs that carry out their functions. And even if the two cells had identical contents, these contents would still have different interactions - repressors bump into cofactors at different times, DNA polymerase slips or doesn't slip at different points in its progress along a chromosome. Understanding the how and why of biological phenomena thus requires us to consider historical and ecological factors that are many orders of magnitude more complex than those of physical systems.

The critical word is probably 'population'. Biologists rarely try to define it, but they use the term everywhere to refer to similar but not identical organisms or cells (or even molecules) that interact in some way. 'Population thinking', the realization that species are populations, not pure types, is said to have been key to Darwin's insight that members of a species undergo natural selection. And population thinking is probably what makes biology so much more complex than the physical sciences.

Of course we can't consider all of the differences all of the time, so at different levels of study we biologists try to pull out the factors that we think will matter most. Molecular and cell biologists work with populations of molecules, but they keep everything else as identical as possible. Developmental biologists study how cells become different, but they use pure-breeding lines and clones to ensure that the genetic properties of their organisms are as identical as possible. Ecologists pay attention to the big differences between species, but under conditions where they can ignore the differences between the individuals of each species.

I don't think population thinking is addressed in high school biology. We can't really blame their teachers, because the issues probably were never made clear to them either. Instead high school teachers pass on the facts they remember from what they themselves learned at university. The result is that their students enter university expecting their biology education to consist mainly of memorizing lots of new facts.

We instructors want our new students to start focusing on understanding complex processes and interactions, between entities that are themselves populations of diverse and somewhat unpredictable entities. We're thus asking them to set aside all the learning strategies that worked well for them in high school biology, and to learn in a new way. To students this probably seems the height of foolishness, and they're understandably reluctant to take the chance. So one big challenge, for instructors and for our students, is to find ways to ease this transition. We need to give students confidence that deep understanding will bring better grades than will rote memorization, and that saying "What I don't understand is..." is not an admission of failure but the essential first step to this understanding.