Population Genetics. Matthew B. Hamilton

it directly in the future.

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      Simulations are an effective means to understand some of the fundamental predictions of populations genetics. Mathematical expressions are frequently used to express dynamics and equilibria in population genetics, but the equations alone can be opaque at first. Simulations provide a means to explore the relationships among variables that are summarized in the compact language of mathematics. Many people feel that a set of mathematical equations is much more meaningful after having the chance to explore what they describe with some actual numerical values. Simulation provides the means to explore what equations predict and can make learning population genetics an easier, more rewarding experience.

Carrying out simulations has the potential to make the expectations of population genetics much more accessible and understandable. Conducting simulations is not much extra work, especially once you get into the practice of using the text and simulation software in concert. You can approach simulations as if they are games, where each one shows a visual scene that helps to solve a puzzle. In addition, simulations can help you develop a more intuitive understanding of population genetic predictions so you do not have to approach the expectations of population genetics as disembodied or unanimated “facts.”

      It is important to approach simulations in a systematic and organized fashion, not as just a collection of buttons to press and text entry boxes to be filled in on a whim. It is absolutely imperative that you understand the meaning behind each variable that you can control as well as the meaning of the results you obtain. To do so successfully, you will need to be aware of both specific details and larger patterns, or both the individual trees and the forest that they compose. For example, in a simulation that presents results as a graph, it is important that you understand the details of what variables are represented on each axis and the range of axis values. Sometimes these details are not always completely obvious in simulation software, requiring you to use both your intuition and knowledge of the population genetic processes being simulated.

      Once you are comfortable with the details of a simulation, you will also want to keep track of the “big picture” patterns that emerge as you view simulation results. Seeing these patterns will often require that you examine the results over a range of conditions. Try approaching simulations as experiments by changing only one variable at a time until you understand its effects on the outcome. Changing several things all at once can lead to confusion and an inability to see cause‐and‐effect relationships, unless you have fully understood the effects of individual variables. Finally, try writing down parameter values you have tried in a simulation and sketching or tabulating results on paper as you work with a simulation. Use all of your skills as a scientist and student when conducting simulations, and they will become a powerful learning tool. Eventually, you may even use scripting and programming to carry out your own simulations specifically designed to explore your own genetic hypotheses.

Chapter 1 review

       Both general principles and direct measurements taken in actual populations combine to form comprehensive expectations about amounts, patterns, and cause‐and‐effect relationships in population genetics.

       The theory of population genetics is the collection of well‐accepted expectations used to articulate a wide array of predictions about the biological processes that shape genetic variation.

       Parameters are idealized quantities that are exact, while parameter estimates wear notational “hats” to remind us that they have statistical uncertainty.

       Population genetics uses both inductive reasoning to generalize from the knowledge of specifics and deductive reasoning to build up predictions from general principles that can be applied to specific situations.

       Population genetics is not a spectator sport! Direct participation through computer simulation provides the opportunity to see population genetic processes in action. You can learn by trial and error and test your own understanding by making predictions and then comparing them with simulation results.

Further reading

      For a history of population genetics from Darwin to the 1930s, see:

      1 Provine, W.B. (1971). The Origins of Theoretical Population Genetics. Chicago, IL: University of Chicago Press.For a concise history of population genetics since the mid‐1960s that highlights major conceptual advances as well as technical innovations to measure genetic variation, see:

      2 Charlesworth, B. and Charlesworth, D. (2017). Population genetics from 1966 to 2016. Heredity 118: 2–9.For two personal and historical essays on the past, present, and assumptions of theoretical population genetics, see:

      3 Lewontin, R.C. (1985). Population genetics. In: Evolution: Essays in Honour of John Maynard Smith (eds. P.J. Greenwood, P.H. Harvey and M. Slatkin), 3–18. Cambridge: Cambridge University Press.

      4 Wakeley, J. (2005). The limits of theoretical population genetics. Genetics 169: 1–7.

CHAPTER 2 Genotype frequencies

      2.1 Mendel's model of particulate genetics

       Mendel's breeding experiments.

       Independent assortment of alleles.

       Independent segregation of loci.

       Some common genetic terminology.

In the nineteenth century, there were several theories of heredity, including inheritance of acquired characteristics and blending inheritance. Jean‐Baptiste Lamarck is most commonly associated with the discredited hypothesis of inheritance of acquired characteristics (although it is important to recognize his efforts in seeking general causal explanations of evolutionary change). He argued that individuals contain “nervous fluid” and that organs or features (phenotypes) employed or exercised more frequently attract more nervous fluid, causing the trait to become more developed in their offspring. His widely known example is the long neck of the giraffe, which he said developed because individuals continually stretched to reach leaves at the tops of trees. Later, Charles Darwin and many of his contemporaries subscribed to the idea of blending inheritance. Under blending inheritance, offspring display phenotypes that are an intermediate combination of parental phenotypes (Figure 2.1).

      From 1856 to 1863, the Augustinian monk Gregor Mendel carried out experiments with pea plants that demonstrated the concept of particulate inheritance. Mendel showed that phenotypes are determined by discrete units that are inherited intact and unchanged through generations. His hypothesis was sufficient to explain three common observations: (i) phenotype is sometimes identical between parents and offspring; (ii) offspring phenotype can differ from that of the parents; and (iii) “pure” phenotypes of earlier generations could skip generations and reappear in later generations. Neither blending inheritance nor inheritance of acquired characteristics are satisfactory explanations for all of these observations. It is hard for us to fully appreciate now, but Mendel's results were truly revolutionary and served as the very foundation of population genetics. The lack of an accurate mechanistic model of heredity severely constrained biological explanations of cause and effect up to the point that Mendel's results were “rediscovered” in the year 1900.

      It is worthwhile to briefly review the experiments with pea plants that Mendel used to demonstrate independent assortment of both alleles within a locus and of multiple loci, sometimes dubbed Mendel's first and second laws. We need to remember that this was well before the Punnett square, which originated in about 1905. Therefore, the conceptual tool we would use now to predict progeny genotypes from parental genotypes was a thing of the future. So, in revisiting Mendel's experiments, we will not use the Punnett square in an attempt to follow his logic. Mendel only observed the phenotypes of generations of pea plants that he had hand‐pollinated. From