Guides
One tutorial per module, written for students and for the people teaching them. Each one states the model, shows figures drawn by the module's own simulation code, and ends with exercises to run in the module. 40 guides so far, about 464 minutes of reading.
Allele and genotype frequencies
- The De Finetti diagram Genotype frequencies at one locus plot as a point in a triangle, and Hardy-Weinberg populations lie on a parabola.
- Genotype frequencies and Hardy-Weinberg Two allele frequencies fix three genotype frequencies after one generation of random mating.
- Testing Hardy-Weinberg with chi-square Three genotype counts, one statistic and one critical value decide whether a sample fits random mating.
Genetic drift
- Genetic drift Allele frequencies change by chance alone, faster in small populations, until an allele is fixed or lost.
- The bottleneck effect A crash to a few survivors resamples the gene pool, and regrowth restores the headcount but not the lost diversity.
- The founder effect A few founders carry a random sample of the source gene pool, and each new colony then drifts from its own starting frequency.
- Drift and selection together Selection pushes an allele one way every generation, and chance decides whether a small population follows.
- Drift and mutation together Mutation pulls every population towards one balance point, and the size of the population sets how far drift scatters them around it.
- Drift, selection and mutation A harmful allele that mutation keeps creating settles at a low frequency in a large population and wanders in a small one.
- Drift as a Markov chain The exact probability of every allele count, generation by generation, with no random numbers at all.
- Heterozygosity decline Drift removes heterozygosity at a fixed rate of 1/2Ne per generation, on average, and single populations scatter around that average.
Mating models
- Autosomal locus Genotype counts give allele frequencies, and one generation of random mating moves any sample onto the Hardy-Weinberg parabola.
- X-linked loci When the sexes start with different allele frequencies, an X-linked locus zigzags between them and settles on the weighted mean (2pf + pm)/3.
- Assortative mating Mating by resemblance removes heterozygotes without changing allele frequency; mating by difference keeps them and moves the allele frequency.
- The assortative mating matrix A 3 by 3 grid of allowed crosses, plus a rule for forbidden ones, decides which genotypes survive and where the allele frequency ends up.
Mutation
- Two-way mutation and its equilibrium Opposing mutation rates fix an equilibrium frequency, and real rates take tens of thousands of generations to reach it.
- Irreversible mutation One-way mutation lowers an allele frequency by the same fraction every generation, so the half-life depends on the mutation rate alone.
- Neutral mutations Most new neutral mutations are lost within a few generations, and the few that fix do so with probability 1/2Ne.
- Muller's ratchet In an asexual population drift can remove the least-loaded class of genomes, and each loss raises the minimum mutation load for good.
Natural selection
- Natural selection at one locus Three fitnesses decide whether an allele sweeps, settles at a balance, or depends on where it starts.
- Dominance and the speed of selection The same harmful allele is removed in 175 generations or in more than 1000, depending on how dominant it is.
- Selection when rare is fit A cost that grows with a genotype's own frequency can hold two alleles together without heterozygote advantage.
Gene flow and structure
- Continent-island migration One-way gene flow pulls an island to the continent frequency, and the gap shrinks by the same fraction every generation.
- Island-island migration Two populations that exchange migrants meet at a common frequency set by the two migration rates.
- Stepping-stone migration When populations in a line exchange migrants only with neighbours, neighbours converge fast and the two ends converge slowly.
- F-statistics Drift builds differences between populations, migration removes them, and F_ST settles at a value set by Nm.
- The Wahlund effect Pooling subpopulations that differ in allele frequency leaves too few heterozygotes, by exactly twice the variance of p among them.
Gametic disequilibrium
- Linkage disequilibrium from gamete counts Four haplotype counts give D, D′, r² and a chi-square test of whether two loci are associated.
- How fast recombination removes disequilibrium D shrinks by the factor (1 − r) every generation, so tightly linked loci stay associated for hundreds of generations.
- Reading linkage disequilibrium from bar charts Each gamete bar differs from its expected height by exactly D, so the picture shows the sign and size of the association.
Advanced
- Molecular population genetics Two estimates of the same mutation rate, one from segregating sites and one from pairwise differences, disagree when population size has changed.
- Quantitative traits, heritability and selection Ten additive loci plus environmental noise give a trait whose heritability drift erodes and selection uses up.
Genomics and NGS
- Sequencing a population at low coverage A few reads per person cannot fix genotypes, and hard calls from them inflate rare variants and hide heterozygotes.
- Pooled sequencing and allele frequencies A pool is sampled twice, once when its chromosomes are drawn and once when its reads are drawn, and only the second error shrinks with depth.
- The site frequency spectrum and demography The count of variable sites at each allele frequency has a known neutral shape, and growth, bottlenecks and structure bend it in different ways.
- Selective sweeps and hitchhiking A beneficial mutation drags its neighbours to fixation and leaves a valley of diversity that recombination narrows.
- Population structure with PCA Principal components turn allele-frequency differences between populations into axes, as long as the differences are large enough to see.
- GWAS and population stratification A scan that pools two populations flags SNPs that only track ancestry, and principal components remove most of that signal.
- Linkage disequilibrium and effective size Drift builds association between nearby sites, recombination breaks it, and the balance tells you the population size.
- Runs of homozygosity and inbreeding Long homozygous stretches mark chromosome segments inherited from one ancestor through both parents, and their lengths date the shared ancestor.
Guides for the other modules are being written. Every module already has a Help panel and an Explain walkthrough on its own page.