Population genetics Study Guide

📖 Core Concepts Population genetics: the study of how genetic variation is distributed within and among populations and how evolutionary forces (selection, drift, mutation, migration) change allele frequencies over time. Allele frequency ($p$): proportion of a particular allele in the gene pool. Effective population size ($Ne$): the size of an idealized population that experiences the same amount of genetic drift as the real population. Fitness ($w$): reproductive success of a genotype; often expressed as $w = 1 - s$, where $s$ is the selection coefficient. Hardy–Weinberg equilibrium (HWE): the null expectation for genotype frequencies when no evolutionary forces act (allele frequencies stay constant). Linkage disequilibrium (LD): non‑random association of alleles at different loci; broken down by recombination but can persist because of hitchhiking or background selection. Origin‑fixation dynamics: the rate of evolutionary change = mutation rate ($\mu$) × fixation probability of a new allele. --- 📌 Must Remember HWE condition: allele frequencies remain constant if no selection, mutation, migration, or drift. Selection vs. drift threshold: selection overcomes drift when $s > \frac{1}{Ne}$. Fixation probability of a new advantageous mutation ≈ $2s$ (for diploids, $Ne \gg 1$). Deterministic mutation–selection balance: equilibrium frequency of a deleterious allele $f = \frac{u}{s}$ (where $u$ = mutation rate). Neutral theory prediction: nucleotide diversity $\pi \approx 4Ne\mu$ (for diploids) or $Ne\mu$ (haploids). McDonald–Kreitman test: excess of fixed differences relative to polymorphisms ⇒ positive selection; proportion of adaptive substitutions = $\alpha$. Inbreeding coefficient $F$: measures excess homozygosity; $F{ST}$ quantifies population differentiation. Hill–Robertson effect: linkage reduces the efficacy of selection on beneficial mutations. Drift‑barrier hypothesis: the smallest attainable mutation rate is limited by the ability of selection to act, i.e., $s > \frac{1}{Ne}$. --- 🔄 Key Processes Mutation → New Alleles Mutation introduces neutral, deleterious, or beneficial alleles; bias can favor certain changes. Selection Acts on Fitness Differences Convert fitness differences ($w = 1 - s$) into allele‑frequency change each generation. Genetic Drift (Random Sampling) In each generation, alleles are sampled from $2Ne$ copies; variance in $p$ after one generation ≈ $\frac{p(1-p)}{2Ne}$. Gene Flow (Migration) Introduces alleles from other populations; can reduce $F{ST}$ or create a migration load if maladaptive alleles enter. Recombination Breaks down LD, allowing beneficial mutations at different loci to combine; rate determines how quickly Hill–Robertson interference is relieved. Fixation (Origin‑Fixation) Rate of fixation $= \mu \times P{\text{fix}}$; for a beneficial mutation $P{\text{fix}} \approx 2s$. --- 🔍 Key Comparisons Selection vs. Drift Selection: deterministic, proportional to $s$; effective when $s > 1/Ne$. Drift: stochastic, dominates when $|s| < 1/Ne$. Neutral Theory vs. Selectionist View Neutral: most polymorphisms are effectively neutral; diversity driven by $\mu$ and $Ne$. Selectionist: linked selection (background selection, selective sweeps) reduces neutral diversity beyond neutral expectations. Genetic Drift vs. Genetic Draft Drift: random sampling of alleles. Draft: stochastic change caused by linked selective sweeps; mimics drift but is driven by selection elsewhere. Hardy–Weinberg Equilibrium vs. Disequilibrium HWE: genotype frequencies $p^2$, $2pq$, $q^2$. LD: deviation from independent assortment; measured by $D$, $r^2$. Mutation‑Selection Balance vs. Mutation–Drift Balance Balance with selection: $f = u/s$ for deleterious alleles. Balance with drift: allele frequency distribution shaped by $Ne$ and $u$, often approximated by diffusion equations. --- ⚠️ Common Misunderstandings “Neutral = No selection” – neutral theory allows selection at linked sites (background selection, hitchhiking). “Drift always random” – linked selection (genetic draft) creates non‑random fluctuations. “Higher $Ne$ always means more diversity” – selection at linked sites can depress diversity even in large populations. “Recombination completely eliminates LD” – recombination reduces but does not instantly erase LD; hitchhiking can maintain it. “All mutations are deleterious” – many are neutral; a fraction are beneficial and can drive rapid adaptation. --- 🧠 Mental Models / Intuition Bag‑of‑alleles: imagine the gene pool as a bag; each draw (gamete) samples alleles randomly → drift. Fitness landscape: peaks = adaptive optima; selection pushes populations uphill, drift can push them off peaks, and migration can move them between peaks. Traffic jam analogy for linked selection: beneficial mutations behind a “traffic jam” of linked deleterious alleles progress slowly (Hill–Robertson). Mutation bias as a wind: the direction of most frequent mutational changes pushes the evolutionary trajectory like a prevailing wind. --- 🚩 Exceptions & Edge Cases Small $Ne$ & strong drift: even mildly deleterious alleles can fix; selection coefficient $s$ must be > $1/Ne$ to be effective. High migration load: when gene flow introduces maladaptive alleles faster than selection can purge them. Diminishing‑returns epistasis: each additional beneficial mutation gives a smaller fitness gain on already high‑fitness backgrounds. Synergistic epistasis: combined deleterious mutations cause a larger-than‑expected fitness drop, intensifying purifying selection. Horizontal gene transfer: can introduce completely novel functions bypassing mutation‑selection steps (especially in prokaryotes). --- 📍 When to Use Which | Situation | Tool / Formula | Decision Rule | |-----------|----------------|---------------| | Testing if a population is at HWE | $\chi^2$ or exact test on genotype counts | Use when you have genotype frequencies and want to detect non‑random mating, selection, or structure. | | Quantifying population differentiation | $F{ST}$ | Apply when comparing allele frequencies across subpopulations; high $F{ST}$ → strong structure. | | Detecting recent positive selection | LD‑based sweep scans, reduced diversity, high $r^2$ | Look for long haplotypes with low heterozygosity. | | Measuring adaptive substitution proportion | McDonald–Kreitman test → compute $\alpha$ | Use when you have polymorphism and divergence data for synonymous (neutral) and nonsynonymous (potentially selected) sites. | | Predicting fixation probability of a new allele | $P{\text{fix}} \approx \frac{2s}{1 - e^{-4Nes}}$ (approx $2s$ if $Nes \gg 1$) | Choose based on whether $s$ is known and $Ne$ is large. | | Estimating equilibrium frequency of deleterious allele | $f = u/s$ | Use when selection is strong enough that drift is negligible. | | Modeling allele‑frequency change over generations | Wright‑Fisher diffusion equation | Use for large $Ne$ and when stochastic effects are important. | | Inferring demographic history | Site‑frequency spectrum (e.g., ∂a∂i) | Apply when you have genome‑wide SNP data across multiple populations. | | Assessing impact of linked selection | Background selection model, Hill–Robertson effect | Use when recombination rate is low and many selected sites are nearby. | --- 👀 Patterns to Recognize Selective sweep signature: high LD, low nucleotide diversity, a “valley” of variation around the selected site. Background selection: uniformly reduced diversity in low‑recombination regions, but without the LD spikes seen in sweeps. Elevated $F{ST}$ at specific loci → candidate for local adaptation or barriers to gene flow. Excess of nonsynonymous fixed differences vs. polymorphisms → positive selection (McDonald–Kreitman). Skewed allele‑frequency spectrum (excess rare alleles) → recent population expansion or purifying selection. Correlation of mutation bias with substitution spectrum → mutational bias driving adaptation (e.g., GC‑biased gene conversion). --- 🗂️ Exam Traps Confusing drift with draft – answer choices may attribute reduced diversity solely to drift; remember linked selective sweeps (draft) can mimic drift. Misapplying $s > 1/Ne$ – the inequality tells when selection can overcome drift, not that selection always dominates; context matters. Assuming all mutation is deleterious – many mutations are neutral; some are beneficial and drive adaptation. Treating recombination as a magic eraser of LD – recombination reduces but does not instantly eliminate LD; hitchhiking can maintain it. Using HWE test on a structured population – population subdivision creates apparent disequilibrium; the correct test is $F{ST}$ or STRUCTURE analysis. Interpreting a high $F{ST}$ as evidence of selection – could also result from genetic drift in small isolated populations; need complementary evidence. Forgetting dominance coefficient ($h$) – fixation probabilities differ for recessive vs. dominant beneficial mutations; ignoring $h$ leads to wrong predictions. ---