AlleleA1 Tutorial: Population Genetics Simulation | Bio 202L

In two-locus population genetics models, haplotype frequencies change due to recombination and selection, where linkage disequilibrium (D = x11x22 - x12x21) measures non-random associations between alleles at different loci; recombination reduces linkage disequilibrium over time (D' = D(1 - r)), while selection can either increase or decrease haplotype frequencies depending on whether their marginal fitness exceeds the population mean, creating a fundamental trade-off where recombination both generates genetic diversity for selection to act upon and breaks down beneficial allele associations.

This video covers advanced population genetics concepts including linkage analysis (determining if disease-causing genes are near known markers), LOD scores (logarithm of odds) for measuring linkage strength where values above 3 indicate linkage and below -2 indicate independence, multipoint linkage analysis for precise gene localization, autozygosity mapping for recessive disorders in consanguineous families, and linkage disequilibrium (non-random allele associations indicating recent mutations). The video also discusses medical interventions and their effects on genetic load, explaining how increased survival and reproduction can increase disease allele frequencies, with calculations showing it takes approximately 45 generations to halve allele frequencies in autosomal recessive disorders.

Linkage disequilibrium (D) measures the non-random association between alleles at different loci, calculated as D = f(AB)f(ab) - f(Ab)f(aB); even with maximum recombination rate (r = 0.5), D decays exponentially over generations following D_new = D_old × (1 - r), meaning linkage disequilibrium persists for many generations and can be used to infer evolutionary history such as human migration patterns.

Linkage disequilibrium describes non-random association of alleles at linked loci, with closely linked loci showing stronger disequilibrium because recombination hasn't had time to shuffle combinations. Factors affecting disequilibrium include chromosome location, GC content, Alu elements, and recombination hotspots (~every 50-100 kb). Natural selection creates detectable signatures: under neutrality, new variants increase slowly and recombination breaks down associations, while under positive selection, variants spread rapidly before recombination can shuffle nearby SNPs, creating extended regions of high linkage disequilibrium and homozygosity. This allows identification of loci undergoing recent adaptive evolution. Tibetan populations show strong selection signatures at two genes in the hypoxia-inducible factor pathway, with selected haplotypes associated with reduced hemoglobin levels protecting against polycythemia at high altitude.

Linkage disequilibrium is the tendency of alleles to be transmitted together more or less often than expected by chance alone, which occurs when genes are located close together on the same chromosome and recombination is less likely; conversely, linkage equilibrium occurs when alleles are far apart on the same chromosome and recombine frequently, making them behave as if they were on separate chromosomes.

The extinction vortex is a downward spiral where small, rare populations experience accelerated extinction through interconnected genetic and demographic factors: reduced population size leads to loss of genetic diversity, which exacerbates inbreeding depression and decreases individual fitness, resulting in lower reproduction and higher mortality that further reduces population numbers until demographic instability causes complete extinction; conservation genetics helps identify populations at risk and develop strategies to mitigate these genetic factors.

Simulation outputs include deterministic and stochastic growth rates, extinction probability, expected population size at future timepoints, and genetic diversity metrics. Stochastic results are always lower than deterministic ones because they incorporate catastrophic events and demographic variability. Results should be reported with standard deviations or standard errors to indicate uncertainty. Graphical representation shows population trajectories with error bars representing outcome ranges. Genetic diversity metrics track evolutionary potential and inbreeding risks. Median time-to-extinction indicates the midpoint of possible extinction times, helping prioritize conservation efforts for populations at greatest risk.

The extinction vortex can only be broken by increasing genetic diversity within struggling populations. The Santa Cruz long-toed salamander project represents a real-world test of whether genetic crossing between healthy and struggling populations can reverse population decline. By introducing genetic material from northern populations into southern ones, conservationists aim to restore adaptive potential lost through isolation. Success depends on whether crossbred offspring survive, reproduce, and pass their genes to future generations, ultimately determining whether this intervention can rescue the species from irreversible decline.

Small-population conservation focuses on identifying species with very small populations and helping boost their numbers and genetic diversity. Low population size and low genetic diversity create a dangerous feedback loop called the extinction vortex: small populations suffer from inbreeding and genetic drift, leading to even less diversity, which causes lower reproduction rates and higher mortality, making the population smaller still. This dynamic ultimately causes species to spiral toward extinction.

Cultural memory loss is a critical concept in conservation biology where species lose accumulated behavioral knowledge when individuals are removed from the wild. Parrots learn from one another, and when trappers removed adult birds, they erased accumulated behavioral knowledge that could not be reconstructed in a laboratory. By 2008, researchers identified a bornavirus behind the disease affecting captive birds, making management possible. Ornithologist Cromwell Purchase developed artificial insemination protocols with veterinarian Daniel Newman to produce genetically diverse birds. The goal was to pull the population back from the edge of the extinction vortex by deliberately managing which individuals contributed to the next generation. In May 2013, the first artificially inseminated Spix's macaw chicks hatched, finally getting the population out of the genetic bottleneck that had been closing around it for decades.

The simple bacterial evolution model successfully reproduces empirical SNP distribution data from real bacterial populations. By fitting model predictions to observed distributions at various divergence levels, researchers can estimate key evolutionary parameters: the ratio between mutation and recombination rates, average recombined segment length, and transfer efficiency. This demonstrates how minimal models can extract meaningful biological parameters from complex genomic data.

This concluding section synthesizes theoretical frameworks and empirical validation. Universality classes in coalescent theory reveal that different models can produce identical statistical behavior based on offspring variance properties. The infinite allele model and Ewens sampling formula provide testable predictions for neutral genetic variation. Empirical validation comes from SNP frequency spectra, which exhibit characteristic 1/k decay consistent with neutral theory predictions. This convergence between mathematical theory and empirical observation demonstrates the power of neutral population genetics in explaining patterns of genetic diversity across species.

Simulation models must be verified through both empirical data comparison and theoretical expectations. Empirical verification involves comparing model predictions against actual population genetic data to confirm accuracy. Theoretical verification tests whether models produce expected rates of genetic differentiation, loss of genetic diversity, fecundity patterns, and dispersal abilities based on population genetics theory. Both approaches confirm that models work correctly when parameters are properly calibrated, though biological parameterization remains the most challenging aspect of model development.

ABC is one solution to the likelihood-free inference problem, proposed in the early 2000s by scientists in genetics and population biology. The method treats the simulator as a black box and compares synthetic observations generated from parameter values against actual observations using summary statistics. If the distance between compressed representations is below a threshold epsilon, the parameter value is accepted. As epsilon approaches zero with sufficient summary statistics, the sampling distribution converges to the true posterior.

Computer simulations using AlphaSimR compared estimation methods across three demographic scenarios over 25 generations: constant effective population size (97), sudden bottleneck (from 207 to 97 at generation 16), and gradual decrease. Simulations used 31 chromosomes with 682,000 SNPs per chromosome, mimicking high-density SNP chip data. In constant scenarios, GONE provided estimates closest to true values, while SNaP consistently underestimated. ROH-based estimates also underestimated but less severely. In bottleneck scenarios, most estimators overestimated Ne during large-population periods because they average over entire demographic history. Restricting analysis to post-bottleneck periods improved estimates significantly. GONE captured sudden drops reasonably well but not perfectly, while SNaP severely underestimated in bottleneck scenarios. Historical estimation using GONE outperformed current-only estimates.