Computationally Efficient Composite Likelihood Statistics for Demographic Inference

Abstract

Many population genetics tools employ composite likelihoods, because fully modeling genomic linkage is challenging. But traditional approaches to estimating parameter uncertainties and performing model selection require full likelihoods, so these tools have relied on computationally expensive maximum-likelihood estimation (MLE) on bootstrapped data. Here, we demonstrate that statistical theory can be applied to adjust composite likelihoods and perform robust computationally efficient statistical inference in two demographic inference tools: ∂a∂i and TRACTS. On both simulated and real data, the adjustments perform comparably to MLE bootstrapping while using orders of magnitude less computational time.

Inferring Recent Demography from Isolation by Distance of Long Shared Sequence Blocks

“…In the more complex model, D e ðtÞ ¼ t 2b ; the growth rate parameter b was estimated to be close to one. The increase of likelihood was small ðDL ¼ 1:1Þ; especially when considering that there are correlations in the data that make the difference of true likelihood even smaller (Coffman et al 2016). Similarly, fitting several, more complex, density functions as sums of power terms did not significantly increase the likelihood.…”

“…However, maximizing the likelihood of actually correlated observations (composite likelihood) is a widely used practice in inference from genetic data (e.g., Fearnhead and Donnelly 2002). It still gives consistent and asymptotically normal estimates, although the errors calculated from the curvature of the maximum likelihood surface at its maximum (Fisher information matrix) will be too tight when the observations are actually correlated (Lindsay 1988;Coffman et al 2016). Moreover, in many cases, correlations among blocks can be expected to remain fairly weak, since initial correlations in spatial movement are broken up quickly by recombination.…”

Triallelic Population Genomics for Inferring Correlated Fitness Effects of Same Site Nonsynonymous Mutations

“…To account for this, we calculated parameter uncertainties for each model fit, using the Godambe information matrix (Coffman et al 2016), which adjusts the composite-likelihood statistic to account for the effects of linkage. To do so, we generated 1000 bootstrap data sets by dividing the D. melanogaster autosomal genome into 1000 regions of equal length and resampling among these regions.…”

Adaptation in a fibronectin binding autolysin ofStaphylococcus saprophyticus

“…In addition to being a cause of human UTI, S. saprophyticus can be 42 found in the environment, in food, and associated with animals. After discovering that 43 UTI strains of S. saprophyticus are for the most part closely related to each other, we 44 sought to determine whether these strains are specially adapted to cause disease in 45 humans. We found evidence suggesting that a mutation in the gene aas is 46 advantageous in the context of human infection.…”

“…We 234 compared five demographic models (constant size, instantaneous population size 235 change, exponential population size change, instantaneous population size change 236 followed by exponential, and two instantaneous population size changes , Figure 9) and 237 used bootstrapping to estimate the uncertainty of the parameters and to adjust the 238 composite likelihoods using the Godambe Information Matrix implemented in ∂ a∂i (43). 239 We found significant evidence for an expansion in all models ( Table 2).…”