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Register a new userHow to make any method fail: BAMM at the kangaroo court of false equivalency
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Daniel L Rabosky
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The software program BAMM has been widely used to study the dynamics of speciation, extinction, and phenotypic evolution on phylogenetic trees. The program implements a model-based clustering algorithm to identify clades that share common macroevolutionary rate dynamics and to estimate rate parameters. A recent simulation study published in Evolution (2017) by Meyer and Wiens (M&W) claimed that (i) simple (MS) estimators of diversification rates perform much better than BAMM, and (ii) evolutionary rates inferred with BAMM are weakly correlated with the true rates in the generating model. I demonstrate that their assessment suffers from two major conceptual errors that invalidate both primary conclusions. These statistical considerations are not specific to BAMM and apply to all methods for estimating parameters from empirical data where the true grouping structure of the data is unknown. First, M&Ws comparisons between BAMM and MS estimators suffer from false equivalency because the MS estimators are given perfect prior knowledge of the locations of rate shifts on the simulated phylogenies. BAMM is given no such information and must simultaneously estimate the number and location of rate shifts from the data, thus resulting in a massive degrees-of-freedom advantage for the MS estimators.When both methods are given equivalent information, BAMM dramatically outperforms the MS estimators. Second, M&Ws experimental design is unable to assess parameter reliability because their analyses conflate small effect sizes across treatment groups with error in parameter estimates. Nearly all model-based frameworks for partitioning data are susceptible to the statistical mistakes in M&W, including popular clustering algorithms in population genetics, phylogenetics, and comparative methods.
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Empirical studies show that epidemiological models based on an epidemics initial spread rate often fail to predict the true scale of that epidemic. Most epidemics with a rapid early rise die out before affecting a significant fraction of the population, whereas the early pace of some pandemics is rather modest. Recent models suggest that this could be due to the heterogeneity of the target populations susceptibility. We study a computer malware ecosystem exhibiting spread mechanisms resembling those of biological systems while offering details unavailable for human epidemics. Rather than comparing models, we directly estimate reach from a new and vastly more complete data from a parallel domain, that offers superior details and insight as concerns biological outbreaks. We find a highly heterogeneous distribution of computer susceptibilities, with nearly all outbreaks initially over-affecting the tail of the distribution, then collapsing quickly once this tail is depleted. This mechanism restricts the correlation between an epidemics initial growth rate and its total reach, thus preventing the majority of epidemics, including initially fast-growing outbreaks, from reaching a macroscopic fraction of the population. The few pervasive malwares distinguish themselves early on via the following key trait: they avoid infecting the tail, while preferentially targeting computers unaffected by typical malware.
In this paper, decision theory was used to derive Bayes and minimax decision rules to estimate allelic frequencies and to explore their admissibility. Decision rules with uniformly smallest risk usually do not exist and one approach to solve this problem is to use the Bayes principle and the minimax principle to find decision rules satisfying some general optimality criterion based on their risk functions. Two cases were considered, the simpler case of biallelic loci and the more complex case of multiallelic loci. For each locus, the sampling model was a multinomial distribution and the prior was a Beta (biallelic case) or a Dirichlet (multiallelic case) distribution. Three loss functions were considered: squared error loss (SEL), Kulback-Leibler loss (KLL) and quadratic error loss (QEL). Bayes estimators were derived under these three loss functions and were subsequently used to find minimax estimators using results from decision theory. The Bayes estimators obtained from SEL and KLL turned out to be the same. Under certain conditions, the Bayes estimator derived from QEL led to an admissible minimax estimator (which was also equal to the maximum likelihood estimator). The SEL also allowed finding admissible minimax estimators. Some estimators had uniformly smaller variance than the MLE and under suitable conditions the remaining estimators also satisfied this property. In addition to their statistical properties, the estimators derived here allow variation in allelic frequencies, which is closer to the reality of finite populations exposed to evolutionary forces.
The availability of a large number of assembled genomes opens the way to study the evolution of syntenic character within a phylogenetic context. The DeCo algorithm, recently introduced by B{e}rard et al. allows the computation of parsimonious evolutionary scenarios for gene adjacencies, from pairs of reconciled gene trees. Following the approach pioneered by Sturmfels and Pachter, we describe how to modify the DeCo dynamic programming algorithm to identify classes of cost schemes that generates similar parsimonious evolutionary scenarios for gene adjacencies, as well as the robustness to changes to the cost scheme of evolutionary events of the presence or absence of specific ancestral gene adjacencies. We apply our method to six thousands mammalian gene families, and show that computing the robustness to changes to cost schemes provides new and interesting insights on the evolution of gene adjacencies and the DeCo model.
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