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One way to tease apart these hypotheses is to test the underlying assumptions of selection for expanded host use across systems.
Through this snowball sampling method, we were able to select a diverse sample and, although not representative for the total health care network population, there are no assumptions of selection bias that might be related to our topic of study.
This tool is included in the PAML4 package [ 88] and calculates maximum likelihood estimates for the fit of models with different assumptions of selection patterns to the sequence data.
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Using multiple estimators with different strengths and weaknesses but all based on the same identifying assumption of "selection on observed variables" provides a clear indication of the sensitivity of the empirical findings to details of the estimation strategy.
OLS models that are also based on the assumption of selection on observables are fundamentally not robust to the substantial differences in the pre-treatment distribution of covariates between treatment and control groups with observational data when the linearity assumption of the outcome equation fails.
Indeed, it has been shown that similar global network topological properties can emerge due to non-adaptive processes, such as simple birth-and-death models [ 21, 22], without any assumption of selection [ 23].
Finally, the remaining regions of heterozygosity in RIL may have survived due to selection, whereas these calculations rely on assumptions of no selection or mutation and so are not appropriate to capture such phenomena.
This commonness of cooperative behaviors challenged the assumptions of natural selection and necessitated a re-evaluation of the evolutionary framework.
For a mathematical evaluation of the underlying assumptions of model selection criteria and their considerations, see [22], [23], [24].
Tree length is the product of substitution rate and time [ 51] but can be significantly affected by the assumptions of model selection [ 75].
Under the assumptions of weak selection, we evaluate this recursion for the case when v i = v j = v, where v is the trait in question.
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