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Of interest to the infectious disease modeler is the frequency with which a disease will be introduced under the pipe model, and not introduced under the full model (and vice-versa).
The likelihood ratio expresses how many times more likely the data are under the full model than the partial model.
Let θ̂ be the MLE of θ under the full model, σ̂ be the corresponding variance estimator.
The probability of an isolation benefit varied widely across the units, e.g. 27-82% under the full model.
Under the full model, the posterior probability of observing virus and serum locations given immunological data is factored.
This might partly explain the relatively small reduction of residual variance observed (see Table 2) for significant QTL under the full model.
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Quite strikingly, the level of niche fitness, species cohesion and phenotypic clustering evolved in the null model under assortative mating is very similar to that evolved in the full model under fully random mating.
We confirm this by running simulations with the standard TDDM formulation and show that the simplified formulation approximates well the full model under steady-state conditions.
In a future study we plan to test this hypothesis by studying the evolution of assortative mating under conditions where it is far less easy for assortativeness to evolve (see eg. [ 1, 5, 7, 14- 16]) to see whether indeed assortativeness can evolve in the full model under conditions where it can not evolve in the null model.
Our model reduction procedure ensures that the reduced model mimics the full model well under the conditions of a specific dynamic event.
We explained in detail the mechanism that, in the full model, enables phenotypic differentiation under random mating and enhances it under assortative mating, focusing on a few typical simulations in which default model parameter settings were used.
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Justyna Jupowicz-Kozak
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