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Copy file name to clipboardExpand all lines: README.md
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# Background
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This tutorial will show how to configure and run a model with progressive changes in birth and death rates, using the ClaDS tree prior implemented in the BEAST2 package ClaDS.
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The Cladogenetic Diversification rate Shift (ClaDS) model is a birth-death process which is designed to represent gradual, progressive changes in rates throughout a phylogeny. It is similar in principle to an autocorrelated clock model, as new birth and death rates are drawn for each edge from a distribution which depends on the ancestral rates.
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As an example, we consider a lineage {% eqinline N %}, with its associated birth rate {% eqinline \lambda_N %} and death rate {% eqinline \mu_N %}. At the next birth event, the lineage {% eqinline N %} splits into lineages {% eqinline N' %} and {% eqinline N" %}. The new birth rates {% eqinline \lambda_N' %} and {% eqinline \lambda_N" %} are drawn from a lognormal distribution with mean {% eqinline M = log(\alpha \times \lambda_N %} and standard deviation {% eqinline S = \sigma %}. {% eqinline \alpha %}, {% eqinline \sigma %}, and the birth rate at the root {% eqinline \lambda_0 %} are parameters of the model and can be estimated by the inference.
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As an example, we consider a lineage {% eqinline N %}, with its associated birth rate {% eqinline \lambda_N %} and death rate {% eqinline \mu_N %}. At the next birth event, the lineage {% eqinline N %} splits into lineages {% eqinline N^\prime %} and {% eqinline N^{\prime\prime} %}. The new birth rates {% eqinline \lambda_N^\prime %} and {% eqinline \lambda_N^{\prime\prime} %} are drawn from a lognormal distribution with mean {% eqinline M = \log(\alpha \times \lambda_N ) %} and standard deviation {% eqinline S = \sigma %}. The model parameters {% eqinline \alpha %}, {% eqinline \sigma %}, and the birth rate at the root, {% eqinline \lambda_0 %}, can be estimated by the inference.
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The package includes two separate options for sampling the death rate:
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1. New death rates are not sampled separately, but controlled by the turnover parameter {% eqinline \epsilon %}, which is the same throughout the phylogeny and can be estimated by the inference. Thus for each lineage {% eqinline N %}, we have {% eqinline \mu_N = \epsilon \times \lambda_N %}. This is the parametrization by default.
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2. New death rates are sampled from the ancestral rates, following a similar lognormal distribution to the birth rates. Thus, for lineage {% eqinline N %} with descendants {% eqinline N' %} and {% eqinline N" %}, we draw the new death rates {% eqinline \mu_N' %} and {% eqinline \mu_N" %} from a lognormal distribution with mean {% eqinline M = log(\alpha_M \times \mu_N %} and standard deviation {% eqinline S = \sigma_M %}. In this case and similar to the birth rate, {% eqinline \alpha_M %}, {% eqinline \sigma_M %}, and the death rate at the root {% eqinline \mu_0 %} are parameters of the model and can be estimated by the inference.
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2. New death rates are sampled from the ancestral rates, following a similar lognormal distribution to the birth rates. Thus, for lineage {% eqinline N %} with descendants {% eqinline N^\prime %} and {% eqinline N^{\prime\prime} %}, we draw the new death rates {% eqinline \mu_N^\prime %} and {% eqinline \mu_N^{\prime\prime} %} from a lognormal distribution with mean {% eqinline M = \log(\alpha_M \times \mu_N ) %} and standard deviation {% eqinline S = \sigma_M %}. In this case and similar to the birth rate, {% eqinline \alpha_M %}, {% eqinline \sigma_M %}, and the death rate at the root, {% eqinline \mu_0 %}, are parameters of the model and can be estimated by the inference.
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The choice of death rate parametrization is left to the user, and will depend on the dataset and on which characteristics are thought to drive the variations in rate. The first parametrization is appropriate when the variations of both rates are tied to the same factor and thus strongly correlated, whereas the second parametrization is more appropriate when the variations in birth rates and death rates are uncorrelated. The first parametrization is also more simple and contains less parameters, and thus may be easier to use when the available data is limited.
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Finally, it is also possible to set either the birth rate or the death rate to be constant throughout the phylogeny, by setting the corresponding trend parameter {% eqinline \alpha %} or {% eqinline \alpha_M %} to 1 and the corresponding standard deviation parameter {% eqinline \sigma %} or {% eqinline \sigma_M %} to 0. This will lead to {% eqinline \lambda_N = \lambda_0 %} or {% eqinline \mu_N = \mu_0 %} for all lineages.
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<figcaption>Figure 7: Taxon set editor.</figcaption>
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</figure>
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<br>
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### The parameter priors
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Most of the default parameter priors are reasonable, so we will not change them. However, the default prior for the mean clock rate is a uniform distribution from 0 to Infinity, which allows values which are too large for most datasets. A reasonable value for the global substitution rate of primates is on the order of 10^-2 substitution/site/My, so we will set a exponential prior around this value.
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Most of the default parameter priors are reasonable, so we will not change them. However, the default prior for the mean clock rate is a uniform distribution from 0 to Infinity, which allows values which are too large for most datasets. A reasonable value for the global substitution rate of primates is on the order of {% eqinline 10^{-2} %} substitution/site/My, so we will set a exponential prior around this value.
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> Use the dropdown menu on the right of **clockRate.c:primates** to select a **Exponential** distribution for this prior.
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> Click on the arrow left to **clockRate.c:primates** to open the detailed options. Set the **Mean** parameter to **0.01**.
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