ivy.birthdeath module¶

Equations from Magallon and Sanderson 2001

ivy.birthdeath.Alpha(epsilon, r, t)[source]¶

Calculate Alpha

Parameters:	epsilon (float) – Relative extinction rate(d/b) r (float) – Net diversification rate (b-d). t (float) – Elapsed time
Returns:	Alpha
Return type:	Float

ivy.birthdeath.Beta(epsilon, r, t)[source]¶

Calculate Beta

Parameters:	epsilon (float) – Relative extinction rate(d/b) r (float) – Net diversification rate (b-d). t (float) – Elapsed time.
Returns:	Beta
Return type:	Float

ivy.birthdeath.Kendall1948(i, t, r, epsilon)[source]¶

Probability of observing i species given single ancestor after time t

Parameters:	i (int) – Number of extant species t (float) – Elapsed time r (float) – Net diversification rate (b-d) epsilon (float) – Relative extinction (d/b)

ivy.birthdeath.Nbar(t, a, r, epsilon)[source]¶

Mean clade size conditional on survival of the clade

Parameters:	t (float) – Elapsed time a (int) – Number of lineages at t=0 r (float) – Net diversification rate (b-d) epsilon (float) – Relative extinction (d/b)

ivy.birthdeath.condKendall1948(i, t, r, epsilon)[source]¶

Probability of observing i species given a single ancestor after time t conditional on the clade surviving to time t

Parameters:	i (int) – Number of extant species t (float) – Elapsed time r (float) – Net diversification rate (b-d) epsilon (float) – Relative extinction (d/b)

ivy.birthdeath.condPrN(i, t, a, r, epsilon)[source]¶

Conditional probability of i species after time t, given the probability of survival

Parameters:	i (int) – Number of extant species t (float) – Elapsed time a (int) – Number of lineages at t=0 r (float) – Net diversification rate (b-d) epsilon (float) – Relative extinction (d/b)

ivy.birthdeath.logLT(t, n, r, epsilon)[source]¶

Log-likelihood of terminal taxa

Parameters:	t – vector of stem ages n – vector of diversities r (float) – net diversification epsilon (float) – Relative extinction

ivy.birthdeath.prN(i, t, a, r, epsilon)[source]¶

Probability of observing i species after time t

Parameters:	i (int) – Number of extant species t (float) – Elapsed time a (int) – Number of lineages at t=0 r (float) – Net diversification rate (b-d) epsilon (float) – Relative extinction (d/b)