Run two simulations with identical rates. The trees still look nothing alike.

The birth-death process is the canonical null model for how lineages diversify over time. Every speciation and every extinction is a stochastic event, so two runs under the same parameters can produce trees with wildly different sizes and shapes. Adjust the controls below and run it twice.

The simulator

What are you looking at?

Each panel simulates a birth-death process starting from a single lineage. At any moment, each living lineage can speciate (split into two daughters, rate λ) or go extinct (rate μ). Both simulations use the same parameter values (λ and μ). Because speciation and extinction are stochastic events, the resulting trees are different every time. The rates are identical; the outcomes are not.

Two consequences worth knowing. (1) The pull of the present. Empirical phylogenies are conditioned on the clade surviving to the present. Lineages that went extinct early are simply absent. This conditioning systematically biases naive extinction-rate estimates downward, and is why "extinction rate ≈ 0" estimates from molecular phylogenies should always be read with skepticism (Nee, May & Harvey 1994; Rabosky 2010). (2) Tree shape statistics (the Colless and Sackin imbalance indices, the gamma statistic) quantify how lopsided or front-loaded a tree is. The simulator's two trees can have very different Colless values despite identical rates, which is exactly why tree shape alone is a poor estimator of diversification rates: shape is a statistic of one stochastic realization, not a robust signal of the underlying process.

Colored branches are lineages that survive to the present. Muted branches went extinct before the end time. Small dots mark extinction events.

This variability is why two clades evolving at the same rates can end up with very different numbers of species, and why detecting shifts in diversification rate requires careful statistical methods. A lot of the apparent signal can just be noise. Try increasing μ toward λ (high turnover) and watch how often complete extinction occurs. Try low μ and high λ for explosive radiations.

The net diversification rate is r = λ − μ. When r is small or negative, trees frequently go extinct entirely. Even with a positive expected trajectory, any single realization can die out by chance (the stochastic extinction problem).