Possible Origin of Stagnation and Variability of Earth’s Biodiversity

The magnitude and variability of Earth’s biodiversity have puzzled scientists ever since paleontologic fossil databases became available. We identify and study a model of interdependent species where both endogenous and exogenous impacts determine the nonstationary extinction dynamics. The framework provides an explanation for the qualitative difference of marine and continental biodiversity growth. In particular, the stagnation of marine biodiversity may result from a global transition from an imbalanced to a balanced state of the species dependency network. The predictions of our framework are in agreement with paleontologic databases.

Figure 1

Sketch of the model. The species in purple (crosses) become extinct at level 1 by exogenous causes and at higher levels due to their dependence on species at lower levels. The species in green (gray) originate from existing species (arrows).

Figure 2

Sketch of a dependency network in the balanced state (a) and the imbalanced state (b). Both networks consist of the same number of species. The dashed line is close to a half-normal distribution.

Figure 3

Temporal development of a plateau. Single realization for extinction probability $\lambda =0.985$ and $n_1(0)=1000$ initial species. (a) The total diversity curve with three indicated points of effectively constant diversity. (b) The diversity distribution $n_l$ at the three indicated times in (a). While the total diversity stagnates, the dependency network reorganizes from the imbalanced state (Filled downward triangle) to a half-Gaussian distribution (Filled upward triangle).

Figure 4

Frequency of periods of imbalanced states lasting longer than a duration $d$. Each realization was stopped at the time step when the diversity reached 1000 species. The inset shows the probability $P_{\mathrm{im}}$ for an imbalanced state, based on 400 realizations.

Figure 5

(a) Marine and continental diversity. The lines are fitted to the data in the time range $-200$ to 0 Ma, yielding $\alpha =0.0055(2){\mathrm{Ma}}^{-1}$ for marine diversity ($R=0.987$, $P<0.001$) and $\alpha =0.0121(3){\mathrm{Ma}}^{-1}$ for continental diversity ($R=0.990$, $P<0.001$). (b) Survival probability (cumulative lifetime distribution) of marine and continental families. Best fits are $\mu =0.01786(3){\mathrm{Ma}}^{-1}$ for marine data ($R=-0.998$, $P<0.001$) and $\mu =0.0269(1){\mathrm{Ma}}^{-1}$ for continental data ($R=-0.990$, $P<0.001$).

Figure 6

Percent extinction of total diversity against percent origination for each stage. The solid line and the dashed line show the most frequent slope for marine and continental data found by the least-squares method in $10^6$ bootstrap samples. The inset shows the bootstrap distribution of the data. The gray areas are the 2.5% quantiles. The maxima are at slopes 0.683 (marine) and 0.567 (continental).