Why extinction estimates from extant phylogenies are so often zero

Time-calibrated phylogenies comprising only extant lineages are widely used to estimate historical speciation and extinction rates. Such extinction rate estimates have long been controversial as many phylogenetic studies report zero extinction in many taxa, a finding in conflict with the fossil record. To date, the causes of this widely observed discrepancy remain unresolved. Here we provide a novel and simple explanation for these “zero-inflated” extinction rate estimates, based on the recent discovery that there exist many alternative “congruent” diversification scenarios that cannot possibly be distinguished on the sole basis of extant timetrees. Consequently, estimation methods tend to converge to some scenario congruent to (i.e., statistically indistinguishable from) the true diversification scenario, but not necessarily to the true diversification scenario itself. This congruent scenario may in principle exhibit negative extinction rates, a biologically meaningless but mathematically feasible situation, in which case estimators will tend to hit and stick to the boundary estimate of zero extinction. To test this explanation, we estimated extinction rates using maximum likelihood for a set of simulated trees and for 121 empirical trees, while either allowing or preventing negative extinction rates. We find that the existence of congruence classes and imposed bounds on extinction rates can explain the zero-inflation of previous extinction rate estimates, even for large trees (1000 tips) and in the absence of any detectable model violations. Not only do our results likely resolve a long-standing mystery in phylogenetics, they demonstrate that model congruencies can have severe consequences in practice.

A Boundary Estimate for Singular Sub-Critical Parabolic Equations

We prove an estimate on the modulus of continuity at a boundary point of a cylindrical domain for local weak solutions to singular parabolic equations of $p$-Laplacian type, with $p$ in the sub-critical range $\big(1,\frac{2N}{N+1}\big]$. The estimate is given in terms of a Wiener-type integral, defined by a proper elliptic $p$-capacity.

An estimate of the terrestrial carbon budget of Russia using inventory-based, eddy covariance and inversion methods

We determine the net land to atmosphere flux of carbon in Russia, including Ukraine, Belarus and Kazakhstan, using inventory-based, eddy covariance, and inversion methods. Our high boundary estimate is −342 Tg C yr−1 from the eddy covariance method, and this is close to the upper bounds of the inventory-based Land Ecosystem Assessment and inverse models estimates. A lower boundary estimate is provided at −1350 Tg C yr−1 from the inversion models. The average of the three methods is −613.5 Tg C yr−1. The methane emission is estimated separately at 41.4 Tg C yr−1. These three methods agree well within their respective error bounds. There is thus good consistency between bottom-up and top-down methods. The forests of Russia primarily cause the net atmosphere to land flux (−692 Tg C yr−1 from the LEA. It remains however remarkable that the three methods provide such close estimates (−615, −662, −554 Tg C yr–1) for net biome production (NBP), given the inherent uncertainties in all of the approaches. The lack of recent forest inventories, the few eddy covariance sites and associated uncertainty with upscaling and undersampling of concentrations for the inversions are among the prime causes of the uncertainty. The dynamic global vegetation models (DGVMs) suggest a much lower uptake at −91 Tg C yr−1, and we argue that this is caused by a high estimate of heterotrophic respiration compared to other methods.