Push of the past

The push of the past[1][2] is a type of survivorship bias associated with evolutionary diversification when extinction is possible.

[3] This gives rise to an exponential distribution, with the number of species in a particular clade N at any time t given by

In the special case of there being no extinction, this simplifies to the so-called "Yule process".

A different type of plot of diversity through time, called a “lineage through time” (LTT) plot, retrospectively reconstructs the number of lineages that led to the living species of a group.

This is equivalent to constructing a dated phylogeny and then counting how many branches are present at each time interval.

If a BDM is forward-modelled, i.e. if the fate of an original single species is modelled through time, then a wide range of possible outcomes can occur, as the process is stochastic.

Imposing the condition of survival on a clade implies that rates of early diversification will be higher than expected.

It can be shown that for a long-lived clade, the expected initial short-term rate of diversification is approximately

Long-lived clades should thus show a characteristic early burst of diversification that quickly declines to the long-term rate, an effect called the "push of the past".

For a normal-sized clade, the push of the past is only observed in the raw count of species through time (e.g. that reconstructed from the fossil record), but the rate of lineage increase is affected as the present is approached.

in the present - living species by definition have an observed zero extinction rate.

This theoretical apparent increase in the rate of lineage production has been termed the "pull of the present".

This conundrum has been much discussed, and two major solutions have been proposed: first, that diversification is diversity dependent,[5] so that as the carrying capacity of the environment is reached the rate of lineage production slows; secondly, that our modern species concept does not properly capture the “lineages” of BDM, and that speciation as we recognize it is only the end point of a drawn-out process of splitting of subpopulations through time, each of which could be considered to be a lineage in itself.

Such high rates have often been observed at the origin of major groups such as the animals and angiosperms.

It is possible that such striking diversifications are thus simply an effect of survivorship bias, and that if overall rates could be measured at their time of origin (including those of groups that quickly went extinct) no unusual rates would be observed.

Consideration of the null hypothesis of survivorship bias is thus important when assigning causes to apparent cases of early rapid diversification, The effect of the push of the past appears to be the reason that crown groups tend to emerge early within the history of a group as a whole: groups that diversify readily tend to create early new lineages.

The push of the past is an expected effect whenever a small group is diversifying and its future survival is known to have occurred.

Log plots of species numbers for both raw species (blue lines) and lineages through time (red line) when diversification is conditioned on survival to the past. In A, the rapid early diversification rate in the blue line is the push of past, and the late increase along the red line is the pull of the present. Shading gives 95% confidence intervals. In B and C, the observed slowdown in rates of diversification through time and relative to diversity are plotted. From Budd and Mann (2018). [ 2 ]