The biologist’s theories about how environments prompt rapid species evolution and extinction propelled her onto the world stage. The biologist’s theories about how environments prompt rapid species evolution and extinction propelled her onto the world stage.

It is a pleasure to be invited to contribute to the celebration of the publication of “punctuated equilibria” (“punk eek”) 50 years ago—the canonical version I did with Steve Gould (Eldredge and Gould 1972) at the behest of Tom Schopf for his visionary project to inject more thought, more interpretation and theory, into the working lives of paleontologists.

Punctuated equilibria is a theory of evolution that suggests that species go through periods of stability followed by sudden changes in phenotype. This theory has been debated for decades in evolutionary biology, but recent findings of stasis and punctuated change in evolutionary systems such as tumour dynamics, viral evolution, and artificial evolution have attracted attention from a broad range of researchers. There is a risk of interpreting punctuated change from a phenomenological, or even metaphorical, standpoint and thus opening the possibility of repeating similar debates that have occurred in the past. How to translate the lessons from evolutionary models of the fossil record to explain punctuated changes in other biological scales remains an open question. To minimize confusion, we recommend that the step-like pattern seen in many evolutionary systems be referred to as punctuated evolution rather than punctuated equilibria, which is the theory generally linked with the similar pattern in the fossil record. Punctuated evolution is a complex pattern resulting from the interaction of both external and internal eco-evolutionary feedback. The interplay between these evolutionary drivers can help explain the history of life and the whole spectrum of evolutionary dynamics, including diversification, cyclic changes, and stability.

For five decades, paleontologists, paleobiologists, and ecologists have investigated patterns of punctuated equilibria in biology. Here, we step outside those fields and summarize recent advances in the theory of and evidence for punctuated equilibria, gathered from contemporary observations in geology, molecular biology, genetics, anthropology, and sociotechnology. Taken in the aggregate, these observations lead to a more general theory that we refer to as punctuated evolution. The quality of recent datasets is beginning to illustrate the mechanics of punctuated evolution in a way that can be modeled across a vast range of phenomena, from mass extinctions hundreds of millions of years ago to the possible future ahead in the Anthropocene. We expect the study of punctuated evolution to be applicable beyond biological scenarios.

The process of evolution and the structures it produces are best understood in the light of hierarchy theory. The biota traditionally is described by either the genealogical Linnaean hierarchy or economic hierarchies of communities or ecosystems. Here we describe the Bretskyan hierarchy-a hybrid eco-genealogical hierarchy that consists of nested sets of different-sized, usually polyphyletic communities of interacting individuals separated from other such communities in space and time at multiple scales. The Bretskyan hierarchy consists of elements that have both genealogical and economic properties and functions-situated between, and connecting the elements of, the economic hierarchies (Vernadskyan) and the genealogical (Linnaean) hierarchy. The described hierarchy at lower tiers is populated by holobionts, individuals composed of multiple polyphyletic lineages integrated by functional interactions or biotically fabricated structures, such as membranes. At larger spatial tiers and longer time scales, the members of the Bretskyan hierarchy are of a more diffuse nature, partially due to the small size and relatively short duration of us as observers of larger and longer-lasting structures, here described as geobiomes. Their individuality is externally forced and directly tied to the spatial and temporal physical structures of our planet. These are sub-bioprovinces and bioprovinces-large and effectively isolated spatiotemporal structures of biota integrated internally by coevolution and individuated externally by a hierarchy of barriers. Gaia is here understood as the largest eco-genealogical individual compartmentalized by the outer space of the Earth and integrated at long time scales by biotic interactions and plate tectonic mixing of biota. The existence of a hierarchy of barriers and multilevel allopatry suggests that geographic isolation takes part not only in individuating species lineages, but also in producing coherent complexes of separate lineages forming bioprovinces at multiple space and time scales. The sizes, configurations, and durations of Bretskyan units are directly tied to geodynamics, demonstrating the central role of the physical planet in the processes of individuation and merging of geobiomes and the control of coevolution, and all its ramifications, at multiple space and time scales. The Bretskyan hierarchy also allows the integration of previously unconnected themes-"egalitarian" major transitions in individuality (e.g., eukaryogenesis) and some of the megatrajectories in the history of life-into a single theoretical framework of spatial and temporal scaling of eco-genealogy. The pervasive scaling of geodynamical processes and the direct connection of geodynamics to the dynamics of Bretskyan units allows us to formulate conjectures on the scales and limits of spatial and temporal contingency and competitiveness of biotas in evolution.

Natural selection is believed to universally work to lower mutation rates (MR) due to the negative impact of mutations on individual fitness. Mutator alleles can be co-selected by genetic linkage with adaptive alleles in asexual organisms. However, sexual reproduction disrupts genetic linkage, allowing selection to efficiently eradicate mutator alleles, lowering MR to the extent limited by the overall selection efficiency.In the present paper, we apply Monte Carlo in silico experimentation to study MR evolution in sexually reproducing populations.We demonstrate that both higher and lower MR can evolve depending on the mode of selection acting on adaptive phenotypic traits. We reveal a previously unreported co-selective process that determines the direction of MR evolution. We show that MR evolution is substantially influenced by multigenic inheritance of both MR and adaptive traits. Our study corroborates that MR evolution is significantly impacted by genetic drift; however, its primary source appears to be the amount of standing genetic variation, with a lesser role for population size.Based on our study, we propose an expanded population genetics theory of MR evolution in sexually reproducing populations, with potential implications for understanding rapid adaptive speciation and related macroevolutionary patterns, as well as for human health.Lay summary Natural selection is believed to always work to lower mutation rates in sexual organisms. Here we apply a Monte Carlo model of a sexually reproducing population and demonstrate that both lower and higher mutation rates can evolve, contingent on selection acting on adaptive traits in a sexually reproducing population.### Competing Interest StatementThe authors have declared no competing interest.

We propose that the onset and progressive destructive action of cancer within an individual bears a profound and striking similarity to the onset and progressive human-engendered destruction of global ecosystems and the extinction of entire species. Cancer in the human body and our human role in planetary, especially biotic, degradation are uncannily similar systems. For starters, they are the only two known complex systems where a discrete component changes its normal ecological role and function—turning on and potentially killing its host, and in so doing, itself. Both are “hostile takeovers.” Clearly, humans are integral to both systems. With cancer we are the host and victims of the rogue behavior of what starts out as a normal, healthy, and functionally important part of our bodies. With the biodiversity crisis, we are the part of the system that has changed, expanded, and proven so destructive to the system in which we live. We argue that given that these threats to our bodies and Earth are both essentially ecological diseases, understanding the critical role of ecological interdependencies for avoiding both cancer’s and humankind’s destruction of their respective homes should hopefully promote better stewardship of both by the only animal capable of recognizing the problems—us.