Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets

An integrated understanding of molecular and developmental biology must consider the large number of molecular species involved and the low concentrations of many species in vivo. Quantitative stochastic models of molecular interaction networks can be expressed as stochastic Petri nets (SPNs), a mathematical formalism developed in computer science. Existing software can be used to define molecular interaction networks as SPNs and solve such models for the probability distributions of molecular species. This approach allows biologists to focus on the content of models and their interpretation, rather than their implementation. The standardized format of SPNs also facilitates the replication, extension, and transfer of models between researchers. A simple chemical system is presented to demonstrate the link between stochastic models of molecular interactions and SPNs. The approach is illustrated with examples of models of genetic and biochemical phenomena where the UltraSAN package is used to present results from numerical analysis and the outcome of simulations.

Declines of biomes and biotas and the future of evolution

Although panel discussants disagreed whether the biodiversity crisis constitutes a mass extinction event, all agreed that current extinction rates are 50–500 times background and are increasing and that the consequences for the future evolution of life are serious. In response to the on-going rapid decline of biomes and homogenization of biotas, the panelists predicted changes in species geographic ranges, genetic risks of extinction, genetic assimilation, natural selection, mutation rates, the shortening of food chains, the increase in nutrient-enriched niches permitting the ascendancy of microbes, and the differential survival of ecological generalists. Rates of evolutionary processes will change in different groups, and speciation in the larger vertebrates is essentially over. Action taken over the next few decades will determine how impoverished the biosphere will be in 1,000 years when many species will suffer reduced evolvability and require interventionist genetic and ecological management. Whether the biota will continue to provide the dependable ecological services humans take for granted is less clear. The discussants offered recommendations, including two of paramount importance (concerning human populations and education), seven identifying specific scientific activities to better equip us for stewardship of the processes of evolution, and one suggesting that such stewardship is now our responsibility. The ultimate test of evolutionary biology as a science is not whether it solves the riddles of the past but rather whether it enables us to manage the future of the biosphere. Our inability to make clearer predictions about the future of evolution has serious consequences for both biodiversity and humanity.