Researchers from Indian Institute of Science Education and Research (IISER) Pune propose a change in the way epidemiologists estimate the growth and adaptation rate of bacteria. The paper, to be published in Evolutionary Biology, poses this challenge to both theoreticians and experimentalists who are studying the growth of asexual populations subject to periodic bottlenecks.
Bacteria enter the body of a host organism and multiply into billions. But the population is not steadily growing within the body. There are periodic instances, known as bottlenecks, when they are purged in huge numbers. This could be, for example, when the host sneezes or defecates. On these occasions the bacteria gets into the body of a second host and spreads there. So the number of bacteria in the first host decreases considerably at the time of bottlenecks. In performing calculations, it is of interest to know which number to take as the estimate of population size of the bacteria, as this will also decide how they grow and proliferate. This size is related to and directly affects the extent or rate of adaptation, which is a measure of how much a trait has changed compared to the ancestor. The rate or extent of adaptation is ultimately the quantity that researchers seek to estimate or measure.
Harmonic mean
A longstanding assumption made by researchers is that a quantity called the harmonic mean decides the rate of adaptation of the bacteria. The harmonic mean is the product of the population size at the bottleneck ( N O ) and the number of generations between two successive bottlenecks ( g ). However, there has been no empirical or theoretical test for the validity of the harmonic mean as a predictor of the extent of adaptation.
“As a starting point, we performed experiments on E. coli populations to test if the harmonic mean of population size ( N O g ) can predict extent of adaptation. Our experiments revealed that this does not hold,” says Sutirth Dey of IISER Pune who is an author of the paper.
Knowing the extent of adaptation is of interest, both theoretically and practically. When epidemiologists estimate the way a disease spreads, they frequently have to make predictions about the rate at which various types of bacteria will evolve under different conditions.
The researchers then simulated the growth of asexual populations (those that multiply via fission) using their proposed model and found g, the number of generations between bottlenecks, to have a complex relationship with the rate of adaptation. While it partly enhances the extent of adaptation, they also obtained the counter-intuitive result that higher values of g decreased the extent of adaptation. This is counter-intuitive, because when there are more generations between two bottlenecks, it would appear that there are more fissions, and hence a greater scope for variation and adaptation. Because of this they propose in this paper that rather than using N O g , the factor N O /g where g varies inversely should be used to calculate extent of adaptation.
“We have not yet provided an analytical proof for this – we are working on it. Meanwhile this result is an invitation for theoreticians and experimentalists to re-examine some fundamental assumptions about how bacteria evolve,” says Dr Dey.
