The paper, by William Basener and John Sanford, shows that the continuous flow of new mutations that would continuously replenish a population’s genetic variability and enable Darwinian evolution does not really happen. (Paper.)

Much discussion has followed here and here.

Basener has replied to Bob O’H, and for reader convenience, we are reproducing the comments here:

First, Bob O’H:

tjguy – The maths isn’t troubling (except that I’ sure they could have gone further). The simulation section shows that fitness can decrease, but we already knew this. Basener & Sanford don’t say what mutation rate they use though.

It’s obvious, I think, that the paper will be used to claim that mutations mean that evolution can’t work, so it’s a shame they don’t provide such an important parameter.

William Basener replies:

Bob O’H, RE 17: Your question regarding the mutation rate we used in the paper is pertinent. As you stated it has long been known that a high mutation rate can lead to decline in fitness while a low mutation rate allows for adaptation, observed in biological populations and mutation-selection models in the literature discussed in Section 2.2 (differential equations with an infinite-population). Thank you for the good question.

The mutation rate used in the paper is 1 mutation per generation. As with all the parameters in the paper we chose this parameter so that if there is any bias, the parameter selection favors selection and increasing fitness.

This is in the mathematics in the paper, but you are certainly correct that we did not state this as the mutation rate and that would have been helpful to readers. In the math, Equation 5.1 for $f_{i,j}$ is the probability distribution provided by Kimura to estimate the effect of a single mutation on fitness. We modify this distribution to add beneficial mutations (at a rate and magnitude that are greater than observed estimates), and this is used as the net effect of all mutations for $f_{i,j}$ in Equation 3.2.

Anyone who wishes to explore parameters can use the JavaScript simulation I posted at my RIT web page (referenced in the paper):

https://people.rit.edu/wfbsma/evolutionary%20dynamics/EvolutionaryModel.html

This was used to create the figures in the paper, and thus provides full transparency and opportunity to validate/reproduce/modify our results.

I agree with you that it would have been nice to go further with the math, and done an exploration of the parameters space. But the paper is at 34 pages, and we wanted to provide proper support for the model (hence the beefy literature review in Section 2) and give proper context with regards to Fisher. I think you and I agree that determining behavior for parameters spanning the space of realistic values is an important next step. I think it would beneficial to have multiple different groups explore results for varying parameters.

We’ll keep readers posted re further discussions.

The discussion on this point continues in the comments below, with Bob O’H at 1.

This is Bob O’Hara:

My career has been dedicated to discovering whether I am a biologist or a statistician – I intend to retire once I come to a definite answer. Most of my work has been on ecology and evolution, using statistical methods to put data and models together to try to learnmore about the real world.

My main interest at the moment is the development of methods to model the distributions and dynamics of species an communities, where we have a variety of data sources that need to be respected, and models of the unobserved true distributions and dynamics from which we want to infer what drives the distributions of species, and oredict how this will change in the near future.

*See also:* “Fisher’s Proof of Darwinism Has Been Flipped” paper is making waves – Twitter displeased

and

Fisher’s proof of Darwinian evolution has been flipped?