A new peer-reviewed paper in the Journal of Theoretical Biology, “On the waiting time until coordinated mutations get fixed in regulatory sequences,” is authored by three key scientists in the intelligent design (ID) research program: Ola Hössjer, Günter Bechly, Ann Gauger. The paper is part of the “Waiting Times” project, spurred by Discovery Institute as part of its ID 3.0 initiative, and it investigates a question of vital interest to the theory of intelligent design: How long does it take for traits to evolve when multiple mutations are required to give an advantage? A previous peer-reviewed publication from this team appeared as a chapter in the 2018 Springer volume Stochastic Processes and Applications. This latest paper is lengthy, technical, and math intensive. In other words, it’s not for the fainthearted, but it’s open access and free to read here. If you feel up to the challenge download and read! 

Exponential Increase

The basic mathematical principles behind the paper aren’t too hard to appreciate. The idea is that as more nucleotides need to be present (fixed) in order to generate some trait, the amount of time required for those mutations to appear goes up at an exponential rate. To see why, let’s say that you have a huge bag of blue and red marbles, always distributed in equal numbers in the bag. You want to pick out varying numbers of consecutive blue marbles. If you want to pick just one blue marble, the likelihood of doing this by chance is 1/2. If you want to pick out two blue marbles in a row the likelihood is 1/4. The likelihood of obtaining 3 blue marbles in a row is 1/8.  

Now let’s convert these odds to “waiting times.” Let’s say that you can pick 1 marble per second. On average it will take 2 seconds to obtain 1 blue marble. To obtain two consecutive blue marbles you’d need 4 seconds. To pick 3 blue marbles in a row you’d need 8 seconds, and so on. You can see that the waiting time (T) to pick N consecutive blue marbles is approximated as follows: 

T = 2^N marbles * 1 second / marble

The more consecutive blue marbles you have to pick, the longer the waiting time for the event to occur — and the waiting time increases at an exponential rate with each additional marble that’s required. 

Now let’s go back to the paper. It opens by observing that “A classical problem of population genetics is to study the time until new genetic variants first appear through germline mutations and then get fixed, i.e. spread to all individuals of a species, as it adapts to a new environment and evolves over time.” It notes that in previous studies “analyzing evolution of whole DNA sequences of nucleotides of length L, written on the four letter alphabet A, C, G, T,” the waiting time where each is neutral (i.e., gives no selective advantage) “increases either polynomially or exponentially with L.” (A “polynomial” increase refers to a value that depends on the sum of multiple terms, where at least one of the terms has an exponent.) 

Coordinated Mutations

This paper develops a complex mathematical model for calculating the waiting time for the evolution of a trait that requires L nucleotides in order to function. Although this is strictly a methodological paper, one potential application could be the evolution of regulatory regions which control the expression of a gene. Changes to transcription are thought to be important to evolving new body plans or biological systems. Regulatory regions such as enhancers or promoters may have a length of 1000 nucleotides, and for expression to occur special proteins called transcription factors must bind to these regulatory regions at binding sites, which may be 6 to 10 nucleotides in length. They explain how this works:

The waiting time until the expression of the gene changes, is modeled as the time until the random walk hits the target, and it depends on the mutation rate, the selective advantage of the mutated regulatory sequence, the size of the population, the length of the regulatory sequence and the length of the binding site.

However, evolving new traits is often far more complex than simply changing the expression of a single gene. Many traits are controlled by multiple genes, and the traits won’t arise until expression of those genes is modified in a coordinated manner. The paper explains how their model might be applied to such an evolutionary question:

For more complex adaptations of a species, it is necessary that several genes are modified in a coordinated manner, either through mutations in the coding sequence, or through changed expression of these m genes. … In this paper we focus on the coordinated evolution of gene expression of existing genes, and ask the question how long time T_m it would take for a species to change the expression of m distinct genes. This corresponds to the time it would take for the required binding sites, in the regulatory sequences of m distinct genes, to evolve in a coordinated way. The microevolutionary process is then a random walk on a fitness landscape of regulatory arrays, that is, a random walk on mx L matrices, whose rows are the regulatory sequences of all m genes.

In other words, the paper calculates how long it would take for m genes to evolve new regulatory sequences by chance, assuming that such changes in the expression of all of these genes would be required for some new complex adaptation to arise. 

Abrupt Appearance

Do we have evidence that traits appear abruptly in the fossil record, and that these sorts of calculations apply? The introduction to the paper provides a rich review of examples of this from biological history, showing that their model is highly applicable to biological reality:

For instance, the fossil record is often interpreted as having long periods of stasis, interrupted by more abrupt changes and “explosive” origins. These changes include, for instance, the evolution of life, photo-synthesis, multicellularity and the “Avalon Explosion”, animal body plans and the “Cambrian Explosion”, complex eyes, vertebrate jaws and teeth, terrestrialization (e.g., in vascular plants, arthropods, and tetrapods), insect metamorphosis, animal flight and feathers, reproductive systems, including angiosperm flowers, amniote eggs, and the mammalian placenta, echolocation in whales and bats, and even cognitive skills of modern man. Based on radiometric dating of the available windows of time in the fossil record, these genetic changes are believed to have happened very quickly on a macroevolutionary timescale. In order to evaluate the chances for a neo-Darwinian process to bring about such major phenotypic changes, it is important to give rough but reasonable estimates of the time it would take for a population to evolve so that the required multiple genetic changes occur. (internal citations omitted)

There is thus ample precedent for investigating such a question in biohistory. Many complex features of living organisms appear abruptly in the fossil record, where it seems that multiple coordinated changes were necessary before any advantageous functional trait arose. The mathematical model developed in this paper is aptly suited to understanding how long it would take for such a trait to arise. 

As I noted, this paper is methodological, meaning it’s only developing a mathematical model and not yet applying it to real world biological systems. One hopes in the future the team will apply their model to real biological systems. We will then see what the implications are for the viability of standard evolutionary mechanisms to account for the origin of such traits.