Population Genetics
Numerical Population Genetics and Mendel’s Accountant
The traditional approach that population geneticists have used since the 1930’s to understand how mutation and selection affect population dynamics is by hand solution (that is, with pencil and paper) of analytical equations. However, advances in numerical simulation and the wide availability of inexpensive computational resources have made possible an alternative way to investigate how the genetic makeup of populations change over time. Numerical simulation offers the power and flexibility to treat complex biological situations for which the traditional pencil and paper approach would be cumbersome, if not impossible. Numerical simulation allows investigation of complex interactions of large numbers of biological parameters simultaneously. The numerical approach also provides great flexibility and allows a researcher or student to explore parameter space quite rapidly, without detailed expertise in specialized mathematical techniques on which the traditional approach has come to rely.
Aware of the benefits of the numerical approach, in 2005 Dr. John Sanford, a Cornell geneticist, assembled a small team to create such a numerical population genetics program. The team consisted of Sanford, John Baumgardner, Wes Brewer, Paul Gibson, and Walter ReMine. Most of the development of the code took place at the Institute for Creation Research located in Santee, CA. The program came to be named Mendel’s Accountant.
Mendel’s Accountant was written to provide a biologically realistic forward-time numerical simulation of mutation accumulation in a population of sexually reproducing diploid organisms (the option for asexual organisms was added later). This innovative software for the first time simultaneously included natural mutation distributions, environmental variance, treatment of chromosomal linkage/recombination, and a continuous range of mutational fitness effects from lethal to beneficial and varying in expression from fully dominant to fully recessive. Notably, the program was designed to track extreme numbers of distinct individual mutations in a detailed manner from parents to progeny through large numbers of generations. Each mutation’s unique identifier encodes its genotypic fitness effect, whether it is recessive or dominant, and its location within the genome (the specific linkage block where it resides within a specific chromosome). This allows realistic treatment of linkage of mutations along segments of chromosomes.
The following papers provide a sampling of the history of contributions Mendel’s Accountant has made to understanding how the processes of mutation and selection alter the fitness of a population under a variety of circumstances. In what follows, we will often refer to the program simply as “Mendel.”
The traditional approach that population geneticists have used since the 1930’s to understand how mutation and selection affect population dynamics is by hand solution (that is, with pencil and paper) of analytical equations. However, advances in numerical simulation and the wide availability of inexpensive computational resources have made possible an alternative way to investigate how the genetic makeup of populations change over time. Numerical simulation offers the power and flexibility to treat complex biological situations for which the traditional pencil and paper approach would be cumbersome, if not impossible. Numerical simulation allows investigation of complex interactions of large numbers of biological parameters simultaneously. The numerical approach also provides great flexibility and allows a researcher or student to explore parameter space quite rapidly, without detailed expertise in specialized mathematical techniques on which the traditional approach has come to rely.
Aware of the benefits of the numerical approach, in 2005 Dr. John Sanford, a Cornell geneticist, assembled a small team to create such a numerical population genetics program. The team consisted of Sanford, John Baumgardner, Wes Brewer, Paul Gibson, and Walter ReMine. Most of the development of the code took place at the Institute for Creation Research located in Santee, CA. The program came to be named Mendel’s Accountant.
Mendel’s Accountant was written to provide a biologically realistic forward-time numerical simulation of mutation accumulation in a population of sexually reproducing diploid organisms (the option for asexual organisms was added later). This innovative software for the first time simultaneously included natural mutation distributions, environmental variance, treatment of chromosomal linkage/recombination, and a continuous range of mutational fitness effects from lethal to beneficial and varying in expression from fully dominant to fully recessive. Notably, the program was designed to track extreme numbers of distinct individual mutations in a detailed manner from parents to progeny through large numbers of generations. Each mutation’s unique identifier encodes its genotypic fitness effect, whether it is recessive or dominant, and its location within the genome (the specific linkage block where it resides within a specific chromosome). This allows realistic treatment of linkage of mutations along segments of chromosomes.
The following papers provide a sampling of the history of contributions Mendel’s Accountant has made to understanding how the processes of mutation and selection alter the fitness of a population under a variety of circumstances. In what follows, we will often refer to the program simply as “Mendel.”
2007 Proceedings of the 7th International Conference on Computer Science
This paper applies Mendel to study mutation accumulation in the human population. Using realistic estimates for the relevant biological parameters, the results show that deleterious mutations accumulate steadily, linear with generation count, across a large portion of the relevant parameter space. This is because the vast majority of deleterious mutations have fitness effects too small for the selection process to eliminate. The problem of mutation accumulation and consequent fitness decline becomes extreme when mutation rates are high. These numerical simulations strongly support earlier theoretical and mathematical studies which indicate that mutation accumulation in the current human population ought to be of serious concern.
2007 Using Computer Simulation to Understand Mutation Accumulation Dynamics and Genetic Load
2007 Scalable Computing: Practice and Experience
This paper provides a detailed description of the features and capabilities of Mendel as a user-friendly biologically realistic simulation program for investigating the processes of mutation and selection in sexually reproducing diploid populations. New features include variable mutation effect and environmental variance that affects phenotype. In Mendel, as in nature, mutations have a continuous range of effect from lethal to beneficial and may vary in expression from fully dominant to fully recessive. Mendel allows mutational effects to be combined in either a multiplicative or additive manner and provides the option of either truncation or probability selection. Environmental variance is specified via a heritability parameter and a non-scaling noise standard deviation. Mendel is computationally efficient, so many problems of interest can be run on ordinary personal computers. Parallelized using MPI, Mendel readily handles large population sizes and population substructure on cluster computers. The paper reports a series of validation experiments which show consistently that Mendel results conform to theoretical predictions. Its graphical user interface is designed to make problem specification intuitive and simple, and it provides a variety of visual representations in the program output. The program is a versatile research tool and is useful also as an interactive teaching resource.
2007 Mendel's Accountant: A Biologically Realistic Forward - Time Population Genetics Program
2008 Proceedings of the 6th International Conference on Creationism
Mendel is a state-of-the-art forward-time population genetics model that tracks millions of individual mutations with their unique effects on fitness and unique location within the genome through large numbers of generations. It treats the process of natural selection in a precise way. It allows a user to choose values for a large number of parameters such as those specifying the mutation effect distribution, reproduction rate, population size, and variations in environmental conditions. Mendel is thus a versatile and capable research tool that can be applied to problems in human genetics, plant and animal breeding, and management of endangered species. With its user-friendly graphical user interface and its ability to run on laptop computers it can also be fruitfully employed in teaching genetics and genetic principles, even at a high school level. Mendel is freely available to users and can be downloaded from the web. When biologically realistic parameters are selected, Mendel shows consistently that genetic deterioration is an inevitable outcome of the processes of mutation and natural selection. The primary reason is that most deleterious mutations are too subtle to be detected and eliminated by natural selection and therefore accumulate steadily generation after generation and inexorably degrade fitness.
2008 Mendel’s Accountant: A New Population Genetics Simulation Tool for Studying Mutation and Natural Selection
2008 Proceedings of the 6th International Conference on Creationism
Evolutionary genetic theory has a series of apparent “fatal flaws” which are well known to population geneticists, but which have not been effectively communicated to other scientists or the public. While population geneticists have generally been highly reluctant to acknowledge these theoretical problems openly, numerical simulation now provides a definitive tool for demonstrating the reality of these flaws. The program Mendel’s Accountant was developed for this purpose. When any reasonable set of biological parameters is used, Mendel provides overwhelming empirical evidence that all of the apparent fatal flaws inherent in evolutionary genetic theory are real. This leaves evolutionary genetic theory effectively falsified—with a degree of certainty which should satisfy any reasonable and open-minded person.
2008 Using Numerical Simulation to Test the Validity of Neo-Darwinian Theory
2013 Biological Information — New Perspectives
Most deleterious mutations have very slight effects on total fitness, and it has become clear that below a certain fitness effect threshold, such low-impact mutations fail to respond to natural selection. The existence of such a selection threshold suggests that many low-impact deleterious mutations should accumulate continuously, resulting in relentless erosion of genetic information. In this paper, we apply the program Mendel’s Accountant to examine the issue of selection threshold, which we define as the fitness effect for which deleterious mutations accumulate at exactly half the rate expected in the absence of selection. Our investigations reveal that under a very wide range of parameter values, selection thresholds for deleterious mutations are surprisingly high. Our analyses indicate that even with minimal levels of noise accumulation of low-impact mutations persistently degrades fitness and this degradation is far more serious than has been previously acknowledged. Indeed, we find that under most realistic circumstances, the large majority of harmful mutations are essentially unaffected by natural selection and continue to accumulate unhindered. This finding has major theoretical implications and raises the question, “What mechanism can preserve the many low-impact nucleotide positions that constitute most of the information within a genome?”
2013 Can Purifying Natural Selection Preserve Biological Information?
2013 Biological Information — New Perspectives
There is now abundant evidence that the continuous accumulation of deleterious mutations within natural populations poses a major problem for neo-Darwinian theory. It has been proposed that a viable evolutionary mechanism for halting the accumulation of deleterious mutations might arise if fitness depends primarily on an individual’s “mutation-count”. In this paper the hypothetical “mutation-count mechanism” (MCM) is tested using Mendel’s Accountant to determine the viability of the hypothesis and to determine what biological factors affect the relative efficacy of this mechanism. The MCM is shown to be very strong when all the following un-natural conditions occur together: mutations all have an equal effect, environmental variance is small, and full truncation type of selection applies. By contrast, the MCM effect disappears when any one of the following natural conditions is present: probability selection applies, fitness effects obey a natural distribution that span several orders of magnitude, realistic levels of environmental variance exist, or reproduction is asexual. Because MCM is not capable of halting deleterious mutation accumulation except in highly artificial circumstances, it cannot be invoked as a general rescue device for neo-Darwinian theory.
2013 Using Numerical Simulation to Test the “Mutation-Count” Hypothesis
2013 Biological Information — New Perspectives
In a companion paper in this volume, we applied Mendel’s Accountant to demonstrate that there is a quantifiable selection threshold, below which low-impact deleterious mutations escape purifying selection and therefore accumulate without limit. In this paper we apply Mendel’s Accountant to determine whether or not a selection threshold also exists for beneficial mutations. When biologically reasonable parameters are employed except for the beneficial mutation rate (which we choose to be many orders of magnitude higher than observed to be able to study the effect), we find that selection threshold for beneficial mutations indeed exists. We find that this threshold is sufficiently high that the overwhelming majority of beneficial mutations that arise are not amplified in frequency by the selection process and therefore, like most deleterious mutations, are unselectable. We find that the selection threshold for beneficial mutations is similar in magnitude to the selection threshold for deleterious ones. Most functional nucleotides in a large genome have fractional contributions to fitness far, far smaller than the selection thresholds we compute. The obvious implication is that the explanation for the origin of the typical functional nucleotide lies outside the framework of neo-Darwinian theory.
2013 Selection Threshold Severely Constrains Capture of Beneficial Mutations
2013 Biological Information — New Perspectives
The phenomenon of mutations interacting with one another to yield increased effects on fitness is known as synergistic epistasis (SE). Many population geneticists have argued that SE should enhance selective elimination of mutations and thereby diminish the problem of genetic degeneration. We apply numerical simulation to test this non-intuitive perception. We find that under biologically realistic conditions, synergistic epistasis exerts little to no discernible influence on mutation accumulation and genetic degeneration. When the synergistic effect is greatly exaggerated, mutation accumulation is not significantly affected, but genetic degeneration accelerates markedly. As the synergistic effect is exaggerated still more, degeneration becomes catastrophic and leads to rapid extinction. Our results therefore strongly argue that the belief held by many in the population genetics community that synergistic epistasis can halt mutation accumulation is incorrect.
2013 Can Synergistic Epistasis Halt Mutation Accumulation? Results from Numerical Simulation
2015 Theoretical Biology and Medical Modelling
This paper applies numerical simulation to explore the time scale required to fix short, specific nucleotide strings via the processes of random mutation and selection in a human-like population. The program Mendel’s Accountant was modified so that both a starting string of nucleotides as well as a target string could be specified. We assumed population sizes of 10,000 and greater, a generation time of 20 years, and very strong selection (50% of the offspring eliminated each generation). Random point mutations were introduced within the string in random individuals each generation. Whenever an instance of the target string arose, all individuals carrying the target string were assigned a specified reproductive advantage. When natural selection had successfully amplified an instance of the target string to the point of fixation, the experiment was halted, and the waiting time statistics were tabulated. Using this methodology we tested the effect of mutation rate, string length, fitness benefit, and population size on waiting time to fixation. These simulations revealed that a population of this type requires extreme waiting times to fix even the shortest nucleotide strings. For example, fixing a string of two nucleotides requires on average 84 million years! Fixing a string of five nucleotides requires on average 2 billion years. We found that waiting times are reduced by higher mutation rates, stronger fitness benefit, and larger population sizes. However, even using the most generous plausible parameters settings, the resulting extreme waiting times imply that the human genome is hopelessly beyond the reach of random mutation and selection to explain.
2015 The Waiting Time Problem in a Model Hominin Population
2018 Proceedings of the 8th International Conference on Creationism
Two arguments today involving genetics against a literal Adam and Eve are, first, that it is impossible for a single human couple to give rise to the genetic diversity seen in the modern human population and, second, that the currently observed human allele frequency patterns could not arise from a single couple. In this paper we apply numerical simulation to examine these two assertions. Our analyses highlight the genetic mechanisms that do account for the human allele frequency distributions seen today beginning from a literal Adam and Eve who lived only about 200 generations ago. We show that two people, if they contain designed alleles and a modest level of heterozygosity, can after only 200 generations indeed give rise to allele frequency distributions of the very same type as are now seen in the human population.
2018 Adam and Eve, Designed Diversity, and Allele Frequencies
This paper applies Mendel to study mutation accumulation in the human population. Using realistic estimates for the relevant biological parameters, the results show that deleterious mutations accumulate steadily, linear with generation count, across a large portion of the relevant parameter space. This is because the vast majority of deleterious mutations have fitness effects too small for the selection process to eliminate. The problem of mutation accumulation and consequent fitness decline becomes extreme when mutation rates are high. These numerical simulations strongly support earlier theoretical and mathematical studies which indicate that mutation accumulation in the current human population ought to be of serious concern.
2007 Using Computer Simulation to Understand Mutation Accumulation Dynamics and Genetic Load
2007 Scalable Computing: Practice and Experience
This paper provides a detailed description of the features and capabilities of Mendel as a user-friendly biologically realistic simulation program for investigating the processes of mutation and selection in sexually reproducing diploid populations. New features include variable mutation effect and environmental variance that affects phenotype. In Mendel, as in nature, mutations have a continuous range of effect from lethal to beneficial and may vary in expression from fully dominant to fully recessive. Mendel allows mutational effects to be combined in either a multiplicative or additive manner and provides the option of either truncation or probability selection. Environmental variance is specified via a heritability parameter and a non-scaling noise standard deviation. Mendel is computationally efficient, so many problems of interest can be run on ordinary personal computers. Parallelized using MPI, Mendel readily handles large population sizes and population substructure on cluster computers. The paper reports a series of validation experiments which show consistently that Mendel results conform to theoretical predictions. Its graphical user interface is designed to make problem specification intuitive and simple, and it provides a variety of visual representations in the program output. The program is a versatile research tool and is useful also as an interactive teaching resource.
2007 Mendel's Accountant: A Biologically Realistic Forward - Time Population Genetics Program
2008 Proceedings of the 6th International Conference on Creationism
Mendel is a state-of-the-art forward-time population genetics model that tracks millions of individual mutations with their unique effects on fitness and unique location within the genome through large numbers of generations. It treats the process of natural selection in a precise way. It allows a user to choose values for a large number of parameters such as those specifying the mutation effect distribution, reproduction rate, population size, and variations in environmental conditions. Mendel is thus a versatile and capable research tool that can be applied to problems in human genetics, plant and animal breeding, and management of endangered species. With its user-friendly graphical user interface and its ability to run on laptop computers it can also be fruitfully employed in teaching genetics and genetic principles, even at a high school level. Mendel is freely available to users and can be downloaded from the web. When biologically realistic parameters are selected, Mendel shows consistently that genetic deterioration is an inevitable outcome of the processes of mutation and natural selection. The primary reason is that most deleterious mutations are too subtle to be detected and eliminated by natural selection and therefore accumulate steadily generation after generation and inexorably degrade fitness.
2008 Mendel’s Accountant: A New Population Genetics Simulation Tool for Studying Mutation and Natural Selection
2008 Proceedings of the 6th International Conference on Creationism
Evolutionary genetic theory has a series of apparent “fatal flaws” which are well known to population geneticists, but which have not been effectively communicated to other scientists or the public. While population geneticists have generally been highly reluctant to acknowledge these theoretical problems openly, numerical simulation now provides a definitive tool for demonstrating the reality of these flaws. The program Mendel’s Accountant was developed for this purpose. When any reasonable set of biological parameters is used, Mendel provides overwhelming empirical evidence that all of the apparent fatal flaws inherent in evolutionary genetic theory are real. This leaves evolutionary genetic theory effectively falsified—with a degree of certainty which should satisfy any reasonable and open-minded person.
2008 Using Numerical Simulation to Test the Validity of Neo-Darwinian Theory
2013 Biological Information — New Perspectives
Most deleterious mutations have very slight effects on total fitness, and it has become clear that below a certain fitness effect threshold, such low-impact mutations fail to respond to natural selection. The existence of such a selection threshold suggests that many low-impact deleterious mutations should accumulate continuously, resulting in relentless erosion of genetic information. In this paper, we apply the program Mendel’s Accountant to examine the issue of selection threshold, which we define as the fitness effect for which deleterious mutations accumulate at exactly half the rate expected in the absence of selection. Our investigations reveal that under a very wide range of parameter values, selection thresholds for deleterious mutations are surprisingly high. Our analyses indicate that even with minimal levels of noise accumulation of low-impact mutations persistently degrades fitness and this degradation is far more serious than has been previously acknowledged. Indeed, we find that under most realistic circumstances, the large majority of harmful mutations are essentially unaffected by natural selection and continue to accumulate unhindered. This finding has major theoretical implications and raises the question, “What mechanism can preserve the many low-impact nucleotide positions that constitute most of the information within a genome?”
2013 Can Purifying Natural Selection Preserve Biological Information?
2013 Biological Information — New Perspectives
There is now abundant evidence that the continuous accumulation of deleterious mutations within natural populations poses a major problem for neo-Darwinian theory. It has been proposed that a viable evolutionary mechanism for halting the accumulation of deleterious mutations might arise if fitness depends primarily on an individual’s “mutation-count”. In this paper the hypothetical “mutation-count mechanism” (MCM) is tested using Mendel’s Accountant to determine the viability of the hypothesis and to determine what biological factors affect the relative efficacy of this mechanism. The MCM is shown to be very strong when all the following un-natural conditions occur together: mutations all have an equal effect, environmental variance is small, and full truncation type of selection applies. By contrast, the MCM effect disappears when any one of the following natural conditions is present: probability selection applies, fitness effects obey a natural distribution that span several orders of magnitude, realistic levels of environmental variance exist, or reproduction is asexual. Because MCM is not capable of halting deleterious mutation accumulation except in highly artificial circumstances, it cannot be invoked as a general rescue device for neo-Darwinian theory.
2013 Using Numerical Simulation to Test the “Mutation-Count” Hypothesis
2013 Biological Information — New Perspectives
In a companion paper in this volume, we applied Mendel’s Accountant to demonstrate that there is a quantifiable selection threshold, below which low-impact deleterious mutations escape purifying selection and therefore accumulate without limit. In this paper we apply Mendel’s Accountant to determine whether or not a selection threshold also exists for beneficial mutations. When biologically reasonable parameters are employed except for the beneficial mutation rate (which we choose to be many orders of magnitude higher than observed to be able to study the effect), we find that selection threshold for beneficial mutations indeed exists. We find that this threshold is sufficiently high that the overwhelming majority of beneficial mutations that arise are not amplified in frequency by the selection process and therefore, like most deleterious mutations, are unselectable. We find that the selection threshold for beneficial mutations is similar in magnitude to the selection threshold for deleterious ones. Most functional nucleotides in a large genome have fractional contributions to fitness far, far smaller than the selection thresholds we compute. The obvious implication is that the explanation for the origin of the typical functional nucleotide lies outside the framework of neo-Darwinian theory.
2013 Selection Threshold Severely Constrains Capture of Beneficial Mutations
2013 Biological Information — New Perspectives
The phenomenon of mutations interacting with one another to yield increased effects on fitness is known as synergistic epistasis (SE). Many population geneticists have argued that SE should enhance selective elimination of mutations and thereby diminish the problem of genetic degeneration. We apply numerical simulation to test this non-intuitive perception. We find that under biologically realistic conditions, synergistic epistasis exerts little to no discernible influence on mutation accumulation and genetic degeneration. When the synergistic effect is greatly exaggerated, mutation accumulation is not significantly affected, but genetic degeneration accelerates markedly. As the synergistic effect is exaggerated still more, degeneration becomes catastrophic and leads to rapid extinction. Our results therefore strongly argue that the belief held by many in the population genetics community that synergistic epistasis can halt mutation accumulation is incorrect.
2013 Can Synergistic Epistasis Halt Mutation Accumulation? Results from Numerical Simulation
2015 Theoretical Biology and Medical Modelling
This paper applies numerical simulation to explore the time scale required to fix short, specific nucleotide strings via the processes of random mutation and selection in a human-like population. The program Mendel’s Accountant was modified so that both a starting string of nucleotides as well as a target string could be specified. We assumed population sizes of 10,000 and greater, a generation time of 20 years, and very strong selection (50% of the offspring eliminated each generation). Random point mutations were introduced within the string in random individuals each generation. Whenever an instance of the target string arose, all individuals carrying the target string were assigned a specified reproductive advantage. When natural selection had successfully amplified an instance of the target string to the point of fixation, the experiment was halted, and the waiting time statistics were tabulated. Using this methodology we tested the effect of mutation rate, string length, fitness benefit, and population size on waiting time to fixation. These simulations revealed that a population of this type requires extreme waiting times to fix even the shortest nucleotide strings. For example, fixing a string of two nucleotides requires on average 84 million years! Fixing a string of five nucleotides requires on average 2 billion years. We found that waiting times are reduced by higher mutation rates, stronger fitness benefit, and larger population sizes. However, even using the most generous plausible parameters settings, the resulting extreme waiting times imply that the human genome is hopelessly beyond the reach of random mutation and selection to explain.
2015 The Waiting Time Problem in a Model Hominin Population
2018 Proceedings of the 8th International Conference on Creationism
Two arguments today involving genetics against a literal Adam and Eve are, first, that it is impossible for a single human couple to give rise to the genetic diversity seen in the modern human population and, second, that the currently observed human allele frequency patterns could not arise from a single couple. In this paper we apply numerical simulation to examine these two assertions. Our analyses highlight the genetic mechanisms that do account for the human allele frequency distributions seen today beginning from a literal Adam and Eve who lived only about 200 generations ago. We show that two people, if they contain designed alleles and a modest level of heterozygosity, can after only 200 generations indeed give rise to allele frequency distributions of the very same type as are now seen in the human population.
2018 Adam and Eve, Designed Diversity, and Allele Frequencies