Conference PaperPDF Available

Using Computer Simulation to Understand Mutation Accumulation Dynamics and Genetic Load

May 2007
Lecture Notes in Computer Science

DOI:10.1007/978-3-540-72586-2_55

Source
DBLP

Conference: Computational Science - ICCS 2007, 7th International Conference, Beijing, China, May 27 - 30, 2007, Proceedings, Part II

Authors:

John Sanford

Cornell University

John Baumgardner

Logos Research Associates

Wes Brewer

Computational Solutions LLC

Paul T. Gibson

Makerere University

Show all 5 authorsHide

Long-standing theoretical concerns about mutation accumulation within the human population can now be addressed with numerical simulation. We apply a biologically realistic forward-time population genetics program to study human mutation accumulation under a wide-range of circumstances. Using realistic estimates for the relevant biological parameters, we investigate the rate of mutation accumulation, the distribution of the fitness effects of the accumulating mutations, and the overall effect on mean genotypic fitness. Our numerical simulations consistently show that deleterious mutations accumulate linearly across a large portion of the relevant parameter space. This appears to be primarily due to the predominance of nearly-neutral mutations. The problem of mutation accumulation becomes severe when mutation rates are high. Numerical simulations strongly support earlier theoretical and mathematical studies indicating that human mutation accumulation is a serious concern. Our simulations indicate that reduction of mutation rate is the most effective means for addressing this problem.

(a) Mutation count per individual and (b) mean population fitness, plotted for 5,000 generations. (a) shows that deleterious mutations accumulate in close to a strict linear fashion (reaching 47,730-scale on left). Beneficial mutations also accumulate in a linear manner, but their lower number results in sampling error fluctuations (reaching 498-scale on right). (b) shows a progressive decline in population fitness.

…

Distributions of accumulating mutations are shown above. Red bins represent the expected mutation accumulation when no selection is applied. Blue bins represent actual accumulation of recessive mutations. Green bins represent actual accumulation of dominant mutations. The magnitude of each mutation’s effect is shown on the x-axis, which is a linear scale. The bin nearest zero represents mutations which change fitness by a factor between .0001 and .00001. Mutations with a magnitude of less than .00001 were not tracked or plotted.

…

Mutant allele frequencies are shown above, with rare alleles (<1%) on the far left, and fixed or nearly fixed alleles (>99%) on the far right. Deleterious mutations are shown in red, beneficial mutations are shown in green. In this instance 5,845 deleterious mutations have been fixed after 5,000 generations. No beneficial mutations were fixed in this example.

…

Figures - uploaded by Paul T. Gibson

Content may be subject to copyright.

Content uploaded by Paul T. Gibson

Content may be subject to copyright.

Y. Shi et al. (Eds.): ICCS 2007, Part II, LNCS 4488, pp. 386–392, 2007.

Using Computer Simulation to Understand Mutation

Accumulation Dynamics and Genetic Load

John Sanford1, John Baumgardner2, Wes Brewer3, Paul Gibson4, and Walter ReMine5

1 Dept. Hort. Sci., Cornell University, Geneva, NY, 14456, USA

jcs21@cornell.edu

2 Los Alamos National Laboratory, Los Alamos, NM, USA, retired

3 Computational Engineering, Mississippi State University, MS, USA

4 Dept. Plant, Soil and Agric. Syst., Southern Illinois University, Carbondale, IL, USA

5 Science and Math Dept., Northwestern College, St. Paul, MN, USA

Abstract. Long-standing theoretical concerns about mutation accumulation

within the human population can now be addressed with numerical simulation.

We apply a biologically realistic forward-time population genetics program to

study human mutation accumulation under a wide-range of circumstances.

Using realistic estimates for the relevant biological parameters, we investigate

the rate of mutation accumulation, the distribution of the fitness effects of the

accumulating mutations, and the overall effect on mean genotypic fitness. Our

numerical simulations consistently show that deleterious mutations accumulate

linearly across a large portion of the relevant parameter space. This appears to

be primarily due to the predominance of nearly-neutral mutations. The problem

of mutation accumulation becomes severe when mutation rates are high.

Numerical simulations strongly support earlier theoretical and mathematical

studies indicating that human mutation accumulation is a serious concern. Our

simulations indicate that reduction of mutation rate is the most effective means

for addressing this problem.

Keywords: genetic load, Mendel’s Accountant, mutation accumulation,

population genetics, simulation.

1 Introduction

The problem of genetic load has concerned geneticists for over 50 years [1][2].

Theoretically, high mutation rates and the natural inefficiencies of selection both appear

to ensure the accumulation of deleterious mutations within the genomes of higher

organisms [3]. These concerns have been accentuated by the apparent reduction of

selection pressures within human populations within historical time frames [4]. All

these earlier concerns were based upon purely theoretical considerations.

Advances in computer science and the increasing power of simulation prog-

rams provide us with a new way of understanding the problem of mutation

accumulation. The use of numerical simulation allows us to test empirically previous

mathematical analyses, which are otherwise inherently abstract and difficult to test.

Using Computer Simulation to Understand Mutation Accumulation Dynamics 387

Such simulations allow us to examine in precise detail complex biological scenarios

which otherwise would require extreme simplification and generalization before any

type of mathematical analysis would be possible.

2 The Program

The computer program “Mendel’s Accountant” (hereafter referred to simply as

Mendel) has been developed to provide a biologically realistic forward-time

numerical simulation of mutation accumulation [5]. This is a highly flexible program

which for the first time effectively models natural mutation distributions,

environmental variance, and improved modeling of linkage/recombination. Mendel is

designed to model sexually reproducing diploid organisms. Mendel tracks individual

mutations in a detailed manner from parents to progeny through many generations.

Mutations are modeled so as to have a continuous range of effects from lethal to

beneficial and to vary in expression from fully dominant to fully recessive. 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. Mutational effects may be

combined either in a multiplicative or additive manner to yield an overall genotypic

fitness for each new offspring.

Mendel is designed to track large numbers of distinct mutations by using a single

four-byte integer word to store the mutation’s unique identifier. This allows up to

about four billion different unique mutations to be tracked in a given population. The

number of mutations per individual is limited by the available processor memory and

the population size before selection. As an example, 1.6 GB of memory available for

storing mutation identifiers translates into a maximum of 40,000 mutations in each of

10,000 individuals. Thus, Mendel is effectively an infinite sites model, in contrast

with k-allele and stepwise models that both impose highly restrictive limits on the

number and variety of mutations. Mendel offers the option of tracking only those

mutations whose fitness effect exceeds a user-specified threshold. This threshold

usually is chosen to lie in that region of extremely small mutation effect which is

beyond the reach of selection. Typically, we find that half to two-thirds of all

mutations lie in this un-selectable region. The fitness effects of the untracked

mutations under this option are nevertheless accounted for in the composite fitness

effect of the linkage block where the mutation occurs. This option allows the user to

investigate scenarios that involve two to three times more total mutations that would

be possible otherwise.

Mendel offers the important option of including the effects of environmental

variation. Environmental variance, specified via a heritability parameter and a non-

scaling noise standard deviation, combines with genotypic fitness to yield the

phenotypic fitness. Selection then acts on phenotypic fitness to eliminate that fraction

of the offspring (the population surplus) required to maintain the user-specified

population size. The surplus population is a consequence of the specified fertility, as

implied by the average number of offspring per female. Mendel provides the user the

388 J. Sanford et al.

choice of either natural selection (probability selection) or artificial selection

(truncation selection). Because Mendel is optimized for memory efficiency and speed,

many non-trivial scenarios can be run on a desktop or laptop computer. Moreover,

because Mendel is parallelized with MPI, it readily handles large population sizes and

complex population substructure on cluster computers. Mendel’s graphical user

interface is designed to make the specification of a scenario intuitive and simple,

while also providing a variety of visual representations of the program output. Mendel

is therefore a versatile research tool. It is also useful as an interactive teaching

resource for a variety of settings ranging from introductory courses in biology to more

advanced courses in population genetics.

3 Analysis

Mendel’s input parameters include: number of offspring per female, mutation rate,

fraction of mutations which are beneficial, fraction of mutations that are recessive,

high-impact mutation threshold, fraction of mutations with effect greater than

threshold (two parameters that specify the distribution of mutation effects), number of

linkage blocks, number of chromosomes, genome size, mutation effect combining

method, heritability of genotypic fitness, type of selection, number of generations, and

population size. Mendel’s output report is provided at regular generation intervals and

includes summary statistics on number and types of mutations, mean population

fitness, fitness standard deviation, and related information. In addition, data for each

generation is stored in various files and is also plotted in output figures.

In the example we present below, we employ the following input parameters:

number of offspring per female = 6 (4 surplus offspring selected away), mutation rate

= 10 per offspring, fraction of mutations which are beneficial = 0.01, fraction of

mutations that are recessive = 0.8, high-impact mutation threshold = 0.1, fraction of

mutations with effect greater than threshold = 0.001, number of linkage blocks =

1000, number of chromosomes = 23, genome size = 3 billion, mutation effect

combination method = multiplicative, heritability of genotypic fitness = 0.2, type of

selection = probability, number of generations = 5,000, and population size = 1000.

Although the current human population size is more than six billion, we have found

that population sizes above 1,000 result in only marginal increases in selection

efficiency. It is reasonable to expect that, beyond a certain level, larger population

size will not result in more efficient selection, because of increased environmental

variance.

Some of the output from this example is displayed in the following figures. Fig. 1a

shows the mean mutation count per individual plotted with respect to time. A

noteworthy aspect of this figure is a nearly exact linear accumulation of mutations, a

feature we observe consistently across a broad region of parameter space. The slope

of this line is governed primarily by the mutation rate. Selection intensity modifies the

slope of this line only to a limited degree. This is because of the preponderance of un-

selectable “nearly-neutral” deleterious mutations (as further described below).

Using Computer Simulation to Understand Mutation Accumulation Dynamics 389

Fig. 1. (a) Mutation count per individual and (b) mean population fitness, plotted for 5,000

generations. (a) shows that deleterious mutations accumulate in close to a strict linear fashion

(reaching 47,730–scale on left). Beneficial mutations also accumulate in a linear manner, but

their lower number results in sampling error fluctuations (reaching 498– scale on right). (b)

shows a progressive decline in population fitness.

390 J. Sanford et al.

Fig. 1b shows an initial non-linear genotypic fitness decline, which soon becomes

essentially a linear decline. We observe this pattern across most of the parameter

space we have explored. Mendel defines an individual’s genotypic fitness as 1.0 plus

the combined positive and negative effects of all the individual’s mutations. In this

case mutation effects are being combined multiplicatively. We have found that the

slope of this curve (fitness change over time) is determined primarily by three things

– the mutation rate, the average mutational effect, and the selection intensity.

Fig. 2 shows the distribution of mutation effects of accumulating deleterious

mutations. Mendel employs a distribution of mutation effects (prior to selection),

which reflects what is found in nature – a continuous distribution essentially

exponential in character. Input parameters such as genome size and the fraction of

high-impact mutations define the exact shape of the mutation-effect distribution

curve. Because of the shape of the mutation-effect curve, lethal mutations will always

be very rare, and a large fraction of deleterious mutations will have near-zero impact.

When strong selection is applied, regardless of the other input parameters, high

impact mutations are consistently eliminated quite effectively – especially the

dominant ones. However, across a wide range of parameter space the bins nearest to

Fig. 2. Distributions of accumulating mutations are shown above. Red bins represent the

expected mutation accumulation when no selection is applied. Blue bins represent actual

accumulation of recessive mutations. Green bins represent actual accumulation of dominant

mutations. The magnitude of each mutation’s effect is shown on the x-axis, which is a linear

scale. The bin nearest zero represents mutations which change fitness by a factor between .0001

and .00001. Mutations with a magnitude of less than .00001 were not tracked or plotted.

Using Computer Simulation to Understand Mutation Accumulation Dynamics 391

zero fill at essentially the same rate, regardless of whether or not selection is being

applied. Experimentally, these “nearly-neutral” mutations are consistently found to be

un-selectable – in accordance with mathematical theory [6][7]. Mutations with

intermediate levels of impact accumulate at intermediate rates. The transition zone

between selectable and un-selectable mutations is very wide, especially for recessive

mutations. The actual point at which mutations become un-selectable depends on

numerous input parameters, but is readily apparent in Mendel’s output for any given

scenario.

Fig. 3 shows that over time many alleles move toward fixation. The movement

toward fixation is extremely slow for both deleterious and beneficial mutations –

consistent with the mathematical predictions of Haldane [8]. However, over long

periods of time, even with intense selection, a significant number of deleterious

mutations consistently become fixed.

All these findings strongly support previous theoretical and mathematical analyses

[1], [3], [9], [10] which have predicted that deleterious mutation accumulation in the

human population is a very real biological concern.

Fig. 3. Mutant allele frequencies are shown above, with rare alleles (<1%) on the far left, and

fixed or nearly fixed alleles (>99%) on the far right. Deleterious mutations are shown in red,

beneficial mutations are shown in green. In this instance 5,845 deleterious mutations have been

fixed after 5,000 generations. No beneficial mutations were fixed in this example.

392 J. Sanford et al.

4 Conclusions

The program Mendel’s Accountant provides a biologically realistic platform for

analyzing the problem of mutation accumulation. This program demonstrates that the

problem of deleterious mutation accumulation is very serious under a wide range of

scenarios and across a vast portion of parameter space. The relentless accumulation of

deleterious mutations is primarily due to the existence of un-selectable “nearly-

neutral” mutations, but the genetic load problem is greatly amplified when mutation

rates are high. Intensified natural selection only marginally slows the accumulation of

deleterious mutations. Preliminary Mendel experiments indicate that the most

effective means of slowing mutation accumulation and reducing a population’s

genetic load is by reduction of the mutation rate. This study clearly indicates that

more research is needed. Mendel’s Accountant is freely available to users and can be

downloaded at either http://mendelsaccountant.info or http://sourceforge.net/ projects/

mendelsaccount.

References

1. Muller, H.J.: Our load of mutations. Amer. J. Human Genetics 2 (1950) 111-176.

2. Wallace, B.: Fifty years of genetic load. J. Hered. 78 (1987) 134-142.

3. Kondrashov, A.S.: Contamination of the genome by very slightly deleterious mutations:

why have we not died 100 times over? J. Theor. Biol. 175 (1995) 583-594.

4. Crow, J.F.: The high spontaneous mutation rate: a health risk? PNAS 94 (1997)

8380-8386.

5. Sanford, J., Baumgardner, J., Gibson, P., Brewer, W., Remine, W.: Mendel’s Accountant:

a biologically realistic forward-time population genetics program. SCPE, 8(2) (submitted).

6. Kimura, M.: Model of effectively neutral mutations in which selective constraint is

incorporated. PNAS 76 (1979) 3440-3444.

7. Kimura, M.: Neutral Theory of Molecular Evolution. Cambridge University Press, New

York (1983) 30-31.

8. Haldane, J.B.S.: The cost of natural selection. J. Genetics 55 (1957) 511-524.

9. Muller, H. J.: The relation of recombination to mutational advance. Mutation Research 1

(1964) 2-9.

10. Loewe, L.: Quantifying the genomic decay paradox due to Muller’s ratchet in human

mitochondrial DNA. Genetical Research 87 (2006) 133-159.

The Next Step in Understanding Population Dynamics: Comprehensive Numerical Simulation

Chapter

Full-text available

Aug 2012

Natural populations are always changing. Hardy-Weinberg assumptions are almost never realized because populations are seldom in equilibrium, and many random events (e.g., mutations, population size fluctuations, and environmental perturbations) irrevocably alter the genetic makeup of populations. Such genetic change can be either for the better (some populations adapt and expand) or for the worse (some populations shrink and become extinct). Change that occurs as the result of natural selection is termed adaptive evolution because natural selection favors the survival of organisms that are best adapted to their environments (i.e., have high fitness). On the other hand, nonadaptive evolution refers to change that occurs as the result of factors that act independently of organismal fitness (e.g., random genetic drift or mutation pressure). Because change within a population depends on so many variables and involves innumerable chance events, the study of population dynamics is both challenging and fascinating.

Selection Threshold Severely Constrains Capture of Beneficial Mutations

Conference Paper

Jul 2013

Background. In a companion paper, careful numerical simulation was used to demonstrate that there is a quantifiable selection threshold, below which low-impact deleterious mutations escape purifying selection and, therefore, accumulate without limit. In that study we developed the statistic, STd, which is the mid-point of the transition zone between selectable and un-selectable deleterious mutations. We showed that under most natural circumstances, STd values are surprisingly high, such that the large majority of all deleterious mutations are un-selectable. Does a similar selection threshold exist for beneficial mutations? Methods. As in our companion paper we here employ what we describe as genetic accounting to quantify the selection threshold (STb) for beneficial mutations, and we study how various biological factors combine to determine its value. Results. In all experiments that employ biologically reasonable parameters, we observe high STb values and a general failure of selection to preferentially amplify the large majority of beneficial mutations. High-impact beneficial mutations strongly interfere with selection for or against all low-impact mutations. Conclusions. A selection threshold exists for beneficial mutations similar in magnitude to the selection threshold for deleterious ones, but the dynamics of that threshold are different. Our results suggest that for higher eukaryotes, minimal values for STb are in the range of 10⁻⁴ to 10⁻³. It appears very likely that most functional nucleotides in a large genome have fractional contributions to fitness much smaller than this. This means that, given our current understanding of how natural selection operates, we cannot explain the origin of the typical functional nucleotide. Background. In a companion paper, careful numerical simulation was used to demonstrate that there is a quantifiable selection threshold, below which low-impact deleterious mutations escape purifying selection and, therefore, accumulate without limit. In that study we developed the statistic, STd, which is the mid-point of the transition zone between selectable and un-selectable deleterious mutations. We showed that under most natural circumstances, STd values are surprisingly high, such that the large majority of all deleterious mutations are un-selectable. Does a similar selection threshold exist for beneficial mutations? Methods. As in our companion paper we here employ what we describe as genetic accounting to quantify the selection threshold (STb) for beneficial mutations, and we study how various biological factors combine to determine its value.

Dynamical Systems and Fitness Maximization in Evolutionary Biology

Chapter

Full-text available

Mar 2021

Five years after Charles Darwin put forward his theory of Natural Selection, Herbert Spencer coined the phrase “survival of the fittest.” Survival of the fittest implies that individuals with highest fitness will survive and will pass on their traits – as required for evolution. Since then, scholars have struggled to mathematically model genetic change, inheritance, and selection, and further to define “fitness” to understand how fitness changes in a population over time. For about 90 years, the goal has been to prove that fitness continually increases – fitness maximization – in line with traditional expectation. This chapter presents the history of this issue to date, including proving a new simple and elegant formula for the fundamental theorem of natural selection with mutations, and a new application of the fundamental theorem of dynamical systems to evolutionary models which constrains the possible concept of fitness maximization. Taking a mathematical modeling perspective, we present both experimental genetics and mathematical models. Field biology researchers have observed that generally populations are either in stasis or are in fitness decline, and many mathematicians modeling genetics have rejected the very idea of general fitness maximization. We consider a variety of mutation-selection models, from Fisher’s early work, mutation-limited models that consider one mutation at a time, models that consider a distribution of simultaneous mutations, to the most comprehensive numerical simulations. We conclude that fitness is best understood in terms of net functionality (not just reproduction rate), and that fitness maximization is not a robust biological principle.

The waiting time problem in a model hominin population

Article

Full-text available

Sep 2015
Theor Biol Med Model

Background: Functional information is normally communicated using specific, context-dependent strings of symbolic characters. This is true within the human realm (texts and computer programs), and also within the biological realm (nucleic acids and proteins). In biology, strings of nucleotides encode much of the information within living cells. How do such information-bearing nucleotide strings arise and become established? Methods: This paper uses comprehensive numerical simulation to understand what types of nucleotide strings can realistically be established via the mutation/selection process, given a reasonable timeframe. The program Mendel's Accountant realistically simulates the mutation/selection process, and was modified so that a starting string of nucleotides could be specified, and a corresponding target string of nucleotides could be specified. We simulated a classic pre-human hominin population of at least 10,000 individuals, with a generation time of 20 years, and with very strong selection (50 % selective elimination). Random point mutations were generated within the starting string. 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. Results: Biologically realistic numerical simulations revealed that a population of this type required inordinately long waiting times to establish even the shortest nucleotide strings. To establish a string of two nucleotides required on average 84 million years. To establish a string of five nucleotides required on average 2 billion years. We found that waiting times were reduced by higher mutation rates, stronger fitness benefits, and larger population sizes. However, even using the most generous feasible parameters settings, the waiting time required to establish any specific nucleotide string within this type of population was consistently prohibitive. Conclusion: We show that the waiting time problem is a significant constraint on the macroevolution of the classic hominin population. Routine establishment of specific beneficial strings of two or more nucleotides becomes very problematic.

Suboptimality and complexity in evolution

Article

Full-text available

Jul 2014
COMPLEXITY

A scalable model of biological evolution is presented which includes energy cost for building new elements and multiple paths for obtaining new functions. The model allows a population with a continual increase of complexity, but as time passes, detrimental mutations accumulate. This model shows the crucial importance of accounting for the energy cost of new structures in models of biological evolution. © 2014 Wiley Periodicals, Inc. Complexity, 2014

Dynamical Systems and Fitness Maximization in Evolutionary Biology

Chapter

Aug 2021

The fundamental theorem of natural selection with mutations

Article

Full-text available

Jun 2018
J MATH BIOL

The mutation-selection process is the most fundamental mechanism of evolution. In 1935, R. A. Fisher proved his fundamental theorem of natural selection, providing a model in which the rate of change of mean fitness is equal to the genetic variance of a species. Fisher did not include mutations in his model, but believed that mutations would provide a continual supply of variance resulting in perpetual increase in mean fitness, thus providing a foundation for neo-Darwinian theory. In this paper we re-examine Fisher's Theorem, showing that because it disregards mutations, and because it is invalid beyond one instant in time, it has limited biological relevance. We build a differential equations model from Fisher's first principles with mutations added, and prove a revised theorem showing the rate of change in mean fitness is equal to genetic variance plus a mutational effects term. We refer to our revised theorem as the fundamental theorem of natural selection with mutations. Our expanded theorem, and our associated analyses (analytic computation, numerical simulation, and visualization), provide a clearer understanding of the mutation-selection process, and allow application of biologically realistic parameters such as mutational effects. The expanded theorem has biological implications significantly different from what Fisher had envisioned.

Computational Evolution Experiments Reveal a Net Loss of Genetic Information Despite Selection

Conference Paper

Jul 2013

Computational evolution experiments using the population genetics simulation Mendel's Accountant have suggested that deleterious mutation accumulation may pose a threat to the long-term survival of many biological species. By contrast, experiments using the program Avida have suggested that purifying selection is extremely effective and that novel genetic information can arise via selection for high-impact beneficial mutations. The present study shows that these approaches yield seemingly contradictory results only because of disparate parameter settings. Both agree when similar settings are used, and both reveal a net loss of genetic information under biologically relevant conditions. Further, both approaches establish the existence of three potentially prohibitive barriers to the evolution of novel genetic information: (1) the selection threshold and resulting genetic decay; (2) the waiting time to beneficial mutation; and (3) the pressure of reductive evolution, i.e., the selective pressure to shrink the genome and disable unused functions. The adequacy of mutation and natural selection for producing and sustaining novel genetic information cannot be properly assessed without a careful study of these issues.

The "Eve" Mitochondrial Consensus Sequence

Article

We have calculated the consensus sequence for human mitochondrial DNA using over 800 available sequences. Analysis of this consensus reveals an unexpected lack of diversity within human mtDNA worldwide. Not only is more than 83% of the mitochondrial genome invariant, but in over 99% of the variable positions, the majority allele was found in at least 90% of the individuals. In the remaining 0.22% of the 16,569 positions, which we conservatively refer to as "ambiguous," every one could be reliably assigned to either a purine or pyrimidine ancestral state. There was only one position where the most common allele had an allele frequency of less than 50%, but this has been shown to be a mutational hot spot. On average, the individuals in our dataset differed from the Eve consensus by 21.6 nucleotides. Sequences derived from sub-Saharan Africa were considerably more divergent than average. Given the high mutation rate within mitochondria and the large geographic separation among the individuals within our dataset, we did not expect to find the original human mitochondrial sequence to be so well preserved within modern populations. With the exception of a very few ambiguous nucleotides, the consensus sequence clearly represents Eves mitochondrial DNA sequence.

Mendel's Accountant: A New Population Genetics Simulation Tool for Studying Mutation and Natural Selection

Article

Full-text available

Mendel's Accountant (hereafter referred to as "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.

Mendel's Accountant: A biologically realistic forward-time population genetics program

Article

Full-text available

Jan 2007

Mendel's Accountant (hereafter referred to as "Mendel") is a user-friendly biologically realistic simulation program for investigating the processes of mutation and selection in sexually reproducing diploid populations. Mendel represents an advance over previous forward-time programs in that it incorporates several new features that enhance biological realism including: (a) variable mutation effect and (b) 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 to determine overall genotypic fitness 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 size and population substructure on cluster computers. We report 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.

The Neutral Theory of Molecular Evolution

Article

Jan 1994

The neutral theory claims that the great majority of evolutionary changes at the molecular level are controlled by random genetic drift under continued input of mutations, and that most of the genetic variation within species is maintained by the same mechanisms. The theory leads to a general view that since the origin of life on Earth, neutral evolutionary changes have played a most important role in evolution and predominated over Darwinian evolutionary changes, at least in number, throughout the whole history of life.

The Neutral Theory Of Molecular Evolution

Article

Oct 1983

MOTOO KIMURA

Motoo Kimura, as founder of the neutral theory, is uniquely placed to write this book. He first proposed the theory in 1968 to explain the unexpectedly high rate of evolutionary change and very large amount of intraspecific variability at the molecular level that had been uncovered by new techniques in molecular biology. The theory - which asserts that the great majority of evolutionary changes at the molecular level are caused not by Darwinian selection but by random drift of selectively neutral mutants - has caused controversy ever since. This book is the first comprehensive treatment of this subject and the author synthesises a wealth of material - ranging from a historical perspective, through recent molecular discoveries, to sophisticated mathematical arguments - all presented in a most lucid manner.

Fifty years of genetic load

Article

May 1987
J HERED

Bruce Wallace

This book discusses the radiation effects on Drosophila. It was originally thought that irradiating Drosophila would decrease the average fitness of the population, thereby leading to information about the detrimental effects of mutations. Surprisingly, the fitness of the irradiated population turned out to be higher than that of the control population. The original motivation for the experiment was as a test of genetic load theory. The average fitness of a population is depressed by deleterious alleles held in the population by the balance between mutation and natural selection. The depression is called the genetic load of the population. The load dose not depend on the magnitude of the deleterious effect of alleles, but only on the mutation rate.

The Neutral Theory of Molecular Evolution

Book

Jan 1983

Motoo Kimura

Haldane JBS. The cost of natural selection. J Genet 55: 511-524

Article

Dec 1957

J. B. S. Haldane

Unless selection is very intense, the number of deaths needed to secure the substitution, by natural selection, of one gene for another at a locus, is independent of the intensity of selection. It is often about 30 times the number of organisms in a generation. It is suggested that, in horotelic evolution, the mean time taken for each gene substitution is . about 300 generations. This accords with the observed slowness of evolution.

Contamination of the genome by very slightly deleterious mutations: Why have we not died 100 times over?

Article

Aug 1995

Alexey S. Kondrashov

It is well known that when s, the selection coefficient against a deleterious mutation, is below approximately 1/4Ne, where Ne is the effective population size, the expected frequency of this mutation is approximately 0.5, if forward and backward mutation rates are similar. Thus, if the genome size, G, in nucleotides substantially exceeds the Ne of the whole species, there is a dangerous range of selection coefficients, 1/G < s < 1/4Ne. Mutations with s within this range are neutral enough to accumulate almost freely, but are still deleterious enough to make an impact at the level of the whole genome. In many vertebrates Ne approximately 10(4), while G approximately 10(9), so that the dangerous range includes more than four orders of magnitude. If substitutions at 10% of all nucleotide sites have selection coefficients within this range with the mean 10(-6), an average individual carries approximately 100 lethal equivalents. Some data suggest that a substantial fraction of nucleotides typical to a species may, indeed, be suboptimal. When selection acts on different mutations independently, this implies too high a mutation load. This paradox cannot be resolved by invoking beneficial mutations or environmental fluctuations. Several possible resolutions are considered, including soft selection and synergistic epistasis among very slightly deleterious mutations.

The High Spontaneous Mutation Rate: Is it a Health Risk?*

Article

Sep 1997

James F. Crow

The human mutation rate for base substitutions is much higher in males than in females and increases with paternal age. This effect is mainly, if not entirely, due to the large number of cell divisions in the male germ line. The mutation-rate increase is considerably greater than expected if the mutation rate were simply proportional to the number of cell divisions. In contrast, those mutations that are small deletions or rearrangements do not show the paternal age effect. The observed increase with the age of the father in the incidence of children with different dominant mutations is variable, presumably the result of different mixtures of base substitutions and deletions. In Drosophila, the rate of mutations causing minor deleterious effects is estimated to be about one new mutation per zygote. Because of a larger number of genes and a much larger amount of DNA, the human rate is presumably higher. Recently, the Drosophila data have been reanalyzed and the mutation-rate estimate questioned, but I believe that the totality of evidence supports the original conclusion. The most reasonable way in which a species can cope with a high mutation rate is by quasi-truncation selection, whereby a number of mutant genes are eliminated by one "genetic death."

Natural selection in man

Article

Jan 1956

J. B. S. Haldane

The Relation Of Recombination To Mutational Advance

Article

Jun 1964
MUTAT RES-FUND MOL M

H.J. Muller

The method of calculation is shown wherebt a formula has been derived that approximately the ratio of the rate of accumulation of advantageous mutant genes in a population that undergoes recombination to the rate in an otherwise non-recombining one. A table is given showing the ratios thus found for different frequencies of advantageous mutations and different degrees of their advantage. It is shown that this calculation does not apply for mutant genes that act advantageously only when in some special combinations with one or more other mutant genes, and that as far as these cases of special synergism are concerned recombining lines have no evolutionary advantage over non-recombining ones. Other limitations of the formula are pointed out and assessed.