Biological Evolution

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Evolution Summary

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Encyclopedia of Nonlinear Science

BIOLOGICAL EVOLUTION

The term evolution defines a process that is driven by internal and/or external forces. In quantum mechanics, an evolution operator conducts change in time. Cosmic evolution in the standard model aims at a consistent description of the process from the “big bang” to the present universe. “Prebiotic evolution” deals with chemical precursors of present-day life and is determined by the conditions at the early Earth, be it in the primordial atmosphere, in the surrounding of volcanic hot springs at the sea floor, or at some other location. “Biological evolution” follows the prebiotic scenario, and it shaped and is still shaping the biosphere on Earth. A temporal change in the biosphere manifests itself as the appearance, alteration, and extinction of biological species. This view was not generally accepted before Charles Darwin. Influenced by the geologist Charles Lyell and his concept of uniformitarianism, Darwin and the proponents of the theory of evolution suggested that changes in the biosphere occur gradually, continuously, or at least, in small steps. In this aspect, which is not essential for the mechanism of evolution, Darwin’s theory contrasted the view held by the majority of his contemporaries, who assumed constancy of biological species and change exclusively through catastrophic events leading to mass extinction (Ruse, 1979). The opponents of evolutionary thinking, Louis Agassiz, Georges Cuvier, and others, considered species as invariant entities. The remnants of extinct species in the fossil record were interpreted by them as witnesses from earlier worlds destroyed by punctual events, the great deluge, and other catastrophes that wiped out major parts of the organismic world. In society, the concept of evolution was heavily attacked by representatives of the Christian Churches because it was seen to be in conflict with the Genesis report in the Bible (Ruse, 2001). During the 20th century, European religious thought has reconciled religious belief and the idea of an evolving biosphere. In North America, the strong opposition of some groups of religious fanatics led to the peculiar development of Creationism, whose claim of being an alternative to the theory of evolution is rejected by the established scientific community (NAS, 1999).

The current theory of biological evolution originated from two epochal contributions by Charles Darwin and Gregor Mendel. Darwin conceived a mechanism for evolutionary change of the biosphere based on variation and selection, and he gathered empirical data providing evidence for the action of natural and artificial selection, the latter exercised in animal breeding and nursery gardens. Darwin’s principle (published in On The Origin of Species by Natural Selection in 1859) has two consequences: species adapt to their environments and are related to their ancestors in terms of phylogenies, or branches of an ancestral tree of species. In 1866, Gregor Mendel introduced quantitative statistics into the evaluation of data in biology and performed the first precisely controlled fertilization experiments with plants. He discovered and interpreted correctly the action of genes in determining the properties of organisms. Mendel’s work was considered irrelevant by the evolutionists of the second half of the 19th century and was “rediscovered” around 1900. Only in 1930 were the Darwinian concept of selection and Mendel’s rules of inheritance combined to a common mathematical formalism by the population geneticists Ronald Fisher, John Haldane, and Sewall Wright (for a recent text in population genetics, see Hartl & Clark, 1997). In the 1940s, finally, Darwinian evolution and Mendelian genetics were united in the Synthetic or Neo-Darwinian Theory of Evolution by the works of the experimental biologists Theodosius Dobzhansky, Julian Huxley, Ernst Mayr, and others (Mayr, 1997). In the second half of the 20th century, molecular biology put evolutionary theory on firm fundamentals, chemistry and physics. Comparison of genes and, more recently of whole genomes, allows for reconstruction of phylogenies on the basis of nucleotide sequence divergence through mutation (Judson, 1979); the exploration of molecular structures provides insights into the chemistry of present day life; and knowledge of biomolecular properties eventually led to the construction of laboratory systems that allow for observation of evolution of molecules in the test tube (Spiegelman, 1971; Watts & Schwarz, 1997).

Darwinian evolution results from the interplay of variation and selection, both being consequences of reproduction in populations. Variation operates on genomes or genotypes, which are polynucleotide sequences carrying the genetic information, and occurs in two fundamentally different ways: (i) mutation causes local changes in genomic sequences, whereas (ii) recombination exchanges corresponding segments between two genotypes. Selection is based on differences in fitness being a property of the phenotype. The phenotype is defined as the union of all, structural as well as dynamic, properties of an individual organism. Unfolding of the phenotype is programmed by the genome; but, at the same time, requires a highly specific environment. In addition, it is influenced by epigenetic factors (epigenetic refers to every nonenvironmental factor that interferes with the development of the organism, except those encoded in the nucleotide sequence of DNA; many epigenetic factors are already understood at the molecular level, and involve specific modifications of genomic DNA). Fitness, in essence, counts the number of fertile descendants reaching the reproductive age. It has two major components: (i) the probability of survival to reproduction, and (ii) the number of viable and fertile offspring.

To illustrate selection in a population of n asexually reproducing phenotypes, we consider a continuous-time model that describes change by a differential equation

(1)

The variables denote the frequencies of reproducing variants: with N_i(t) counting the number of individuals with phenotype S_i or genotype I_i at time t. (For several genotypes giving rise to the same phenotype, see neutrality below.) Fitness values f_i when averaged over the entire population yield the mean fitness expressed by a time-dependent flux Φ(t). Frequencies of variants with fitness values above average, f_i>Φ, increase with time, those of below-average variants, f_i<Φ, decrease and as a consequence, the mean fitness increases. The flux Φ(t) is a nondecreasing function of time and selection continues until all variants, except the fittest, have died out (See also Fitness landscape). For two variants, I₀ and I₁, the solution boils down to

where the upper equation refers to continuously varying x(t) and the lower equation refers to population to discrete time variables X_t with synchronized reproduction. The Malthusian fitness difference m=f₁−f₀ is related to the Darwinian relative fitness by (see Hartl & Clark (1997)). The conditions for selection are m>0 or respectively. An example is shown in Figure 1.

Sexual reproduction of diploid organisms involves Mendelian genetics (see Figure 2). Every gene (A) comes in two copies, identical or different, which are chosen from a reservoir of variants A_i called alleles. Recombination occurs in the process of reproduction when the two copies are separated and reassembled in pieces through random combination. The differential equation (1) is extended to describe selection in the diploid case in the form of Fisher’s selection equation:

(2)

Figure 1. Illustration of selection in populations. The plotted curves represent the frequencies of advantageous mutants I₁ in a population of individuals I₀ with a Malthusian fitness difference of m=Δf=f₁−f₀=0.1, 0.02, and 0.01. The population size is N=10,000, and the mutants were initially present in a single copy: N₁(0)=1 or x₁(0)=0.0001.

Figure 2. Mendelian genetics. In sexual reproduction, the two parental genomes are split into pieces and recombined randomly, which means each of the four alleles has a 50% chance to be incorporated in the genome of an offspring. Mendel’s laws are of a statistical nature and hold as mean values in the limit of large numbers of observations. Two cases are shown: (i) the heterozygote unfolds into a phenotype with intermediate properties (gray through blending of black and white), and (ii) the property of one allele (black) is dominant. In the latter case, the other allele (white) is called recessive. Interbreeding of two homozygous individuals (parent generation P) leads to a first offspring generation (F1) of identical heterozygous individuals; the phenotypes in the next (F2) generation show a distribution of 1:2:1 in the intermediate and 1:3 in the dominant/recessive case. Crossing of the (recessive) parent genotype with an F1-individual yields a 1:1 ratio of phenotypes.

with

The variables refer to alleles A_j rather than to whole genomes, and the rate coefficient a_ij represents the individual fitness values for the combination A_iA_j. Fitness is assumed to be independent of the positioning of alleles, A_iA_j or A_jA_i, and hence, a_ij=a_ji holds. The term is the population-averaged mean fitness of the allele combinations carrying A_i at least once: A_iA_j, j=1,…, n. Fisher’s fundamental theorem states that the flux is a nondecreasing function of time, but the outcome of selection need not be unique as optimization might end in a local optimum of Φ (See also Fitness landscape). For example, in the two-allele case, inferiority of the heterozygote A₁A₂, a₁₂<min{a₁₁, a₂₂}, results in bistability since homogenous populations of either homozygote, A₁A₁ or A₂A₂, represent stable equilibrium points. Then, the initial conditions determine the outcome of selection.

The optimization principle is not universally valid: when mutation is included or when more complex cases of recombination are considered, optimization of mean fitness is restricted to certain ranges of initial conditions, whereas different behavior is observed for other starting values. Still, optimization remains an important heuristic in evolution as it is frequently observed.

Innovation is introduced into genes by mutation consisting of a local change in the sequence of nucleotides resulting from an imperfect replication of genetic information or externally caused damage. Two scenarios are distinguished: (i) rare mutation treated by conventional population genetics and typically occurring with multicellular organisms and most bacteria, and (ii) frequent mutation handled by quasispecies theory (Eigen, 1971; Eigen & Schuster, 1977) and determining evolution of viruses. Higher mutation rates are often advantageous because they allow for adaptation, but there exists an error threshold of replication beyond which inheritance breaks down because too many mutations destroy the genetic message. RNA viruses are under a strong selection constraint by the host and their mutation rates are close to the error threshold.

The idea that genotypes and phenotypes are related one-to-one turned out to be wrong. Molecular genetics revealed a high degree of neutrality (Kimura, 1983): many different genotypes give rise to the same phenotype. Advantageous mutations are rare; deleterious mutations are eliminated by selection thus leaving a majority of observed changes in the genomes to result from neutral mutations. Neutrality gives rise to random drift of populations in genotype space, which was also found to be important for the mechanism of evolution since it allows populations to escape from minor local fitness optima or evolutionary traps (Schuster, 1996) and Schuster in Crutchfield & Schuster, 2003). Random drift leads to an almost constant mutation rate per year and nucleotide independent of the species being tantamount to a molecular clock of evolution. This clock is used for dating in the reconstruction of phylogenies from comparison of present-day genome sequences. Molecular clock dates yield substantially longer time spans compared with those from the fossil record. The discrepancy seems to be reconcilable because paleontological datings are too young and molecular clock datings are too old by systematic errors (Benton & Ayala, 2003).

The Darwinian mechanism is powerful because it makes no reference to the specific nature of the reproducing entities. Therefore, it is likewise valid for molecules, viruses, bacteria, or higher organisms. Selection based on the Darwinian principle is observed in many disciplines outside biology, for example, in physics and chemistry, in economics, and in the social sciences.

Since its introduction, the theory of evolution has undergone changes and modifications. The rejection of catastrophic events as an important source of change in the history of life on Earth was a political issue rather than one based on scientific data. Geological evidence for fallings of large meteorites as well as major floods is now available, and such events wiped out substantial parts of the biosphere. The paleontological record reflects the interplay between continuous evolution and external influences, which resulted in epochs of gradual development interrupted by punctuated events. Interestingly, evolution of bacteria or molecules under constant conditions also showed punctuation without external triggers: populations “wait” during quasistationary periods for rare mutations that initiate fast periods of change.

Still, there are open problems in current evolutionary theory. Recent sequence data challenge the idea of a tree of life. Although animal phylogeny appears to be on a firm basis, there are problems with the reconstruction of a tree-like history of plant species. Prokaryote evolution cannot be cast into a tree: archebacteria and eubacteria exchange genetic information across species and kingdoms. Such horizontal gene transfer occurs frequently and obscures the descendance of species. Darwinian evolution, although successful in describing the mechanisms of optimization and adaptations of species, is unable to provide explanations for the major evolutionary transitions that lead from one hierarchical level of life to the next higher forms (Maynard Smith & Szathmáry, 1995; Schuster, 1996). Examples of such transitions are the origin of the genetic code; the transition from the prokaryotic to the eukaryotic cell; the transition from unicellular organisms to multicellular plants, fungi, and animals; the transition from solitary animals to animal societies; and eventually the transition to man and human societies. Common to all these transitions is the integration of individual competitors as cooperating elements into a novel functional unit. Simple model mechanisms have been proposed that can explain cooperation of competitors (see, e.g., the hypercycle Eigen & Schuster, 1978), but no real solution to the problem has been found yet.

PETER SCHUSTER

Biological Evolution

BIOLOGICAL EVOLUTION

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