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Natural selection has been appreciated as an organizing principle of biology since the time of Darwin. More recently, it has become apparent that the same themes that govern natural selection, heritable variation, selection, and amplification, can be applied to the evolution of function in a variety of other systems as well. In particular, it has proven possible to evolve nucleic acid binding species and catalysts in vitro. The sequence "solutions" to functional "problems" that are yielded by in vitro selection experiments are typically diverse and/or divergent, and provide a unique reference point for understanding to what extent the natural universe is functionally optimal or historically constrained. More importantly, comparative analysis of sequence solutions yields what appear to be inherent rules for biopolymer evolution. In some cases these rules are intuitively obvious (i.e., the stringency of selection is directly related to the number of sequence solutions), while in other cases these rules are more intriguing (i.e., large polymers have more evolutionary options than small polymers). We will examine several such rules in more detail, and dwell briefly on their applications to exobiology and biotechnology.
Back to TitlesThe phenomenon of "bistability" or "hysteresis" has recently been observed in simulations of finite populations of genotypes evolving with mutation and recombination on simple (single-optimum) fitness landscapes [2]. Using a Moran birth and death model along the lines of [1] we demonstrate that the qualitative features of bistability can be explained in terms of the effects of recombination on the stationary distribution of optimum genotypes. Specifically, below the error threshold the stationary distribution is bimodal. Recombination has the effect of "pulling the modes apart" and creating a "probability barrier" between the modes. A further effect is inflation of mean waiting times for transitions between the modes. The model also facilitates calculation of and (at least in principle) an analytic expression for the error threshold where recombination is present.
On-line version, Gzip'd PostScript.Elementary considerations from Markov Chain theory applied to a wide array of evolutionary models are used to explain patterns of stasis and punctuation. This analysis explains both gradual and punctuated evolution exhibited in a series of numerical simulations of finite, spatially distributed populations with mutation and genetic drift. Neutral, stabilizing, and rugged selection landscapes are studied. In particular, a multilocus study of rugged fitness landscapes reveals punctuated evolution in average phenotypic value and mean fitness, and that the punctuation in these may not be synchronized in time. Finally, we show that these findings hold independently of the evolution equations, and in particular are not limited to Mendelian inheritance.
Back to TitlesBoolean networks have been discussed as models for the information
processing during gene expression in biological genetic networks [1,2].
The small number of cell types observed in Nature are modeled in terms
of the dynamical attractors in a Boolean network.
One interesting issue in genetic networks is their evolutionary origin.
Genetic networks can be used to define biological species: individuals
with compatible genetic networks belong to a common species. Therefore,
besides the dynamics of the network itself, the larger dynamical
timescale of biological evolution is of interest when studying basic
properties of genetic networks. An evolving Boolean network can be a
first step towards modeling genetic networks on this timescale. In
such a network model, each node is an on-off switch which itself is a
function of the binary output from some other nodes. This connectivity
in a single Boolean network is then evolved, and it has been
demonstrated how the sole requirement of sequential matching of
attractors leads to an evolution that exhibits punctuated equilibrium
[3].
Looking further afield, such a model can serve as a possible link
between models of micro- and macro-evolution of life. In this respect
it demonstrates how genetic network evolution may determine observables
of macroevolution as, for example, the distribution of species lifetimes
which can be observed in the fossil record. It offers the possibility
to reconciliate the observed exponential distribution of genera
lifetimes with the power law distribution of lifetimes which one
observes when averaging over the complete fossil record [3]. In this
model the power law distribution of lifetimes is the result of a
hierarchical superposition of exponential distributions from classes
of networks with different genetic flexibilities, in analogy to the
average over genera taken when considering the full fossil record.
The diversity of form is a major signature of macroevolution, and its
realization is tied to the structure of the genotype-phenotype map.
Phenotypic variation, however, is expressed in hierarchical fashion,
through the nonlinearities and discontinuities characteristic of
developmental pathways. The hierarchical nature of development thus
invites consideration of intervening levels of variation between
genotype and (adult) phenotype, and justifies study of the ontogeny
of phenotypic variation itself as an important element in any general
theory of genotype-phenotype relations.
Statistical characterizations of morphological state-spaces
(morphospaces) in terms of the spread, spacing, location, and
neighborhood relations of forms are presented and discussed in terms
of their bearing on the relationship between development and evolution.
The notions of developmental disparity and developmental morphospaces
(defined by incorporation of developmental data) are illustrated as a
means of approaching issues such as vectors of change in ontogenetic
and evolutionary time, general changes in rate and timing of
development, testing of developmental "laws," and links between
phylogenetic and ontogenetic trends. Emphasis is placed on the
inference of structural constraints and of temporal asymmetries in
evolutionary histories over macroevolutionary time scales. Sea urchins
are used as a case study to evaluate some models of development and
evolution.
George Simpson was right when he said, in effect, that, there being
one single history of life, there must be one single evolutionary
theory to explain it. Yet that single theory has yet to be forged.
Deep connections between the nature and history of biological systems (both
genealogical and ecological) and the physical realm have yet to be fully
specified. The notion that competition among genes (or, more traditionally,
simply organisms) for representation in succeeding generations (i.e.
"reproductive success") constitutes the sole elemental driving force of the
evolutionary process ignores the entire physical context of biological
history. I will develop a model (the "sloshing bucket") that sees a spectrum
from ecosystem disturbance/succession up through the evolutionary responses
to global mass extinction events---as revealed, at all levels, though
repeated historical patterns in the history of life. The model draws on
previous work in biological hierarchy theory. Adaptation through natural
selection remains the cornerstone mechanism underlying the
phenotypic/genotypic history of life---but the generation of that diversity
springs largely from the physical world and its impact (literally as well as
figuratively) on ecosystems---and thus on genealogical systems (e.g. species
and higher taxa). Thus the answer to the question: Is evolution primarily a
deterministic process of adaptation via natural selection, or does chance
play a major role (historical "contingency") is "Yes."
The metaphor of holey adaptive landscapes provides a pictorial representation of the process of speciation as a consequence of genetic divergence. In this metaphor, biological populations diverge along connected clusters of well-fit genotypes in a multidimensional adaptive landscape and become reproductively isolated species when they come to be on opposite sides of a "hole" in the adaptive landscape. No crossing of any adaptive valleys is required. I will review recent analytical and numerical results on the dynamics of speciation on holey adaptive landscapes and discuss some biological implications of these results.
Back to TitlesThe sequencing of complete genomes of cellular species allows the
determination of evolutionary dynamics at various levels of genome
organization. Rates of evolution can be determined, from the sequence
differentiation of individual proteins, the domain organization of
proteins, the gene content of genomes, the regulation of gene
expression and the spatial organization of the genes in the genome, to
the differentiation of metabolic pathways. Comparative analysis of
completely sequenced prokaryotic genomes reveals a high diversity in
all these aspects of the genome, even at comparatively short
phylogenetic distances. Especially the regulation of gene expression,
and the correlation of this regulation between genes via their
occurrence in the same operons, evolves at a relatively high rate. The
gene content of genomes evolves at a lower rate. Even though
the occurrence of horizontal gene transfer has frequently been
documented, the similarity in the gene content of two genomes
correlates well with their divergence time. It can be used to
reconstruct the phylogeny of life on earth.
To exemplify various aspects of genome evolution, one aspect of
metabolism, the TriCarboxyAcid cycle (TCA) will be treated in more
detail. The implementation of the TCA in prokaryotes reveals a
remarkable diversity, both with respect the presence of certain
pathways, the genes that encode the enzymes for these pathways and
their (co)regulation.
The reproduction algorithm employed by natural selection is often viewed as given. Why don't organisms use more successful mechanisms than random blind mutations and blind symmetric recombination to change their genome? The work presented starts by building a framework in which these questions can be addressed---comparing the optimality of the different reproductive mechanisms. Then the framework is used to find the optimal asexual reproductive algorithm in various settings, and an optimal sexual algorithm. It will be shown that in an asexual setting, random mutations are often the best one can do, but that in a sexual setting, there are many ways to be better. These results can also be used to address the question of the role of sexual reproduction for evolutionary systems.
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Back to TitlesThe evolution of cooperative behaviour has been studied extensively by the use of the two-person Prisoner's Dilemma game as a model for interaction between individuals. In such models reciprocity or ``kin selection'' are mechanisms that allow for cooperation to be established. In multi-person games, the problem of avoiding exploitation, or free riders, is more difficult, and cooperation may be harder to achieve. By varying the payoff parameters, noise level, and group size, we investigate in coevolutionary models under what circumstances cooperative behaviour evolves, both in a mean-field situation and in a spatially extended system on a lattice.
Back to TitlesWe investigate the ability of a genetic algorithm to design cellular automata that perform computations. The computational strategies of the resulting cellular automata can be understood using a framework in which "particles" embedded in space-time configurations carry information and interactions between particles effect information processing. This structural analysis can also be used to explain the evolutionary process by which the strategies were designed by the genetic algorithm. More generally, our goals are to understand how evolutionary search can design complex decentralized systems with sophisticated collective computational abilities and to develop rigorous frameworks for understanding how the resulting dynamical systems perform computation.
Back to TitlesWe introduce a model of evolution on a fitness landscape possessing a
tunable degree of neutrality. The model allows us to study the general
properties of molecular species undergoing neutral evolution. We find
that a number of phenomena seen in RNA sequence-structure maps are
present also in our general model. Examples are the occurrence of
"common" structures which occupy a fraction of the genotype space which
tends to unity as the length of the genotype increases, and the formation
of percolating neutral networks which cover the genotype space in such a
way that a member of such a network can be found within a small radius of
any point in the space. We also describe a number of new phenomena which
appear to be general properties of systems possessing selective
neutrality. In particular, we show that the maximum fitness attained
during the adaptive walk of a population evolving on such a fitness
landscape increases with increasing degree of neutrality, and is directly
related to the fitness of the most fit percolating network.
This work was performed in collaboration with Robin Engelhardt, Erik
van Nimwegen and Kim Sneppen.
We describe evolutionary complexification as a process of dynamical
symmetry breaking through which the macroscopic (phenotypic) state
space unfolds into successively higher dimensions. During this, the
population diffuses in a space of microscopic (genetic) degrees of
freedom. This space is symmetric under the selection dynamics in the
sense that the genetic variations that drive the diffusion are
fitness-neutral.
In the general setting, however, the symmetry of the microscopic degrees
of freedom is not complete. By visiting a small "portal" within the
microscopic state space the symmetry can be dynamically broken. This
leads to the appearance of a new macroscopic degree of freedom that
then can be acted on by selection. Once such an innovation occurs, the
population stabilizes in the new, higher dimensional macroscopic space
until another portal in the microscopic space is discovered. The result
is a dynamical picture of the evolutionary process as a series of epochs
of stasis, punctuated by phenotypic innovations---a view that can be
quantitatively analyzed in some detail.
Comparison of model analyses with the pattern of DNA sequence evolution suggests that nearly neutral mutations are abundant. Interaction of selection and drift will be discussed in relating molecular evolution to phenotypic observations, with special reference to slightly deleterious mutations.
Back to TitlesI'll discuss the prospects for fairly general dynamical theories of sets of co-adapting agents, each trying to model each other and/or aggregate properties of their environment. There do seem to be some relatively generic phenomena in such systems, including a transition from mutual equilibrium to complex behavior as exploration or learning rates are increased, and a accuracy-fragility tradeoff (and often break-down cycle) in internal models. Simple dynamical models may be able to capture such phenomena and help to classify and illuminate real co-adapting systems.
Back to TitlesThe mapping from RNA sequences to their secondary structures exhibits a large degree of redundancy; i.e., there are typically many sequences that realize a given structure. The set of all sequences folding into a given molecule are referred to as the "neutral network." It turns out that the graph-theoretic structure of neutral nets is of some importance for the understanding of evolution and evolutionary optimization. Some central questions in this context are:
Evolutionary phenomena are observed in cell-free replication assays of
nucleic acids and can be modeled appropriately by computer simulation.
In these systems evolution is reduced to minimal complexity: (i) the
two fundamental processes are complementary (±) replication and
mutation, (ii) selection is provided by competition for fast replication,
and (iii) genotype and phenotype are represented by two properties of
the same molecule, sequence and structure, respectively. In vitro
evolution of RNA is the only known example where genotype-phenotype
mapping can be analyzed in detail since it is reduced to folding the
molecules into structures.
Computer simulations of RNA evolution were carried out in a kind of
flowreactor which allows to keep the numbers of molecules constant within
natural fluctuations (N ± Sqrt(N)). In order to be able to handle
large numbers of molecules a simplified notion of structure, the so-called
secondary structure, was applied to RNA. Optimization was guided towards
a given target structure---which happened to be tRNAphe---by
means of a fitness function that decreases monotonically with the
distance to the target. Individual computer runs using
population sizes of 1,000 to 10,000 molecules were performed. The
trajectories showed characteristic punctuated course. The runs
were analyzed in terms of relay series representing a posteriori
recordings of the series of phenotypes leading to the target structure.
A molecular interpretation based on the observed changes in structure
is given. Depending on the probability of occurrence continuous transitions
are distinguished from rare, discontinuous ones. Every step in the evolutionary
trajectory is initiated by a discontinuous transition. A notion of
evolutionary nearness of phenotypes is introduced that creates a topology
in shape space.
Sub-populations of cooperators and defectors inhabit sites on a lattice. The interaction among the individuals at a site, determined by the outcome of a prisoners dilemma (PD) game, determine their fitnesses. The PD payoff parameters are chosen so that cooperators are able to maintain a homogeneous population, while defectors are not. Individuals mutate to become the other type and migrate to a neighboring site with low probabilities. Both density dependent and density independent versions of this model are studied. The dynamics of this model can be understood by considering the life-cycle of a population at a site. The life-cycle starts with one cooperator that establishes a population. Then defectors invade and eventually take over resulting finally in the death of the population. During this life-cycle new cooperator populations are founded by single cooperators that migrate out to empty neighboring sites. The system can reach a steady-state where cooperation prevails if the global "birth" rate of populations is equal to the rate of their "death." The steady state is dynamic in nature--cooperation persists although every single population of cooperators dies out. These dynamics enable the persistence of cooperation in a large section of the model's parameter space.
Back to TitlesLandscapes arise in different contexts, from evolutionary biology to
combinatorial optimization. The notion of a landscape---composed of
a (large) set of configurations, a cost function, a topological
structure in "configuration space" which is induced by the search
process--sets the stage for understanding at least the simplest
types of adaptation.
In my presentation I will outline approaches to characterize the most
salient features of landscapes: ruggedness and neutrality.
Many subsystems of organisms are quite robust to mutations, as exemplified by the high tolerance of proteins to amino acid changes, the resilience of metabolic flux to changes in enzyme activity and the robustness of developmental pathways to mutations in their constituent genes. The mechanistic basis for robustness in each of these cases depends on peculiarities of the system studied, raising the possibility that robustness is an intrinsic characteristic of these systems. A more attractive alternative, which we explore, is that observed robustness is a property that itself has evolved because it "protects" an organism against otherwise deleterious mutations. We investigate this possibility on the level of biological macromolecules and on the level of gene networks in developmental pathways.
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