Skills and Expertise
Research Items (31)
- Dec 2018
Viruses are ubiquitous in the biosphere and greatly affect the hosts they infect. It is generally accepted that members of every microbial taxon are susceptible to at least one virus, and a plethora of bacterial viruses are known. In contrast, knowledge of the archaeal virosphere is still limited. Here, a novel lytic archaeal virus is described, designated “Drs3”, as well as its host, Methanobacterium formicicum strain Khl10. This hydrogenotrophic methanogenic archaeon and its virus were isolated from the anaerobic digester of an experimental biogas plant in Germany. The tailed virus has an icosahedral head with a diameter of approximately 60 nm and a long non-contractile tail of approximately 230 nm. These structural observations suggest that the new isolate belongs to the family Siphoviridae, but it could not be assigned to an existing genus. Lysis of the host Khl10 was observed 40-44 h after infection. Lysis of the type strain Methanobacterium formicicum DSMZ 1535 was not observed in the presence of Drs3, pointing towards resistance in the type strain or a rather narrow host range of this newly isolated archaeal virus. The complete 37-kb linear dsDNA genome of Drs3 contains 39 open reading frames, only 12 of which show similarity to genes with predicted functions.
- Jul 2018
The ubiquity of plasmids in all prokaryotic phyla and habitats and their ability to transfer between cells marks them as prominent constituents of prokaryotic genomes. Many plasmids are found in their host cell in multiple copies. This leads to an increased mutational supply of plasmid-encoded genes and genetically heterogeneous plasmid genomes. Nonetheless, the segregation of plasmid copies into daughter cells during cell division is considered to occur in the absence of selection on the plasmid alleles. Here, we investigate the implications of random genetic drift of multicopy plasmids during cell division - termed here segregational drift - to plasmid evolution. Performing experimental evolution of low- and high-copy non-mobile plasmids in Escherichia coli, we find that the evolutionary rate of multicopy plasmids does not reflect the increased mutational supply expected according to their copy number. In addition, simulated evolution of multicopy plasmid alleles demonstrates that segregational drift leads to increased loss frequency and extended fixation time of plasmid mutations in comparison to haploid chromosomes. Furthermore, an examination of the experimentally evolved hosts reveals a significant impact of the plasmid type on the host chromosome evolution. Our study demonstrates that segregational drift of multicopy plasmids interferes with the retention and fixation of novel plasmid variants. Depending on the selection pressure on newly emerging variants, plasmid genomes may evolve slower than haploid chromosomes, regardless of their higher mutational supply. We suggest that plasmid copy number is an important determinant of plasmid evolvability due to the manifestation of segregational drift.
DNA acquisition via recombination is considered advantageous as it has the potential to bring together beneficial mutations that emerge independently within a population. Furthermore, recombination is considered to contribute to the maintenance of genome stability by purging slightly deleterious mutations. The prevalence of recombination differs among prokaryotic species and depends on the accessibility of DNA transfer mechanisms. An exceptional example is the human pathogen Mycobacterium tuberculosis (MTB) where no clear transfer mechanisms have been so far characterized and the presence of recombination is questioned. Here we analyse completely assembled MTB genomes in search for evidence of recombination. We find that putative recombination events are enriched in strains reconstructed by reference-guided assembly and in regions with unreliable alignments. In addition, assembly and alignment artefacts introduce phylogenetic signals that are conflicting the established MTB phylogeny. Our results reveal that the so far reported recombination events in MTB are likely to stem from methodological artefacts. We conclude that no reliable signal of recombination is observed in the currently available MTB genomes. Moreover, our study demonstrates the limitations of reference-guided genome assembly for phylogenetic reconstructions. Rigorously de novo assembled genomes of high quality are mandatory in order to distinguish true evolutionary signal from noise, in particular for low diversity species such as MTB.
The Second Annual Meeting of the European Virus Bioinformatics Center (EVBC), held in Utrecht, Netherlands, focused on computational approaches in virology, with topics including (but not limited to) virus discovery, diagnostics, (meta-)genomics, modeling, epidemiology, molecular structure, evolution, and viral ecology. The goals of the Second Annual Meeting were threefold: (i) to bring together virologists and bioinformaticians from across the academic, industrial, professional, and training sectors to share best practice; (ii) to provide a meaningful and interactive scientific environment to promote discussion and collaboration between students, postdoctoral fellows, and both new and established investigators; (iii) to inspire and suggest new research directions and questions. Approximately 120 researchers from around the world attended the Second Annual Meeting of the EVBC this year, including 15 renowned international speakers. This report presents an overview of new developments and novel research findings that emerged during the meeting.
The evolution of asexual organisms is driven not only by the inheritance of genetic modification but also by the acquisition of foreign DNA. The contribution of vertical and horizontal processes to genome evolution depends on their rates per year and is quantified by the ratio of recombination to mutation. These rates have been estimated for bacteria, however, no estimates have been reported for phages. Here we delineate the contribution of mutation and recombination to dsDNA phage genome evolution. We analyzed 34 isolates of the 936 group of Siphoviridae phages using a Lactococcus lactis strain from a single dairy over 29 years. We estimate a constant substitution rate of 1.9 × 10−4 substitutions per site per year due to mutation that is within the range of estimates for eukaryotic RNA and DNA viruses. The reconstruction of recombination events reveals a constant rate of five recombination events per year and 4.5 × 10−3 nucleotide alterations due to recombination per site per year. Thus, the recombination rate exceeds the substitution rate, resulting in a relative effect of recombination to mutation (r/m) of ∼24 that is homogenous over time. Especially in the early transcriptional region, we detect frequent gene loss and regain due to recombination with phages of the 936 group, demonstrating the role of the 936 group pangenome as a reservoir of genetic variation. The observed substitution rate homogeneity conforms to the neutral theory of evolution; hence, the neutral theory can be applied to phage genome evolution and also to genetic variation brought about by recombination.
Background Filamentous cyanobacteria that differentiate multiple cell types are considered the peak of prokaryotic complexity and their evolution has been studied in the context of multicellularity origins. Species that form true-branching filaments exemplify the most complex cyanobacteria. However, the mechanisms underlying the true-branching morphology remain poorly understood despite of several investigations that focused on the identification of novel genes or pathways. An alternative route for the evolution of novel traits is based on existing phenotypic plasticity. According to that scenario – termed genetic assimilation – the fixation of a novel phenotype precedes the fixation of the genotype. Results Here we show that the evolution of transcriptional regulatory elements constitutes a major mechanism for the evolution of new traits. We found that supplementation with sucrose reconstitutes the ancestral branchless phenotype of two true-branching Fischerella species and compared the transcription start sites (TSSs) between the two phenotypic states. Our analysis uncovers several orthologous TSSs whose transcription level is correlated with the true-branching phenotype. These TSSs are found in genes that encode components of the septosome and elongasome (e.g., fraC and mreB). Conclusions The concept of genetic assimilation supplies a tenable explanation for the evolution of novel traits but testing its feasibility is hindered by the inability to recreate and study the evolution of present-day traits. We present a novel approach to examine transcription data for the plasticity first route and provide evidence for its occurrence during the evolution of complex colony morphology in true-branching cyanobacteria. Our results reveal a route for evolution of the true-branching phenotype in cyanobacteria via modification of the transcription level of pre-existing genes. Our study supplies evidence for the ‘plasticity-first’ hypothesis and highlights the importance of transcriptional regulation in the evolution of novel traits. Electronic supplementary material The online version of this article (doi:10.1186/s12862-017-1053-5) contains supplementary material, which is available to authorized users.
- Sep 2017
A novel archaeal lytic virus targeting species of the genus Methanosarcina was isolated using Methanosarcina mazei strain Gö1 as the host. Due to its spherical morphology, the virus was designated Methanosarcina spherical virus (MetSV). Molecular analysis demonstrated that MetSV contains double-stranded linear DNA with a genome size of 10,567 bp containing 22 open reading frames (ORFs), all oriented in the same direction. Functions were predicted for some of these ORFs, i.e., such as DNA polymerase, ATPase, and DNA-binding protein as well as envelope (structural) protein. MetSV-derived spacers in CRISPR loci were detected in several published Methanosarcina draft genomes using bioinformatic tools, revealing a potential protospacer-adjacent motif (PAM) motif (TTA/T). Transcription and expression of several predicted viral ORFs were validated by reverse transcription-PCR (RT-PCR), PAGE analysis, and liquid chromatography-mass spectrometry (LC-MS)-based proteomics. Analysis of core lipids by atmospheric pressure chemical ionization (APCI) mass spectrometry showed that MetSV and Methanosarcina mazei both contain archaeol and glycerol dialkyl glycerol tetraether without a cyclopentane moiety (GDGT-0). The MetSV host range is limited to Methanosarcina strains growing as single cells (M. mazei, Methanosarcina barkeri and Methanosarcina soligelidi). In contrast, strains growing as sarcina-like aggregates were apparently protected from infection. Heterogeneity related to morphology phases in M. mazei cultures allowed acquisition of resistance to MetSV after challenge by growing cultures as sarcina-like aggregates. CRISPR/Cas-mediated resistance was excluded since neither of the two CRISPR arrays showed MetSV-derived spacer acquisition. Based on these findings, we propose that changing the morphology from single cells to sarcina-like aggregates upon rearrangement of the envelope structure prevents infection and subsequent lysis by MetSV. IMPORTANCE Methanoarchaea are among the most abundant organisms on the planet since they are present in high numbers in major anaerobic environments. They convert various carbon sources, e.g., acetate, methylamines, or methanol, to methane and carbon dioxide; thus, they have a significant impact on the emission of major greenhouse gases. Today, very little is known about viruses specifically infecting methanoarchaea that most probably impact the abundance of methanoarchaea in microbial consortia. Here, we characterize the first identified Methanosarcina-infecting virus (MetSV) and show a mechanism for acquiring resistance against MetSV. Based on our results, we propose that growth as sarcina-like aggregates prevents infection and subsequent lysis. These findings allow new insights into the virus-host relationship in methanogenic community structures, their dynamics, and their phase heterogeneity. Moreover, the availability of a specific virus provides new possibilities to deepen our knowledge of the defense mechanisms of potential hosts and offers tools for genetic manipulation.
Marine ecosystems occupy 71% of the surface of our planet, yet we know little about their diversity. Although the inventory of species is continually increasing, as registered by the Census of Marine Life program, only about 10% of the estimated two million marine species are known. This lag between observed and estimated diversity is in part due to the elusiveness of most aquatic species and the technical difficulties of exploring extreme environments , as for instance the abyssal plains and polar waters. In the last decade, the rapid development of affordable and flexible high-throughput sequencing approaches have been helping to improve our knowledge of marine biodiversity, from the rich microbial biota that forms the base of the tree of life to a wealth of plant and animal species. In this review, we present an overview of the applications of genomics to the study of marine life, from evolutionary biology of non-model organisms to species of commercial relevance for fishing, aquaculture and biomedicine. Instead of providing an exhaustive list of available genomic data, we rather set to present con-textualized examples that best represent the current status of the field of marine genomics.
CRISPR (clustered regularly interspaced short palindromic repeats) is a microbial immune system against foreign DNA. Recognition sequences (spacers) encoded within the CRISPR array mediate the immune reaction in a sequence-specific manner. The known mechanisms for the evolution of CRISPR arrays include spacer acquisition from foreign DNA elements at the time of invasion and array erosion through spacer deletion. Here we consider the contribution of genetic recombination between homologous CRISPR arrays to the evolution of spacer repertoire. Acquisition of spacers from exogenic arrays via recombination may confer the recipient with immunity against unencountered antagonists. For this purpose we develop a novel method for the detection of recombination in CRISPR arrays by modeling the spacer order in arrays from multiple strains from the same species. Because the evolutionary signal of spacer recombination may be similar to that of pervasive spacer deletions or independent spacer acquisition, our method entails a robustness analysis of the recombination inference by a statistical comparison to resampled and perturbed datasets. We analyze CRISPR datasets from four bacterial species: two Gammaproteobacteria species harboring CRISPR type I and two Streptococcus species harboring CRISPR type II loci. We find that CRISPR array evolution in E. coli and S. agalactiae can be explained solely by vertical inheritance and differential spacer deletion. In P. aeruginosa, we find an excess of single spacers potentially incorporated into the CRISPR locus during independent acquisition events. In S. thermophilus, evidence for spacer acquisition by recombination is present in five out of 70 strains. Genetic recombination has been proposed to accelerate adaptation by combining beneficial mutations that arose in independent lineages. However, for most species under study, we find that CRISPR evolution is shaped mainly by spacer acquisition and loss rather than recombination. Since the evolution of spacer content is characterized by a rapid turnover, it is likely that recombination is not beneficial for improving phage resistance in the strains under study, or that it cannot be detected in the resolution of intra-species comparisons. © The Author(s) 2015. Published by Oxford University Press on behalf of the Society for Molecular Biology and Evolution.
Background Large scale transcript analysis of human glomerular microvascular endothelial cells (HGMEC) has never been accomplished. We designed this study to define the transcriptome of HGMEC and facilitate a better characterization of these endothelial cells with unique features. Serial analysis of gene expression (SAGE) was used for its unbiased approach to quantitative acquisition of transcripts. Results We generated a HGMEC SAGE library consisting of 68,987 transcript tags. Then taking advantage of large public databases and advanced bioinformatics we compared the HGMEC SAGE library with a SAGE library of non-cultured ex vivo human glomeruli (44,334 tags) which contained endothelial cells. The 823 tags common to both which would have the potential to be expressed in vivo were subsequently checked against 822,008 tags from 16 non-glomerular endothelial SAGE libraries. This resulted in 268 transcript tags differentially overexpressed in HGMEC compared to non-glomerular endothelia. These tags were filtered using a set of criteria: never before shown in kidney or any type of endothelial cell, absent in all nephron regions except the glomerulus, more highly expressed than statistically expected in HGMEC. Neurogranin, a direct target of thyroid hormone action which had been thought to be brain specific and never shown in endothelial cells before, fulfilled these criteria. Its expression in glomerular endothelium in vitro and in vivo was then verified by real-time-PCR, sequencing and immunohistochemistry. Conclusions Our results represent an extensive molecular characterization of HGMEC beyond a mere database, underline the endothelial heterogeneity, and propose neurogranin as a potential link in the kidney-thyroid axis. Electronic supplementary material The online version of this article (doi:10.1186/1471-2164-15-725) contains supplementary material, which is available to authorized users.
Background CRISPR is a microbial immune system likely to be involved in host-parasite coevolution. It functions using target sequences encoded by the bacterial genome, which interfere with invading nucleic acids using a homology-dependent system. The system also requires protospacer associated motifs (PAMs), short motifs close to the target sequence that are required for interference in CRISPR types I and II. Here, we investigate whether PAMs are depleted in phage genomes due to selection pressure to escape recognition. Results To this end, we analyzed two data sets. Phages infecting all bacterial hosts were analyzed first, followed by a detailed analysis of phages infecting the genus Streptococcus, where PAMs are best understood. We use two different measures of motif underrepresentation that control for codon bias and the frequency of submotifs. We compare phages infecting species with a particular CRISPR type to those infecting species without that type. Since only known PAMs were investigated, the analysis is restricted to CRISPR types I-C and I-E and in Streptococcus to types I-C and II. We found evidence for PAM depletion in Streptococcus phages infecting hosts with CRISPR type I-C, in Vibrio phages infecting hosts with CRISPR type I-E and in Streptococcus thermopilus phages infecting hosts with type II-A, known as CRISPR3. Conclusions The observed motif depletion in phages with hosts having CRISPR can be attributed to selection rather than to mutational bias, as mutational bias should affect the phages of all hosts. This observation implies that the CRISPR system has been efficient in the groups discussed here. Electronic supplementary material The online version of this article (doi:10.1186/1471-2164-15-663) contains supplementary material, which is available to authorized users.
Here, we describe a novel virulent bacteriophage that infects Bacillus weihenstephanensis, isolated from soil in Austria. It is the first phage to be discovered that infects this species. Here, we present the complete genome sequence of this podovirus.
Background: The CRISPR/Cas system is known to act as an adaptive and heritable immune system in Eubacteria and Archaea. Immunity is encoded in an array of spacer sequences. Each spacer can provide specific immunity to invasive elements that carry the same or a similar sequence. Even in closely related strains, spacer content is very dynamic and evolves quickly. Standard models of nucleotide evolution cannot be applied to quantify its rate of change since processes other than single nucleotide changes determine its evolution. Methods: We present probabilistic models that are specific for spacer content evolution. They account for the different processes of insertion and deletion. Insertions can be constrained to occur on one end only or are allowed to occur throughout the array. One deletion event can affect one spacer or a whole fragment of adjacent spacers. Parameters of the underlying models are estimated for a pair of arrays by maximum likelihood using explicit ancestor enumeration. Results: Simulations show that parameters are well estimated on average under the models presented here. There is a bias in the rate estimation when including fragment deletions. The models also estimate times between pairs of strains. But with increasing time, spacer overlap goes to zero, and thus there is an upper bound on the distance that can be estimated. Spacer content similarities are displayed in a distance based phylogeny using the estimated times.We use the presented models to analyze different Yersinia pestis data sets and find that the results among them are largely congruent. The models also capture the variation in diversity of spacers among the data sets. A comparison of spacer-based phylogenies and Cas gene phylogenies shows that they resolve very different time scales for this data set. Conclusions: The simulations and data analyses show that the presented models are useful for quantifying spacer content evolution and for displaying spacer content similarities of closely related strains in a phylogeny. This allows for comparisons of different CRISPR arrays or for comparisons between CRISPR arrays and nucleotide substitution rates.
The kingdom of fungi provides model organisms for biotechnology, cell biology, genetics, and life sciences in general. Only when their phylogenetic relationships are stably resolved, can individual results from fungal research be integrated into a holistic picture of biology. However, and despite recent progress, many deep relationships within the fungi remain unclear. Here, we present the first phylogenomic study of an entire eukaryotic kingdom that uses a consistency criterion to strengthen phylogenetic conclusions. We reason that branches (splits) recovered with independent data and different tree reconstruction methods are likely to reflect true evolutionary relationships. Two complementary phylogenomic data sets based on 99 fungal genomes and 109 fungal expressed sequence tag (EST) sets analyzed with four different tree reconstruction methods shed light from different angles on the fungal tree of life. Eleven additional data sets address specifically the phylogenetic position of Blastocladiomycota, Ustilaginomycotina, and Dothideomycetes, respectively. The combined evidence from the resulting trees supports the deep-level stability of the fungal groups toward a comprehensive natural system of the fungi. In addition, our analysis reveals methodologically interesting aspects. Enrichment for EST encoded data-a common practice in phylogenomic analyses-introduces a strong bias toward slowly evolving and functionally correlated genes. Consequently, the generalization of phylogenomic data sets as collections of randomly selected genes cannot be taken for granted. A thorough characterization of the data to assess possible influences on the tree reconstruction should therefore become a standard in phylogenomic analyses.
Supertree methods combine overlapping input trees into a larger supertree. Here, I consider split-based supertree methods that first extract the split information of the input trees and subsequently combine this split information into a phylogeny. Well known split-based supertree methods are matrix representation with parsimony and matrix representation with compatibility. Combining input trees on the same taxon set, as in the consensus setting, is a well-studied task and it is thus desirable to generalize consensus methods to supertree methods. Here, three variants of majority-rule (MR) supertrees that generalize majority-rule consensus trees are investigated. I provide simple formulas for computing the respective score for bifurcating input- and supertrees. These score computations, together with a heuristic tree search minmizing the scores, were implemented in the python program PluMiST (Plus- and Minus SuperTrees) available from http://www.cibiv.at/software/plumist. The different MR methods were tested by simulation and on real data sets. The search heuristic was successful in combining compatible input trees. When combining incompatible input trees, especially one variant, MR(-) supertrees, performed well. The presented framework allows for an efficient score computation of three majority-rule supertree variants and input trees. I combined the score computation with a heuristic search over the supertree space. The implementation was tested by simulation and on real data sets and showed promising results. Especially the MR(-) variant seems to be a reasonable score for supertree reconstruction. Generalizing these computations to multifurcating trees is an open problem, which may be tackled using this framework.
P. L. Erdős and L. A. Székely [Adv. Appl. Math. 10, No. 4, 488–496 (1989; Zbl 0723.05046)] gave a bijection between rooted semilabeled trees and set partitions, which specializes to a bijection between phylogenetic trees and set partitions with classes of size ≥2. L. H. Harper’s results [Ann. Math. Stat. 38, 410–414 (1967; Zbl 0154.43703)] on the asymptotic normality of the Stirling numbers of the second kind translate into asymptotic normality of rooted semilabeled trees with given number of vertices, when the number of internal vertices varies. The asymptotic normality of modified Stirling numbers of the second kind that enumerate partitions of a fixed set into a given number of classes of size ≥2, which is shown in this paper, translates into the asymptotic normality of the number of phylogenetic trees with given number of vertices, when the number of leaves varies. We also obtain the asymptotic normality of the number of phylogenetic trees with given number of leaves and varying number of internal vertices, which is more relevant for phylogeny. By the bijection, this means the asymptotic normality of the number of partitions of n+m-1 elements into m lasses of size ≥2, when n is fixed and m varies. The proofs are adaptations of the techniques of Harper [loc. cit.]. We provide asymptotics for the relevant expectations and variances with error term O(1/n).
The availability of many gene alignments with overlapping taxon sets raises the question of which strategy is the best to infer species phylogenies from multiple gene information. Methods and programs abound that use the gene alignment in different ways to reconstruct the species tree. In particular, different methods combine the original data at different points along the way from the underlying sequences to the final tree. Accordingly, they are classified into superalignment, supertree and medium-level approaches. Here, we present a simulation study to compare different methods from each of these three approaches. We observe that superalignment methods usually outperform the other approaches over a wide range of parameters including sparse data and gene-specific evolutionary parameters. In the presence of high incongruency among gene trees, however, other combination methods show better performance than the superalignment approach. Surprisingly, some supertree and medium-level methods exhibit, on average, worse results than a single gene phylogeny with complete taxon information. For some methods, using the reconstructed gene tree as an estimation of the species tree is superior to the combination of incomplete information. Superalignment usually performs best since it is less susceptible to stochastic error. Supertree methods can outperform superalignment in the presence of gene-tree conflict.
Fungi are abundant in the biosphere. They have fascinated mankind as far as written history goes and have considerably influenced our culture. In biotechnology, cell biology, genetics, and life sciences in general fungi constitute relevant model organisms. Once the phylogenetic relationships of fungi are stably resolved individual results from fungal research can be combined into a holistic picture of biology. However, and despite recent progress, the backbone of the fungal phylogeny is not yet fully resolved. Especially the early evolutionary history of fungi and the order or below-order relationships within the ascomycetes remain uncertain. Here we present the first phylogenomic study for a eukaryotic kingdom that merges all publicly available fungal genomes and expressed sequence tags (EST) to build a data set comprising 128 genes and 146 taxa. The resulting tree provides a stable phylogenetic backbone for the fungi. Moreover, we present the first formal supertree based on 161 fungal taxa and 128 gene trees. The combined evidences from the trees support the deep-level stability of the fungal groups towards a comprehensive natural system of the fungi. They indicate that the classification of the fungi, especially their alliance with the Microsporidia, requires careful revision. Our analysis is also an inventory of present day sequence information for the fungi. It provides insights into which phylogenenetic conclusions can and which cannot be drawn from the current data and may serve as a guide to direct further sequencing initiatives. Together with a comprehensive animal phylogeny, we provide the second of three pillars to understand the evolution of the multicellular eukaryotic kingdoms, fungi, metazoa, and plants, in the past 1.6 billion years.
- Jul 2008
The geometrical representation of the space of phylogenetic trees implies a metric on the space of weighted trees. This metric, the geodesic distance, is the length of the shortest path through that space. We present an exact algorithm to compute this metric. For biologically reasonable trees, the implementation allows fast computations of the geodesic distance, although the running time of the algorithm is worst-case exponential. The algorithm was applied to pairs of 118 gene trees of the metazoa. The results show that a special path in tree space, the cone path, which can be computed in linear time, is a good approximation of the geodesic distance. The program GeoMeTree is a python implementation of the geodesic distance, and it is approximations and is available from www.cibiv.at/software/geometree.
- Mar 2006
Models of RNA secondary structure folding are widely used to study evolution in theory and simulation. However, systematic studies of the parameters involved are rare. In this paper, we study by simulation how RNA evolution is influenced by three different factors, namely the mutation rate, scaling of the fitness function, and distance measure. We found that for low mutation rates the qualitative evolutionary behavior is robust with respect to the scaling of the fitness function. For efficient mutation rates, which are close to the error threshold, scaling and distance measure have a strong influence on the evolutionary behavior. A global distance measure that takes sequence information additively into account lowers the error threshold. When using a local sequence-structure alignment for the distance, we observed a smoother evolution of the fitness over time. Finally, in addition to the well known error threshold, we identify another threshold of the mutation rate, called divergence threshold, where the qualitative transient behavior changes from a localized to an exploratory search.