Mutations as molecular tools : The metabolic-rate dependent molecular clock and DNA barcoding of allied species

Mutation and recombination are the fundamental processes leading to genetic variation in natural populations. This variation forms the raw material for evolution through natural selection and drift. Therefore, studying mutation rates may reveal information about evolutionary histories as well as phylogenetic interrelationships of organisms. In this thesis two molecular tools, DNA barcoding and the molecular clock were examined. In the first part, the efficiency of mutations to delineate closely related species was tested and the implications for conservation practices were assessed. The second part investigated the proposition that a constant mutation rate exists within invertebrates, in form of a metabolic-rate dependent molecular clock, which can be applied to accurately date speciation events. DNA barcoding aspires to be an efficient technique to not only distinguish between species but also reveal population-level variation solely relying on mutations found on a short stretch of a single gene. In this thesis barcoding was applied to discriminate between Hylochares populations from Russian Karelia and new Hylochares findings from the greater Helsinki region in Finland. Although barcoding failed to delineate the two reproductively isolated groups, their distinct morphological features and differing life-history traits led to their classification as two closely related, although separate species. The lack of genetic differentiation appears to be due to a recent divergence event not yet reflected in the beetles molecular make-up. Thus, the Russian Hylochares was described as a new species. The Finnish species, previously considered as locally extinct, was recognized as endangered. Even if, due to their identical genetic make-up, the populations had been regarded as conspecific, conservation strategies based on prior knowledge from Russia would not have guaranteed the survival of the Finnish beetle. Therefore, new conservation actions based on detailed studies of the biology and life-history of the Finnish Hylochares were conducted to protect this endemic rarity in Finland. The idea behind the strict molecular clock is that mutation rates are constant over evolutionary time and may thus be used to infer species divergence dates. However, one of the most recent theories argues that a strict clock does not tick per unit of time but that it has a constant substitution rate per unit of mass-specific metabolic energy. Therefore, according to this hypothesis, molecular clocks have to be recalibrated taking body size and temperature into account. This thesis tested the temperature effect on mutation rates in equally sized invertebrates. For the first dataset (family Eucnemidae, Coleoptera) the phylogenetic interrelationships and evolutionary history of the genus Arrhipis had to be inferred before the influence of temperature on substitution rates could be studied. Further, a second, larger invertebrate dataset (family Syrphidae, Diptera) was employed. Several methodological approaches, a number of genes and multiple molecular clock models revealed that there was no consistent relationship between temperature and mutation rate for the taxa under study. Thus, the body size effect, observed in vertebrates but controversial for invertebrates, rather than temperature may be the underlying driving force behind the metabolic-rate dependent molecular clock. Therefore, the metabolic-rate dependent molecular clock does not hold for the here studied invertebrate groups. This thesis emphasizes that molecular techniques relying on mutation rates have to be applied with caution. Whereas they may work satisfactorily under certain conditions for specific taxa, they may fail for others. The molecular clock as well as DNA barcoding should incorporate all the information and data available to obtain comprehensive estimations of the existing biodiversity and its evolutionary history.

Phylogeny of a taxonomically difficult group and evolution of host location mechanism

The parasitic wasps are one of the largest insect groups and their life histories are remarkably variable. Common to all parasitic wasps is that they kill their hosts, which are usually beetles, butterflies and sometimes spiders. Hosts are often at a larval or pupal stage and live in concealed conditions, such as in plant tissue. Parasitic wasps have two main ways of finding their host. 1) They can detect chemical compounds emitted by damaged plant material or released by larvae living in plant tissue, and 2) detect the larvae by sound vibrations. Even though pupae are immobile and silent, and therefore do not cause vibration, parasitoids have, however, adapted to find passive developmental stages by producing vibration themselves by knocking the substrate with their antennae, and then detecting the echoes with their legs. This echolocation allows a parasitoid to locate its potential hosts that are deeply buried in wood. This study focuses on the relationships of the subfamily Cryptinae (Hymenoptera: Ichneumonidae) and related taxa, and the evolution of host location mechanism. There are no earlier studies of the phylogeny of the Cryptinae, and the position of related taxa are unclear. According to the earlier classification, which is entirely intuitional, the Cryptinae is divided into three tribes: Cryptini, Hemigasterini and Phygadeuontini. Further, these tribes are subdiveded into numerous subtribes. This work, based on molecular characters, shows that the cryptine tribes Cryptini, Phygadeuon¬tini and Hemigasterini come out largely as monophyletic groups, thus agreeing with the earlier classification. The earlier subtribal classification had no support. In addition, it is shown that modified antennal structures are associated with host usage of wood-boring coleopteran hosts. The cryptines have a clear modification series on their antennal tips from a simply tip to a hammer-like structure. The species with strongly modified antennae belong mostly to the tribe Cryptini and they utilise wood-boring beetles as hosts. Also, field observations on insect behaviour support this result.

Role of the triplet state in the green emission peak of polyfluorene films: A time evolution study

The blue emission of ethyl-hexyl substituted polyfluorene (PF2/6) films is accompanied by a low energy green emission peak around 500 nm in inert atmosphere. The intensity of this 500 nm peak is large in electroluminescence (EL) compared to photoluminescence (PL)measurements. Furthermore, the green emission intensity reduces dramatically in the presence of molecular oxygen. To understand this, we have modeled various nonradiative processes by time dependent quantum many body methods. These are (i) intersystem crossing to study conversion of excited singlets to triplets leading to a phosphorescence emission, (ii) electron-hole recombination (e-hR) process in the presence of a paramagnetic impurity to follow the yield of triplets in a polyene system doped with paramagnetic metal atom, and (iii) quenching of excited triplet states in the presence of oxygen molecules to understand the low intensity of EL emission in ambient atmosphere, when compared with that in nitrogen atmosphere. We have employed the Pariser-Parr-Pople Hamiltonian to model the molecules and have invoked electron-electron repulsions beyond zero differential approximation while treating interactions between the organic molecule and the rest of the system. Our time evolution methods show that there is a large cross section for triplet formation in the e-hR process in the presence of paramagnetic impurity with degenerate orbitals. The triplet yield through e-hR process far exceeds that in the intersystem crossing pathway, clearly pointing to the large intensity of the 500 nm peak in EL compared to PL measurements. We have also modeled the triplet quenching process by a paramagnetic oxygen molecule which shows a sizable quenching cross section especially for systems with large sizes. These studies show that the most probable origin of the experimentally observed low energy EL emission is the triplets.

Three-dimensional structure of heat shock protein 90 from Plasmodium falciparum: molecular modelling approach to rational drug design against malaria

We have recently implicated heat shock protein 90 from Plasmodium falciparum (PfHsp90) as a potential drug target against malaria. Using inhibitors specific to the nucleotide binding domain of Hsp90, we have shown potent growth inhibitory effects on development of malarial parasite in human erythrocytes. To gain better understanding of the vital role played by PfHsp90 in parasite growth, we have modeled its three dimensional structure using recently described full length structure of yeast Hsp90. Sequence similarity found between PfHsp90 and yeast Hsp90 allowed us to model the core structure with high confidence. The superimposition of the predicted structure with that of the template yeast Hsp90 structure reveals an RMSD of 3.31 angstrom. The N-terminal and middle domains showed the least RMSD (1.76 angstrom) while the more divergent C-terminus showed a greater RMSD (2.84 angstrom) with respect to the template. The structure shows overall conservation of domains involved in nucleotide binding, ATPase activity, co-chaperone binding as well as inter-subunit interactions. Important co-chaperones known to modulate Hsp90 function in other eukaryotes are conserved in malarial parasite as well. An acidic stretch of amino acids found in the linker region, which is uniquely extended in PfHsp90 could not be modeled in this structure suggesting a flexible conformation. Our results provide a basis to compare the overall structure and functional pathways dependent on PfHsp90 in malarial parasite. Further analysis of differences found between human and parasite Hsp90 may make it possible to design inhibitors targeted specifically against malaria.

Molecular line and continuum studies of the early stages of star formation

New stars form in dense interstellar clouds of gas and dust called molecular clouds. The actual sites where the process of star formation takes place are the dense clumps and cores deeply embedded in molecular clouds. The details of the star formation process are complex and not completely understood. Thus, determining the physical and chemical properties of molecular cloud cores is necessary for a better understanding of how stars are formed. Some of the main features of the origin of low-mass stars, like the Sun, are already relatively well-known, though many details of the process are still under debate. The mechanism through which high-mass stars form, on the other hand, is poorly understood. Although it is likely that the formation of high-mass stars shares many properties similar to those of low-mass stars, the very first steps of the evolutionary sequence are unclear. Observational studies of star formation are carried out particularly at infrared, submillimetre, millimetre, and radio wavelengths. Much of our knowledge about the early stages of star formation in our Milky Way galaxy is obtained through molecular spectral line and dust continuum observations. The continuum emission of cold dust is one of the best tracers of the column density of molecular hydrogen, the main constituent of molecular clouds. Consequently, dust continuum observations provide a powerful tool to map large portions across molecular clouds, and to identify the dense star-forming sites within them. Molecular line observations, on the other hand, provide information on the gas kinematics and temperature. Together, these two observational tools provide an efficient way to study the dense interstellar gas and the associated dust that form new stars. The properties of highly obscured young stars can be further examined through radio continuum observations at centimetre wavelengths. For example, radio continuum emission carries useful information on conditions in the protostar+disk interaction region where protostellar jets are launched. In this PhD thesis, we study the physical and chemical properties of dense clumps and cores in both low- and high-mass star-forming regions. The sources are mainly studied in a statistical sense, but also in more detail. In this way, we are able to examine the general characteristics of the early stages of star formation, cloud properties on large scales (such as fragmentation), and some of the initial conditions of the collapse process that leads to the formation of a star. The studies presented in this thesis are mainly based on molecular line and dust continuum observations. These are combined with archival observations at infrared wavelengths in order to study the protostellar content of the cloud cores. In addition, centimetre radio continuum emission from young stellar objects (YSOs; i.e., protostars and pre-main sequence stars) is studied in this thesis to determine their evolutionary stages. The main results of this thesis are as follows: i) filamentary and sheet-like molecular cloud structures, such as infrared dark clouds (IRDCs), are likely to be caused by supersonic turbulence but their fragmentation at the scale of cores could be due to gravo-thermal instability; ii) the core evolution in the Orion B9 star-forming region appears to be dynamic and the role played by slow ambipolar diffusion in the formation and collapse of the cores may not be significant; iii) the study of the R CrA star-forming region suggests that the centimetre radio emission properties of a YSO are likely to change with its evolutionary stage; iv) the IRDC G304.74+01.32 contains candidate high-mass starless cores which may represent the very first steps of high-mass star and star cluster formation; v) SiO outflow signatures are seen in several high-mass star-forming regions which suggest that high-mass stars form in a similar way as their low-mass counterparts, i.e., via disk accretion. The results presented in this thesis provide constraints on the initial conditions and early stages of both low- and high-mass star formation. In particular, this thesis presents several observational results on the early stages of clustered star formation, which is the dominant mode of star formation in our Galaxy.

Unraveling the packing pattern leading to gelation using SS NMR and X-ray diffraction: direct observation of the evolution of self-assembled fibers

A detailed understanding of the mode of packing patterns that leads to the gelation of low molecular mass gelators derived from bile acid esters was carried out using solid state NMR along with complementary techniques such as powder X-ray diffraction (PXRD), differential scanning calorimetry (DSC), thermogravimetric analysis (TGA) and polarizing optical microscopy (POM). Solid state C-13{H-1} cross polarization (CP) magic angle spinning (MAS) NMR of the low molecularmass gel in its native state was recorded for the first time. A close resemblance in the packing patterns of the gel, xerogel and bulk solid states was revealed upon comparing their C-13{H-1} CPMAS NMR spectral pattern. A doublet resonance pattern of C-13 signals in C-13{H-1}CPMAS NMR spectra were observed for the gelator molecules, whereas the non-gelators showed simple singlet resonance or resulted inthe formation of inclusion complexes/solvates. PXRD patterns revealed a close isomorphous nature of the gelators indicating the similarity in the mode of the packing pattern in their solid state. Direct imaging of the evolution of nanofibers (sol-gel transition) was carried out using POM, which proved the presence of self-assembled fibrillar networks (SAFINs) in the gel. Finally powder X-ray structure determination revealed the presence of two non-equivalent molecules in an asymmetric unit which is responsible for the doublet resonance pattern in the solid state NMR spectra.

Evolution, Homology Conservation, and Identification of Unique Sequence Signatures in GH19 Family Chitinases

The discovery of GH (Glycoside Hydrolase) 19 chitinases in Streptomyces sp. raises the possibility of the presence of these proteins in other bacterial species, since they were initially thought to be confined to higher plants. The present study mainly concentrates on the phylogenetic distribution and homology conservation in GH19 family chitinases. Extensive database searches are performed to identify the presence of GH19 family chitinases in the three major super kingdoms of life. Multiple sequence alignment of all the identified GH19 chitinase family members resulted in the identification of globally conserved residues. We further identified conserved sequence motifs across the major sub groups within the family. Estimation of evolutionary distance between the various bacterial and plant chitinases are carried out to better understand the pattern of evolution. Our study also supports the horizontal gene transfer theory, which states that GH19 chitinase genes are transferred from higher plants to bacteria. Further, the present study sheds light on the phylogenetic distribution and identifies unique sequence signatures that define GH19 chitinase family of proteins. The identified motifs could be used as markers to delineate uncharacterized GH19 family chitinases. The estimation of evolutionary distance between chitinase identified in plants and bacteria shows that the flowering plants are more related to chitinase in actinobacteria than that of identified in purple bacteria. We propose a model to elucidate the natural history of GH19 family chitinases.

Wood-inhabiting Basidiomycetes in the Caucasus Region : Systematics and Biogeography

The Caucasus region is a hotspot of biodiversity and is one of the few areas in the Northern Hemisphere which harbor Pleistocene glacial refugia. The region encompasses Armenia, Azerbaijan, Georgia, the southernmost European Russia, NE Turkey, and northern Iran. The study on fungal composition of the Caucasus region and its connection and possible contribution to the present mycota of Europe has largely escaped empirical scrutiny. Using taxonomic surveys, phylogenetic reconstruction methods, haplotype analysis, and similarity tests, this study has aimed to, 1) summarize the knowledge on the occurrence of corticioids and polypores in the Caucasus region, 2) resolve the phylogenetic relationships of selected, resupinate wood-inhabiting basidiomycetes for which the Caucasus region is currently the mere, or one of the noteworthy areas of distribution, and, 3) assess the similarity of Caucasian corticioid fungi to those of Europe and important areas in the Northern Hemisphere, and to examine the significance of the Caucasus region as a glacial refugium for these fungi. This study provides the first catalogue of corticioids and polypores (635 species) occurring in the Caucasus region. The phylogeny and systematics of the Caucasian resupinate taxa in focus has been resolved and the usefulness of some morphological characters has been re-evaluated. In this context, four new genera and two new species were described and five new combinations were proposed, two of which were supplemented with modern descriptions. The species composition of corticioids in the Caucasus region is found to be distinctly more similar to Europe and North America than to East Asia and India. The highest molecular diversity and within population pairwise distance for Peniophorella praetermissa has been detected in the Caucasus and East Asia, with the isolates of the latter area being highly divergent from the European ones. This, and the assignment of root haplotype to the Caucasian isolates in a haplotype network for Phlebia tuberucalta and P. livida, call attention to the role of the Caucasus region in shaping the current mycota of Europe.

Electronic structures of electron donor-acceptor complexes: results from ultraviolet photoelectron spectroscopy and molecular orbital calculations

HeI photoelectron spectra of 1:1 electron donor-acceptor complexes are discussed in the light of molecular orbital calculations. The complexes discussed include those formed by BH3, BF3 and SO2. Some systematics have been found in the ionization energy shifts of the complexes compared to the free components and these are related to the strength of the donor-acceptor bond. Hel spectra of hydrogen bonded complexes are discussed in comparison with results from MO calculations. Limitations of such studies as well as scope for further investigations are indicated.

X-ray and molecular-dynamics studies on Mycobacterium leprae single-stranded DNA-binding protein and comparison with other eubacterial SSB structures

The crystal structures of two forms of Mycobacterium leprae single-stranded DNA-binding protein (SSB) have been determined at 2.05 and 2.8 A resolution. Comparison of these structures with the structures of other eubacterial SSBs indicates considerable variation in their quaternary association, although the DNA-binding domains in all of them exhibit the same OB-fold. This variation has no linear correlation with sequence variation, but could be related to variation in protein stability. Molecular-dynamics simulations have been carried out on tetrameric molecules derived from the two forms and the prototype Escherichia coli SSB and the individual subunits of both proteins. Together, the X-ray studies and molecular-dynamics simulations yield information on the relatively rigid and flexible regions of the molecule and on the effect of oligomerization on flexibility. The simulations provide insight into the changes in subunit structure on oligomerization. They also provide insight into the stability and time evolution of the hydrogen bonds/water bridges that connect the two pairs of monomers in the tetramer.

Molecular Characterization of Viruses Causing the Cassava Brown Streak Disease Epidemic in Eastern Africa

Cassava brown streak disease (CBSD) was described for the first time in Tanganyika (now Tanzania) about seven decades ago. Tanganyika (now Tanzania) about seven decades ago. It was endemic in the lowland areas of East Africa and inland parts of Malawi and caused by Cassava brown streak virus (CBSV; genus Ipomovirus; Potyviridae). However, in 1990s CBSD was observed at high altitude areas in Uganda. The causes for spread to new locations were not known.The present work was thus initiated to generate information on genetic variability, clarify the taxonomy of the virus or viruses associated with CBSD in Eastern Africa as well as to understand the evolutionary forces acting on their genes. It also sought to develop a molecular based diagnostic tool for detection of CBSD-associated virus isolates. Comparison of the CP-encoding sequences of CBSD-associated virus isolates collected from Uganda and north-western Tanzania in 2007 and the partial sequences available in Genbank revealed occurrence of two genetically distinct groups of isolates. Two isolates were selected to represent the two groups. The complete genomes of isolates MLB3 (TZ:Mlb3:07) and Kor6 (TZ:Kor6:08) obtained from North-Western (Kagera) and North-Eastern (Tanga) Tanzania, respectively, were sequenced. The genomes were 9069 and 8995 nucleotides (nt), respectively. They translated into polyproteins that were predicted to yield ten mature proteins after cleavage. Nine proteins were typical in the family Potyviridae, namely P1, P3, 6K1, CI, 6K2, VPg, NIa-Pro, NIb and CP, but the viruses did not contain HC-Pro. Interestingly, genomes of both isolates contained a Maf/HAM1-like sequence (HAM1h; 678 nucleotides, 25 kDa) recombined between the NIb and CP domains in the 3’-proximal part of the genomes. HAM1h was also identified in Euphorbia ringspot virus (EuRSV) whose sequence was in GenBank. The HAM1 gene is widely spread in both prokaryotes and eukaryotes. In yeast (Saccharomyces cerevisiae) it is known to be a nucleoside triphosphate (NTP) pyrophosphatase. Novel information was obtained on the structural variation at the N-termini of polyproteins of viruses in the genus Ipomovirus. Cucumber vein yellowing virus (CVYV) and Squash vein yellowing virus (SqVYV) contain a duplicated P1 (P1a and P1b) but lack the HC-Pro. On the other hand, Sweet potato mild mottle virus (SPMMV), has a single but large P1 and has HC-Pro. Both virus isolates (TZ:Mlb3:07 & TZ:Kor6:08) characterized in this study contained a single P1 and lacked the HC-Pro which indicates unique evolution in the family Potyviridae. Comparison of 12 complete genomes of CBSD-associated viruses which included two genomes characterized in this study, revealed genetic identity of 69.0–70.3% (nt) and amino acid (aa) identities of 73.6–74.4% at polyprotein level. Comparison was also made among 68 complete CP sequences, which indicated 69.0-70.3 and 73.6-74.4 % identity at nt and aa levels, respectively. The genetic variation was large enough for dermacation of CBSD-associated virus isolates into two distinct species. The name CBSV was retained for isolates that were related to CBSV isolates available in database whereas the new virus described for the first time in this study was named Ugandan cassava brown streak virus (UCBSV) by the International Committee on Virus Taxonomy (ICTV). The isolates TZ:Mlb3:07 and TZ:Kor6:08 belong to UCBSV and CBSV, respectively. The isolates of CBSV and UCBSV were 79.3-95.5% and 86.3-99.3 % identitical at nt level, respectively, suggesting more variation amongst CBSV isolates. The main sources of variation in plant viruses are mutations and recombination. Signals for recombination events were detected in 50% of isolates of each virus. Recombination events were detected in coding and non-coding (3’-UTR) sequences except in the 5’UTR and P3. There was no evidence for recombination between isolates of CBSV and UCBSV. The non-synonomous (dN) to synonomous (dS) nucleotide substitution ratio (ω) for the HAM1h and CP domains of both viruses were ≤ 0.184 suggesting that most sites of these proteins were evolving under strong purifying selection. However, there were individual amino acid sites that were submitted to adaptive evolution. For instance, adaptive evolution was detected in the HAM1h of UCBSV (n=15) where 12 aa sites were under positive selection (P< 0.05) but not in CBSV (n=12). The CP of CBSV (n=23) contained 12 aa sites (p<0.01) while only 5 aa sites in the CP gene of UCBSV were predicted to be submitted to positive selection pressure (p<0.01). The advantages offered by the aa sites under positive selection could not be established but occurrence of such sites in the terminal ends of UCBSV-HAMIh, for example, was interpreted as a requirement for proteolysis during polyprotein processing. Two different primer pairs that simultaneously detect UCBSV and CBSV isolates were developed in this study. They were used successfully to study distribution of CBSV, UCBSV and their mixed infections in Tanzania and Uganda. It was established that the two viruses co-infect cassava and that incidences of co-infection could be as high as 50% around Lake Victoria on the Tanzanian side. Furthermore, it was revealed for the first time that both UCBSV and CBSV were widely distributed in Eastern Africa. The primer pair was also used to confirm infection in a close relative of cassava, Manihot glaziovii (Müller Arg.) with CBSV. DNA barcoding of M. glaziovii was done by sequencing the matK gene. Two out of seven M. glaziovii from the coastal areas of Korogwe and Kibaha in north eastern Tanzania were shown to be infected by CBSV but not UCBSV isolates. Detection in M. glaziovii has an implication in control and management of CBSD as it is likely to serve as virus reservoir. This study has contributed to the understanding of evolution of CBSV and UCBSV, which cause CBSD epidemic in Eastern Africa. The detection tools developed in this work will be useful in plant breeding, verification of the phytosanitary status of materials in regional and international movement of germplasm, and in all diagnostic activities related to management of CBSD. Whereas there are still many issues to be resolved such as the function and biological significance of HAM1h and its origin, this work has laid a foundation upon which the studies on these aspects can be based.

Social selection and the evolution of cooperative groups: The example of the cellular slime moulds

In social selection the phenotype of an individual depends on its own genotype as well as on the phenotypes, and so genotypes, of other individuals. This makes it impossible to associate an invariant phenotype with a genotype: the social context is crucial. Descriptions of metazoan development, which often is viewed as the acme of cooperative social behaviour, ignore or downplay this fact. The implicit justification for doing so is based on a group-selectionist point of view. Namely, embryos are clones, therefore all cells have the same evolutionary interest, and the visible differences between cells result from a common strategy. The reasoning is flawed, because phenotypic heterogeneity within groups can result from contingent choices made by cells from a flexible repertoire as in multicellular development. What makes that possible is phenotypic plasticity, namely the ability of a genotype to exhibit different phenotypes. However, co-operative social behaviour with division of labour requires that different phenotypes interact appropriately, not that they belong to the same genotype, or have overlapping genetic interests. We sketch a possible route to the evolution of social groups that involves many steps: (a) individuals that happen to be in spatial proximity benefit simply by virtue of their number; (b) traits that are already present act as preadaptations and improve the efficiency of the group; and (c) new adaptations evolve under selection in the social context-that is, via interactions between individuals-and further strengthen group behaviour. The Dictyostelid or cellular slime mould amoebae (CSMs) become multicellular in an unusual way, by the aggregation of free-living cells. In nature the resulting group can be genetically homogeneous (clonal) or heterogeneous (polyclonal); in either case its development, which displays strong cooperation between cells (to the extent of so-called altruism) is not affected. This makes the CSMs exemplars for the study of social behaviour.

Variational principles in evolution

For a one-locus selection model, Svirezhev introduced an integral variational principle by defining a Lagrangian which remained stationary on the trajectory followed by the population undergoing selection. It is shown here (i) that this principle can be extended to multiple loci in some simple cases and (ii) that the Lagrangian is defined by a straightforward generalization of the one-locus case, but (iii) that in two-locus or more general models there is no straightforward extension of this principle if linkage and epistasis are present. The population trajectories can be constructed as trajectories of steepest ascent in a Riemannian metric space. A general method is formulated to find the metric tensor and the surface-in the metric space on which the trajectories, which characterize the variations in the gene structure of the population, lie. The local optimality principle holds good in such a space. In the special case when all possible linkage disequilibria are zero, the phase point of the n-locus genetic system moves on the surface of the product space of n higher dimensional unit spheres in a certain Riemannian metric space of gene frequencies so that the rate of change of mean fitness is maximum along the trajectory. In the two-locus case the corresponding surface is a hyper-torus.