Journal of General Biology

Vol. 63, No. 6, 2002

Comparative genetics and evolutionary morphology of symbioses formed by plants with nitrogen-fixing microbes and endomycorrhizal fungi N. A. Provorov, A. Yu. Borisov, I. A. Tikhonovich 451

Principles and methods of geometric morphometrics I. Ya. Pavlinov, N. G. Mikeshina 473

Modeling of school and swarm formation as a consequence of autotaxis I. N. Senina, Yu. V. Tyutyunov 494

The vegetation adventivisation through perspective of current ecological ideas B. M. Mirkin, L. G. Naumova 500

The structure and dynamics of a woodreed Calamagrostis canescens population: a modelling approach N. G. Ulanova. A. N. Demidova. I. N. Klochkova, D. O. Logofet 509


On book "Methodology of biology: new ideas. Synergetics. Semiotics. Coevolution" G. Yu. Lubarsky 522

Comparative Genetics and Evolutionary Morphology of Symbioses Formed by Plants with Nitrogen-fixing Microbes and Endomycorrhizal Fungi N. A. Provorov, A. Yu. Borisov, I. A. Tikhonovich

All-Russia Research Institute of Agricultural Microbiology, Podbelsky St., 3, St. Petersburg, Pushkin 8, 196608, Russia e-mail:

Results of comparative morphological and genetic analyses are described for two major plant-microbe endosymbioses: N-fixing nodules (with rhizobia or actinomycetes Frankia) and arbuscular mycorrhiza (with Glomales fungi). Development from the primordia formed de novo in root tissues is common for all known types of N-fixing nodules. However, their structure varies greatly with respect to: (i) tissue topology (location of vascular bundles is peripheral in legumes but central in non-legumes); (ii) position of nodule primordium (inner or outer cortex in legumes, whereas pericycle in non-legumes); (iii) stability of apical meristem (persistent in the indeterminate nodules, transient in the determinate ones). In addition, legumes vary in ability to form compartments harboring endosymbiotic rhizobia that can be located intercellularly (infection threads) and intracellularly (symbiosomes). Using pea (Pisum sativum) symbiotic mutants, the nodule developmental program is dissected into a range of spatially and temporarily differentiated steps composing four sub-programs (development of endosymbiotic compartments; nodule histogenesis; autoregulation of nodulation; bacteroid differentiation). The developmental mutations are suggested in some cases to reverse the endosymbiotic system into the morphologically simpler forms some of which may correspond to the ancestral stages of nodule evolution. Origination of legume-rhizobial and actinorhizal symbioses is suggested to be based on a set of preadaptations many of which had been evolved in angiosperms during coevolution with arbuscular mycorrhizal fungi (e.g. inter- and intracellular maintenance of symbionts, their control via defence-like reactions and recognition of chitin-like molecules). Analysis of parallel morphological variation in symbiotic mutants and wild-growing legume species enables us to reconstruct the major stages of evolution for N-fixing symbioses. This evolution proceeded to a sufficient degree independently from the basic physiological function of nodules (symbiotic N-fixation) and possibly a recruiting of plant genes that initially fulfilled various "non-symbiotic" functions into the genetic networks monitoring plant-microbe interactions.

Principles and Methods of Geometric Morphometrics

I. Ya. Pavlinov (1), N. G. Mikeshina (2)

(1) Zoological Museum of Moscow State University, Bol. Nikitskaya 6, Moscow 103009, Russia, e-mail:

(2) Department of General Ecology, Biology Faculty, Moscow State University, Leninskie Gory, Moscow 117234, Russia

Dedicated to memory of Leslie Marcus who made an important contribution to development of geometric morphometrics.

The basic concepts, notions and methods of geometric morphometrics (GM) are considered. This approach implies multivariate analysis of landmark coordinates located following certain rules on the surface of a morphological object. The aim of GM is to reveal differences between morphological objects by their shapes as such, the "size factor" being excluded. The GM is based on the concept of Kendall' s space (KS) defined as a hypersphere with points distributed on its surface. These points are the shapes defined as aligned landmark configurations. KS is a non-Euclidian space, its metrics called Procrustes is defined by landmark configuration of a reference shape relative to which other shapes are aligned and compared. The differences among shapes are measured as Procrustes distances between respective points. For the linear methods of multivariate statistics to be applied to comparison of shapes, the respective points are projected onto the tangent plane (tangent space), the tangent point being defined by the reference. There are two principal methods of shape comparisons in GM: the Procrustes superimposition (a version of the least squares analysis) and thin-plate spline analysis. In the first case, Procrustes residuals are the outcome shape variables which remain after isometric alignment of the shapes being compared. Their summation over all landmarks yields Procrustes distances among these shapes. The Procrustes distances can be used in multivariate analyses just as the Euclidian distances. In the second case, the shapes are fitted to the references by stretching/compressing and shearing until complete identity of their landmark confiqurations. Eigenvectors of resulting bending energy matrix are defined as new shape variables, principal warps which yield another shape space with the origin defined by the reference. Projections of the shapes being compared onto principal warps yield partial warps, and their covariance matrix decomposition into eigenvectors yields relative warps which are similar to principal components (in particular, they are mutually orthogonal). Both partial and relative warps can be used in many multivariate statistic analyses as quantitative shape variables. Results of thin-plate spline analysis can be represented graphically by transformation grid which displays type, amount and localization of the shape differences. Basis rules of sample composition and landmark positioning to be used in GM are considered. At present, rigid (with minimal degrees of freedom) 2D morphological objects are most suitable for GM applications. It is important to recognize three type of real landmarks, and additionally semi-landmarks and "virtual" landmarks.

Some procedures of thin-plate spline analysis are considered exemplified by some study cases, as well as applications of some standard multivariate methods to GM results. They make it possible to evaluate correlation between different shapes, as well as between a shape and some non-shape variables (linear measurements etc); to evaluate the differences among organisms by shape of a morphological structure; to identify landmarks which most accound for both correlation and differences between the shapes. An annotated list of most popular softwares for GM is provided.

Modeling of School and Swarm Formation as a Consequence of Autotaxis

I. N. Senina, Yu. V. Tyutyunov

Department of Mathematical Methods in Economics and Ecology, Institute of Mechanics&Appleid Mathematics, Rostov State University, Stachki st. 20011, Rostov-on-Don 344090, Russia, e-mail:,

The simple model of school and swarm formation is proposed within the frameworks of Eulerian space models (reaction-diffusion-advection system). Assuming that the schooling and the processes of birth-and-death act on different time scales, we have excluded the local kinetics of species (the reaction term) from the model. The spatial dynamics of animals is circumscribed by scalar field of density and vector field of velocity. The basis of animal aggregation in space is the ability of animals to move in certain direction, i.e. taxis. As an example of swarming strategy the behavior of midges is taken: we presume that individuals accelerate towards higher swarm density but change direction when the density exceeds some maximum. In other words, acceleration of movement is assumed to be proportional (with density-dependent coefficient of proportionality) to the gradient of species density. This statement poses the equation for species velocity. Thus, our model adds the differential equation for velocity of autotaxis to the standard advection-diffusion model. The linear analysis of ID problem with zero-flux boundary conditions has showed that homogeneous nonzero equilibrium looses its stability when the movement rate of animals (coefficient of proportionality in velocity equation) overpasses some bifurcation value. The numerical experiments have confirmed analytical results, displaying stationary spatially heterogeneous solution (standing waves) for the detected supercritical value of the movement rate.

The Vegetation Adventivisation Through Perspective of Current Ecological Ideas

B. M. Mirkin (1), L. G. Naumova (2)

(1) Dept. of ecology, Bashkir State University, ul. Frunze, 32, Ufa, 450074, e-mail:

(2) Bashkir Pedagogical State University, ul. Oktyabr'skoi revolutsii, 3a, Ufa, 540000

Results of study of vegetation adventivisation (increase in proportion of invasive species) correspond to the theory of present ecology that denies general universal laws. Diverse features of invasive species play different role under various ecological conditions and at various time and space scale. The invasibility of communities under various conditions is determined by combination of different biotic and abiotic factors though it is obvious that most of invasive species are characterized with the high seed production, well developed vegetative propagation, windblown pollination, high plasticity and effective use of resources, low consumption by herbivores. The definition of an "ideal invasive species" or an "ideal invasible community" is impossible. The regularities of vegetation adventivisation can be observed clearly only at very large scale.

The Structure and Dynamics of a Woodreed Calamagrostis canescens Population: a Modelling Approach

N. G. Ulanova (1), A. N. Demidova (1), I. N. Klochkova(2), D. O. Logofet (3)

(1) Dept. of Geobotany, Biological Faculty of Moscow State University, e-mail:

(2) Dept. of Mechanics and Mathematics of Moscow State University

(3) Laboratory of Mathematical Ecology, Institute of Atmospheric Physics, Russian Academy of Science, 3 Pyzhevsky Lane, Moscow, 119017, Russia e-mail:

A scale of ontogenetic states has been developed for woodreed Calamagrostis canescens, a perennial species dominating the grass layer of felled forest areas. The population structure is considered as a set of age-stage groups of individuals differing both in the ontogenetic stage and the chronological age measured in years. To describe the dynamics through years a special kind of matrix formalism has been proposed which is reducible neither to the classic Leslie matrix for an age-structured population, nor to the well-known Lefkovitch matrix for a stage-structured one, and which does not suffer from excessiveness of the "two-dimensional" representation for the structure implying the projection matrix of a block pattern. It has been shown however that the protection matrix corresponding to C. canescens life-history graph embodies the canonical features of matrix formalism for structured population dynamics, such as the exponential population growth or decline, the convergence to a stable equilibrium structure, the calculable indicator of growth/decline/equilibrium (i.e., a measure of the population reproductive potential) as wiell as possibility to determine the relative reproductive value of each group. On the other hand, "left-sidedness of the age spectrum", a property that is often observed in real populations and is inherent in Leslie models of growing populations, may fail in the age-stage-structured model. The aggregation of age-stage groups into the age classes is possible only under special strict relationship among the age-stage-specific vital rates of the population. The both circumstances serve a methodical indication that an additional dimension such as the stages, for example, ought to be introduced into the age structure of the model population.