S. N. Sergeev

‘Island syndrome’ in a population of Arctic foxes ( Alopex lagopus ) from Mednyi Island

Comparative analysis of the biology of insular and mainland populations has demonstrated a number of differences in characteristics of insular populations, termed the ‘island syndrome’. A subspecies of Arctic fox on the Commander Islands (Alopex lagopus semenovi on Mednyi Island) has been isolated for an evolutionarily significant time in small territories at the periphery of the species’ range. The number of foxes on Mednyi had been observed to be very high since the islands were discovered in 1741, but a drastic decline in population density in the late 1970s, owing to mange, has left the population low. The aim of the study was to determine whether the Mednyi Arctic fox population exhibited the features expected in an isolated insular population, such as difference in body size, increased population density, larger social groups, lower tendency to disperse and lower fertility, and whether any behavioural changes were evolutionarily reinforced or were a temporal response to current ecological factors on the island. Eight predictions were identified based on the island syndrome, of which the Mednyi Arctic foxes conformed to seven. We suggest a new prediction, namely that the tendency for increased sex dimorphism in dispersal may also be a distinguishing feature of insular populations. All the features displayed by the insular population on Mednyi – conservative use of space, increased tendency to form complex groups, decreased fertility and dispersal – seemed to be preserved regardless of the currently comparatively low populations. Thus, although foxes have been below carrying capacity for at least 10 generations, island syndrome characteristics have persisted.

Effects of food availability on dispersal and cub sex ratio in the Mednyi Arctic fox

Since the Pleistocene, Arctic foxes, Alopex lagopus, on Mednyi Island in the North Pacific have been isolated in a small area with rich food resources and no other terrestrial carnivores. This situation provides an unusually simple system within which the effect of food dispersion on demography and social organisation was examined. We studied the composition, location and dispersal of 67 Arctic fox groups and mapped their major food resources (seabird colonies) during 1994–2000 on Mednyi. We compared our observations with the predictions of models of sex-ratio determination. Our observations are most consistent with the predictions of Julliards (2000) model, where mothers are expected to produce more offspring of the most dispersing sex in low-quality habitats, and more offspring of the most philopatric sex in high-quality habitats. The polygynous foxes on Mednyi Island lived where the principal food resources were patchily distributed (present on 11% of the shoreline), and cub survival to dispersal age or reproductive adult was higher in rich (25/45) than in poor (24/79) home ranges. Furthermore, dispersal was strongly sex-biased: most females (60%) remained on their natal ranges, whereas very few males (9%) did so. Significantly more female than male cubs (54 compared with 24) emerged from dens in resource rich ranges, whereas the sex ratio on poor ranges was approximately equal (51 females and 56 males). While our observations are also to some extent consistent with the local resource enhancement (LRE) hypothesis (which predicts a bias towards the sex most likely to cooperate with parents), this does not account for the observed spatial variability.

Cyclic projectors and separation theorems in idempotent convex geometry

Semimodules over idempotent semirings like the max-plus or tropical semiring have much in common with convex cones. This analogy is particularly apparent in the case of subsemimodules of the n-fold Cartesian product of the max-plus semiring: It is known that one can separate a vector from a closed subsemimodule that does not contain it. Here we establish a more general separation theorem, which applies to any finite collection of closed subsemimodules with a trivial intersection. The proof of this theorem involves specific nonlinear operators, called here cyclic projectors on idempotent semimodules. These are analogues of the cyclic nearest-point projections known in convex analysis. We obtain a theorem that characterizes the spectrum of cyclic projectors on idempotent semimodules in terms of a suitable extension of Hilberts projective metric. We also deduce as a corollary of our main results the idempotent analogue of Hellys theorem.

Acoustic double-negative media

We consider the possibility of the existence of media in acoustics that are similar in several effects to the widely discussed electrodynamic left-handed media. The density and compressibility of a medium are shown to be the mechanical analogues of negative permittivity and permeability. We discuss the physical meaning of their negativity and mechanical models with such properties. To identify the effects related to the sign of the density and compressibility, we have performed our analysis based on linearized hydrodynamic equations instead of the wave equation or the Helmholtz equation. We have obtained an analogue of the Lippmann—Schwinger equation and constructed a theory of wave scattering by inhomogeneities in a medium with arbitrary values and signs of the density and compressibility. Our numerical simulations have revealed all of the expected effects. We consider the questions concerning the fulfillment of the causality principle and its consequences generalized to the case of negative media in the form of a connection between the damping and dispersion of waves.

The use of low-frequency noise in passive tomography of the ocean

A possible design of the mode tomography of the ocean with the use of a scheme requiring no expensive low-frequency radiators is considered. The design is based on the widely discussed method of estimating the Green’s function from the cross-coherence function of noise field received in a great number of observation points. The relationship between the Green’s function and the noise coherence function is derived from the Helmholtz-Kirchhoff integral. The use of the vertical multielement arrays composed of vector receivers is suggested to decrease the duration of noise signal accumulation required for a reliable determination of the Green’s function. The solution of the tomographic problem is based on the determination of the mode structure of acoustic field from the eigenvectors and eigenvalues of the cross-coherence matrix of the received noise field.

Selection of modes from a shallow-water noise field by single bottom hydrophones for passive tomography purposes

The possibility of selecting modes that propagate between two spaced observation points without the use of vertical arrays and low-frequency emitters is considered. Modes are selected from the cross-correlation function of noise received by single hydrophones. It is shown that modes at frequencies near the minima of the dispersion dependences of their group velocities, where stationary phase regions are observed, make the main contribution to the noise cross-correlation function. This makes it possible to identify modes of different numbers and estimate their propagation times between hydrophones, which can be the basis for shallow-water passive mode tomography using data from single bottom hydrophones. The modes were selected based on data from a experiment carried out in the Barents Sea.

The significance of the choice of basis functions in the problems of acoustic tomography of the ocean

Different approaches to the parametric description of the ocean inhomogeneities of both refraction and kinetic types are discussed in the context of the inhomogeneity reconstruction with the use of tomographic techniques. In addition to bases commonly known and widely used in oceanological problems (such as specification of the inhomogeneity parameters at the grid nodes or in nonoverlapping shapes compactly covering the region of interest), a new nonorthogonal and redundant basis consisting of a set of overlapping bands (and, presumably, more convenient for solving tomographic problems) is considered. The abilities of different bases to reconstruct the ocean inhomogeneities are compared with the use of special theoretical approach. The quality of reconstruction on the band and cell bases is investigated against the relationship between the number and composition of the basis elements. Examples of the reconstruction of ocean inhomogeneities with the use of the aforementioned basis functions are given together with the results of comparison.

A two-dimensional tomography model for the oceanic inhomogeneity reconstruction with wave and ray representations of acoustic field

A model reconstruction of two-dimensional combined oceanic inhomogeneities (of refractive and kinetic types) in tomographic experiments with ray and wave representations of acoustic field is considered. The possibility of a complete reconstruction of two-dimensional flows from the scattering data alone is illustrated. For the realization of the tomographic scheme, a nonorthogonal redundant basis consisting of a number of intersecting stripes is used. The results of reconstruction are presented for model inhomogeneities of kinetic and combined (refractive-kinetic) types. The iterative reconstruction of the flow velocity vector distribution is considered. The tomographic problem in the ray representation is solved by taking into account both the time delays in the signal propagation along the rays and the ray trajectory distortions due to the inhomogeneity of the medium.

Wave effects in acoustic media with a negative refractive index

A method for analyzing media with a negative refractive index in acoustics has been proposed. An analog of the Lippmann-Schwinger equation is derived from the initial hydrodynamical equation and a theory of wave scattering by inhomogeneities of a medium with an arbitrarily specified value and sign of density and compressibility is constructed. Numerical simulation of the effects related to negative refraction is performed.

Ocean acoustic tomography with a nonstandard representation of refractive inhomogeneities

The two-dimensional tomography problem of reconstructing a refractive inhomogeneity in the ocean is considered. A distinction of this paper is the expansion of the inhomogeneity under investigation in a nonstandard (nonorthogonal and overfull) basis. This basis makes it possible to overcome some problems inherent in the conventional schemes dividing the ocean into squares, triangles, and other figures with corners. In addition, the perturbation matrix can be easily constructed in such a basis. The proposed approach can be used in its present form for reconstructing flows and solving combined refractive-kinetic problems. The solution of the tomography problem with the use of the proposed basis is carried out in both ray and wave representations.