The use of wavelets for spatial pattern analysis in ecology

Abstract. We investigate the characteristics of the wavelet transform as an approach to analyzing spatial pattern. Compared to the familiar methods of paired quadrat or blocked quadrat variance calculations, the wavelet method seems to offer several advantages. First, when wavelet variance is plotted as a function of scale, the peak variance height is determined by pattern intensity and does not increase with scale and, depending on the wavelet chosen, the position of the variance peak matches the scale exactly. Second, the method produces only faint resonance peaks, if any, and third, by using several different wavelet forms, different characteristics of the pattern can be investigated. Fourth, the method is able to portray very clearly trends in the data, when the pattern is non-stationary. Lastly, the wavelet position variance can be used to identify patches and gaps in data with random error. We demonstrate these characteristics using artificial data and data from previously published studies for comparison. We show that two versions of the familiar blocked quadrat variance technique are forms of wavelet analysis.     

Successive mapping of dune slack vegetation

Summary The succession of the dune slack vegetation around an artificial lake was studied by means of successive mapping. A succession scheme was prepared on the basis of comparison of the maps made in various years. This scheme was discussed in terms of systems theory, with reference to a kinematic graph prepared on the basis of the transformations. The succession derived from the vegetation maps was compared with that derived from the permanent plots; the results of this comparison indicated that only a small proportion of the total number of succession lines could be detected with the aid of the permanent plots. In addition, the information that could be derived from the permanent plot analysis depended on the degree of change of the vegetation in the area; more information could be derived from drier areas which showed the least degree of change. The best method for the investigation of the succession proved to be a combination of a restricted number of permanent plots and successive mapping. Nomenclature of species follows Heukels-van Ooststroom Flora van Nederland, 16 ed. 1970. R.I.N.-Comm. nr. 107.     

Protein and collagen content of rat skeletal muscle following space flight

Summary Biochemical determinations of non-collagenous protein and hydroxyproline were made on rat skeletal muscles following 7 days of space flight aboard the NASA space shuttle mission SL-3. Relative to ground-based controls, the wet weight of each experimental muscle was significantly reduced. This was concomitant with a reduction in noncollagenous protein in the muscles. Protein concentration, however, was reduced only in slow-twitch muscles. The effect of space flight on the concentration and hydroxyproline content was different among the muscles. As a result, the loss of muscle mass in some muscles was the consequence of a reduction in both collagenous and non-collagenous proteins, while in others it was primarily the result of a non-collagenous protein loss.     

X-Ray Characterization of Melanins—II

Structural modeling of amorphous eumelanin has been carried out by comparing calculated data, S(q) and RDF(r), in reciprocal and real space, respectively, for limited random network models with the experimental X-ray scattering data of tyrosine melanin (Cheng et al., 1994). A basic picture of the atomic arrangements in amorphous eumelanin, which accounts for the short and intermediate range order, has been formulated. This reveals domains of a fundamental “particle” dimension of R～ 15 Å, consisting of a paracrystalline array of disordered planar networks polymerized by 4-8 DHI monomers with a graphite-like stacking spacing of ～ 3.45 Å, 4-5 layers thick.     

A maternal effect mutation leading to deficiencies of organs and homeotic transformations in the adults ofDrosophila

Summary The temperature sensitive mutationfs(l)h is characterized at the restrictive temperature of 29°C by both a maternal effect responsible for the early embryonic lethality and pupal zygotic lethality. The two phenotypes are inseparable and map at a short deletion in the X chromosome (7Dl, 7D5-6). At semipermissive temperatures, hemizygous mutant females produce adults with morphological defects, such as organ deficiencies and homeotic transformations of haltere to wing and third leg to second leg. These defects depend on the maternal genotype and are governed by an early temperature sensitive period, which covers the end of oogenesis and the first hours of embryogenesis. Furthermore, this maternal effect mutation interacts with some dominant mutations of the bithorax system. These properties suggest thatfs(l)h is somehow involved in segmental determination.     

Wood Grain Pattern Formation: A Brief Review

In trees, new wood develops from a layer of stem cells called the vascular cambium. A subpopulation of cambial cells—the fusiform initials—are elongated and capable of coordinated reorientation in response to internal and external stimuli. Changes in the orientation of fusiform initials in turn leads to changes in the grain pattern of developing wood. This article reviews the phenomenon of cambial orientation, with an emphasis on a recent computer model that takes the plant hormone auxin as the orienting signal. New model results are presented that demonstrate the surprisingly complex grain patterns that can emerge from simple initial conditions, in qualitative agreement with similar patterns found in wood. Lastly, an alternative theory of wood grain pattern that takes mechanical stress as the orienting signal is critically evaluated.     

Pollen exine development precedes microtubule rearrangement inVigna unguiculata (Fabaceae): A model for pollen wall patterning

Summary Although patterns on pollen exines are highly conserved, heritable traits, there is no prevailing explanation for control of pattern development. InVigna unguiculata (Fabaceae), the exine reticulum is unusually coarse so that development of the reticulum can be followed by light microscopy. Developing exine patterns were compared with the arrangement of microtubules in the microspore using immunofluorescence labeling of microtubules. Exine pattern developed in microspores at stages with a regular microtubule pattern. At later stages of exine formation, microtubules were arranged in patches under the lumina of the reticulum. We conclude that microtubules do not determine exine pattern. The developing exine appears to rearrange microtubules. We interpret this as evidence for the selfpatterning of exine based on intrinsic properties of the matrix between the microspore and the callose wall.Abbreviations DIC differential interference contrast - ECM(s) extracellular matrix(ces) - MT(s) microtubule(s) - PBS phosphate buffered saline - SEM scanning electron microscopy     

Dynamical effects of nonlocal interactions in discrete-time growth-dispersal models with logistic-type nonlinearities

The paper is devoted to the study of discrete time and continuous space models with nonlocal resource competition and periodic boundary conditions. We consider generalizations of logistic and Ricker's equations as intraspecific resource competition models with symmetric nonlocal dispersal and interaction terms. Both interaction and dispersal are modeled using convolution integrals, each of which has a parameter describing the range of nonlocality. It is shown that the spatially homogeneous equilibrium of these models becomes unstable for some kernel functions and parameter values by performing a linear stability analysis. To be able to further analyze the behavior of solutions to the models near the stability boundary, weakly nonlinear analysis, a well-known method for continuous time systems, is employed. We obtain Stuart–Landau type equations and give their parameters in terms of Fourier transforms of the kernels. This analysis allows us to study the change in amplitudes of the solutions with respect to ranges of nonlocalities of two symmetric kernel functions. Our calculations indicate that supercritical bifurcations occur near stability boundary for uniform kernel functions. We also verify these results numerically for both models.     

Multi-species pattern analysis of Mediterranean pastures in three stages of ecological succession

Multi-species patterns were analyzed in three stages of ecological succession in oligotrophic pastures in Central Spain using a new method of analysis. The method is based on plotting the species coordinates of principal components analysis undertaken at different block sizes. It allows the detection of any heterogeneity present and reveals both microtopographical and macrotopographical trends in species patterns.Nomenclature follows Tutin et al., 1964–1980, Flora Europaea.     

Pattern formation in plant epidermis through inhibition of immediately adjacent cells by pattern elements

Summary Examples of short-range inhibition in plant development were sought which satisfy four criteria for simplicity of expression. The range of inhibition extends only to adjacent cells and these criteria are (1) pattern of expression is within a two-dimensional array of cells, (2) cells of the array do not proliferate during pattern formation, (3) spacing between special cells extends only for a distance of one cell, and (4) no unequal cell divisions occur to complicate the pattern of cell arrangement. In one case of hairs or trichomes, the cells are evenly dispersed over the adaxial surface of the sepal ofSalvia splendens L. The R value of Clark and Evans is 1.64 for hair arrangement and hairs are formed from 21.1% of the epidermal cells. Based on cell behavior and an assumed method of inhibition, ordinary differential equations were written for formation of three types of cells in the tissue, free cells (F), trichome-bearing cells (T), and inhibited cells (I). Computer generated numerical solutions for these equations give cell type frequencies of 0.056 (F), 0.198 (T), and 0.745 (I), close to the observed values of 0.057 (F), 0.211 (T), and 0.731 (I). A similar approach was employed in analysis for the deployment of the cotton fibers in the ovular epidermis ofGossypium hirsutum L. and for that of the floating stomata of the fernAnemia phyllitidis (L). Sw. In general, these three patterns of epidermal deriviatives are most easily explained by one-cell wide inhibition fields between inhibiting special cells and inhibited contiguous cells. Other patterns in plants cannot be explained by this mechanism.