Univariate Character Research Articles

A Multiscale Cost–Benefit Analysis of Digital Soil Mapping Methods for Sustainable Land Management

With the emergence of machine learning methods during the past decade, alternatives to conventional geostatistical methods for soil mapping are becoming increasingly more sophisticated. To provide a complete overview of their performance, this study performed cost–benefit analysis of four soil mapping methods based on five criteria: accuracy, processing time, robustness, scalability and applicability. The evaluated methods were ordinary kriging (OK), regression kriging (RK), random forest (RF) and ensemble machine learning (EML) for the prediction of total soil carbon and nitrogen. The results of these mechanisms were objectively standardized using the linear scaling method, and their relative importance was quantified using the analytic hierarchy process (AHP). EML resulted in the highest cost–benefit score of the tested methods, with maximum values of accuracy, robustness and scalability, achieving a 55.6% higher score than the second-ranked RF method. The two geostatistical methods ranked last in the cost–benefit analysis. Despite that, OK could retain its place as the most frequent method for soil mapping in recent studies due to its widespread, user-friendly implementation in GIS software and its univariate character. Further improvement of machine learning methods with regards to computational efficiency could additionally improve their cost–benefit advantage and establish them as the universal standard for soil mapping.

Complex frequency characteristic and Green’s function for cantilever beam under longitudinal oscillations

Relevant objective of this article is elaboration of methods of efficient determination of the dynamic characteristics of the materials both within the framework of well-known and classical models as well as within the advanced ones in the context of interaction with the environment under the impact of external dynamic loads. In the present work free and forced oscillations are studied with a help of spectral methods what allows to compare theoretical results with experimental data, obtained by other authors. The key point of the work is theoretical determination of the proper functions of the oscillatory system, its frequency characteristic using Green’s function. We examine longitudinal oscillations, caused by the substitute load, which provokes oscillations of a sound spectrum. Univariate character of the task is determined by the linearity organization of the longitudinal oscillations of a beam. The oscillations are modeled with a help of the substitute load, which is a subject to Dirac impulse function, which belongs to a class of generalized functions. The obtained solution makes it possible to use the proposed approach in order to determine frequency characteristics in the acoustic spectrum, taking into account that the oscillations are included in a full frequency spectrum and can be used for an adequate valuation of the possibility of the appearance of resonance phenomena.

Multivariate probabilistic estimates of heat stress for rice across China

Heat stress, a major threat to rice (Oryza sativa) production across China, would tend to increase in frequency and intensity under warming climate. Unlike probabilistic analysis via a univariate character, heat stress events, characterized by three variables (i.e., duration, peak and accumulated detrimental intensity), were identified in the past years. Nine distribution functions (i.e., Beta, Cauchy, Logistic, Normal, Exponential, Gamma, Lognormal, Weibull and Generalized Extreme Value) were firstly introduced and compared to select the best-fit marginal distribution of univariable by using Kolmogorov–Smirnov test, and seven copula functions (i.e., Normal and t, Gumbel–Hougaard, Clayton, Frank, Joe, Ali-Mikhail-Haq) were applied in the distributions of multivariables by Akaike Information Criterion statistics. It was obvious that higher magnitude was in the eastern parts in the context of heat stress frequency and characteristic variables. Critical values of heat stress variables corresponding to the certain return periods (i.e. 5, 10, 20 and 50 years) successively expanded in intensity and spatial scope. Inter-correlations of heat stress variables were significant, enlightening the importance of copula in connecting heat stress variables. The combined and co-occurrence bivariate and trivariate return period at certain univariate value corresponding to the given return periods, were consistent at the spatial scale. Accordingly, it was highlighted that eastern parts, especially Zhejiang, central-northern Fujian and eastern Jiangxi, were prone to heat stress, as a consequence of not only univariate but also multivariate probabilistic analysis. These results can be helpful in quantitatively assessing the vulnerability of rice to heat stress and provide us desired information of prevention strategies for heat stress.

Clines Arc through Multivariate Morphospace.

Evolutionary biologists typically represent clines as spatial gradients in a univariate character (or a principal-component axis) whose mean changes as a function of location along a transect spanning an environmental gradient or ecotone. This univariate approach may obscure the multivariate nature of phenotypic evolution across a landscape. Clines might instead be plotted as a series of vectors in multidimensional morphospace, connecting sequential geographic sites. We present a model showing that clines may trace nonlinear paths that arc through morphospace rather than elongating along a single major trajectory. Arcing clines arise because different characters diverge at different rates or locations along a geographic transect. We empirically confirm that some clines arc through morphospace, using morphological data from threespine stickleback sampled along eight independent transects from lakes down their respective outlet streams. In all eight clines, successive vectors of lake-stream divergence fluctuate in direction and magnitude in trait space, rather than pointing along a single phenotypic axis. Most clines exhibit surprisingly irregular directions of divergence as one moves downstream, although a few clines exhibit more directional arcs through morphospace. Our results highlight the multivariate complexity of clines that cannot be captured with the traditional graphical framework. We discuss hypotheses regarding the causes, and implications, of such arcing multivariate clines.

Morphological Variation in a Unisexual Whiptail Lizard (Aspidoscelis exsanguis) and One of Its Bisexual Parental Species (Aspidoscelis inornata) (Reptilia: Squamata: Teiidae): Is the Clonal Species Less Variable?

ABSTRACT Two clonal lineages, each comprising multiple generations of unisexual A. exsanguis, were produced in the laboratory from two lizards that were collected at the same locality in the field. Based on 10 meristic and four additional characters, we assessed morphological scores and relative variation as follows: (1) between the two laboratory lineages; (2) between these lineages pooled and samples of A. exsanguis and the bisexual (gonochoristic) A. inornata from the field; and (3) between field samples of the clonal lizards and A. inornata from a nearby locality. The two lineages differed significantly in the means and variances of two univariate characters and the two most informative multivariate characters. Contrary to expectations, the pooled sample of cloned laboratory lineages of A. exsanguis were as variable as the bisexual species in all 10 univariate characters and four important multivariate characters.

Mistaken view of taxonomic validity undermines conservation of an evolutionarily distinct mouse: a response to Ramey et al. (2005)

1 Department of Biology, University of Washington, Seattle, WA, USA 2 Department of Fisheries and Wildlife Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA, USA 3 Department of Biology, Valdosta State University, Valdosta, GA, USA 4 New Mexico Museum of Natural History, Albuquerque, NM, USA 5 Department of Environmental, Population, and Organismic Biology, University of Colorado, Boulder, CO, USA 6 School of Molecular and Life Sciences, University of Limpopo, Sovenga, South Africa

Changes in colonial development, intraspecific heterochrony, morphological integration, and character heritabilities in two populations of the bryozoan speciesBatostoma jamesifrom the Kope Formation (Upper Ordovician, Cincinnatian)

Populations of the Upper Ordovician trepostome bryozoanBatostoma jamesiwere collected from two different paleoenvironmental settings in the Kope Formation of southeastern Indiana. Within each colony and population, morphologic changes were analyzed during colony growth, or astogeny. Morphological measurements of zooecia, mesozooecia, and acanthostyles display similar patterns of change during colony growth in both populations but magnitudes are generally larger in the high diversity population.Canonical variates analyses provided multivariate confirmation of univariate character differences found within each population. Statistically significant multivariate morphological differences between growth stages persist even if assignments of colonies to populations are ignored. Results suggest different potentials for altering growth trajectories in different environments with early growth stage flexibility in colonies from lower diversity settings and later-stage flexibility in colonies from higher diversity settings.Heterochronic changes occur between species populations. Relative to the high-diversity population, the low-diversity population displays the following: 1) progenesis and hypermorphosis for zooecia, reflecting the ability to exist over a broader range of areal densities and surface areas than in populations from high-diversity associations; 2) postdisplacement and progenesis for mesozooecia, producing mature mesozooecial densities earlier in growth and at smaller sizes while the onset of mesozooecial development is delayed; and 3) acceleration, predisplacement, and progenesis for acanthostyles, resulting in a more rapid rate of development, an earlier onset of style development and more styles, and an earlier time of maturation, respectively.The estimated level of morphological integration is higher in the high diversity population regardless of stage of colony growth. Within populations, integration is stronger during early growth stages in colonies from high diversity settings and during later growth stages in colonies from low diversity settings. Character heritabilities are high in both diversity-level populations, suggesting that these patterns of morphological integration were not the result of non-heritable phenotypic plasticity. Mean heritability is greater in the high diversity population and differs statistically only between the late growth stages of populations. Patterns of morphological integration may result from differing levels of stabilizing selection in different environments. Depending on the timing of selection, these different levels of integration are capable of affecting the outcome of selection on species populations.

CHANGES IN COLONIAL DEVELOPMENT, INTRASPECIFIC HETEROCHRONY, MORPHOLOGICAL INTEGRATION, AND CHARACTER HERITABILITIES IN TWO POPULATIONS OF THE BRYOZOAN SPECIES BATOSTOMA JAMESI FROM THE KOPE FORMATION (UPPER ORDOVICIAN, CINCINNATIAN)

Abstract Populations of the Upper Ordovician trepostome bryozoan Batostoma jamesi were collected from two different paleoenvironmental settings in the Kope Formation of southeastern Indiana. Within each colony and population, morphologic changes were analyzed during colony growth, or astogeny. Morphological measurements of zooecia, mesozooecia, and acanthostyles display similar patterns of change during colony growth in both populations but magnitudes are generally larger in the high diversity population. Canonical variates analyses provided multivariate confirmation of univariate character differences found within each population. Statistically significant multivariate morphological differences between growth stages persist even if assignments of colonies to populations are ignored. Results suggest different potentials for altering growth trajectories in different environments with early growth stage flexibility in colonies from lower diversity settings and later-stage flexibility in colonies from higher...

Why Morphometrics is Special: The Problem With Using Partial Warps as Characters for Phylogenetic Inference

There has been a dispute among morphometricians (Fink and Zelditch, 1995; Zelditch, Fink, and Swiderski, 1995; Adams and Rosenberg, 1998; Rohlf, 1998; Swiderski, Zelditch, and Fink, 1998; Zelditch, Fink, Swiderski, and Ludrigan, 1998) on the possibility of using morphometric data, ex? pressed as shape variables (particularly par? tial warps) extracted by geometric morpho? metrics methods, in phylogenetic analyses. Much has been said against and in favor of this particular combination of geometric morphometrics and cladistics, but the issue is not yet resolved. This is probably because the single point that makes the partial warps unsuitable as characters cladistic analysis, was not thoroughly considered: the lack of biological significance in partial warps when treated as single univariate characters. To project a multidimensional space into a set of single dimensions by different rotations parsimony analysis, the single dimensions must have biological significance by them? selves (what cannot be expected from partial warps, Rohlf, 1998). This problem is derived from the shape nonmonotonicity theorem, originally published by Bookstein (1980), that asserts: for any three triangles of land? marks, no two of which have exactly the same shape, and any of three triangles, there exist indefinitely many shape measures consistent with that ordering (Bookstein, 1994, p. 206). In other words, the ordination patterns in shape space are not consistent all possible shape variables, although the dis? tances among shapes are always preserved. Our perception of the world is deeply de? pendent on the dimensions we can observe. Natural phenomena are usually expressed in a multivariate fashion, even though most of us are limited to visualizing things in a max? imum of three dimensions. To understand

MORPHOMETRIC VARIABILITY IN CONTINENTAL AND ATLANTIC ISLAND POPULATIONS OF CHAFFINCHES (FRINGILLA COELEBS).

The magnitudes of phenotypic variances in peripherally isolated populations of common chaffinches (Fringilla coelebs) in the Azores, Madeira, and Canaries relative to their continental source populations in Iberia and Morocco have played a pivotal role in the formulation of competing hypotheses of phenotypic evolution in these isolates. Because Van Valen's niche variation hypothesis and Grant's model of island evolution were based on museum skins prone to measurement error and temporal variation, we re-examined the patterns of phenotypic variability using more precise skeletal measurements from freshly collected specimens. Levene's tests showed that univariate character variances were homogeneous in all island and continental populations, although there was a consistent trend for the magnitude of the variances to be lower for all characters in all Canary island populations. Multivariate Levene's tests, however, revealed significantly reduced total variances in the Hierro and Madeira populations compared to some Azores and continental populations. The Azores and continental populations did not differ in variability, and lower variances in the Canaries were not related to the presence or absence of the congeneric blue chaffinch (F. teydea), contrary to the predictions of Van Valen's niche variation hypothesis. Population variability was not inversely related to differentiation or isolation within the Azores or Canaries archipelagoes, opposite to the association reported by Grant. Our results also differ from both previous studies which reported much larger differences in population variabilities, and this likely reflects the use of heterogeneous samples of museum specimens, less precise external characters, and the use of tests sensitive to sample size. Differentiation among populations has been markedly greater in the Canary islands, implicating founder events and possibly historically stronger directional selection as determinants of this enhanced divergence relative to the Azores. These variance-reducing processes are unlikely to explain current lower levels of phenotypic variability because there has been sufficient time since colonization for replenishment of variability in polygenic characters. Average heterozygosities at putatively neutral allozyme loci are 1.6 times higher in the Azores compared to the Canaries, and support the view that effective population sizes are smaller in the latter archipelago. We argue that reduced variances in the Canary island populations represent lower equilibrium levels maintained by drift and mutation in populations with smaller long-term effective sizes, consistent with Lynch and Hill's neutral model of phenotypic evolution. Although episodes of selection in the past may have been interspersed with long periods of effective neutralism and drift, adaptationist hypotheses invoking a primary role for variance-reducing selection appear to be unwarranted.

Resolution of Cryptic Species in Appalachian Red Crossbills

Two distinct and sympatric forms of Red Crossbill (Loxia curvirostra) from breeding populations in Virginia and North Carolina were resolved using multivariate analysis of vocalizations and morphology. Five characters were used to describe individually distinctive flight calls of 135 adults which were also measured for a set of nine bill and body size characters. Call notes were bimodal for two characters, and a principal components plot separated birds into two clusters based on call note shape. Univariate distributions of morphological data showed some weak bimodalities and higher coefficients of variation than other passerine bird populations. Distributions along multivariate first principal component axes from morphological data (sexes in separate analyses) were bimodal, dividing fully grown adults into two distinct bill and body size classes. The vocal and morphological multivariate clusterings of individuals were entirely congruent, but no univariate character in either data set could completely separate the two forms. The matrix correlations between vocal and morphological interindividual distances were 0.441 for males and 0.423 for females and were highly significant using Mantel tests. However, within each hypothetical cryptic species, vocal and morphological characteristics were uncorrelated, showing a lack of pattern in the sample beyond the division into two nonreducible clusters. Other vocal differences between the two forms are described, and observations of ecological differences are summarized. The type specimens representing the two names which have been applied to Appalachian crossbills, L. c. pusilla (Gloger 1834) and L. c. minor (Brehm 1845), were compared to birds of known vocalizations. The type of pusilla matched the larger Appalachian form, but the type of minor was smaller than all adult males in the sample. The taxonomic problem of L. curvirostra is discussed, and an argument is made in favor of the species level for the two Appalachian vocal and morphological forms.

Germination and Morphology of Progeny From Controlled Pollinations of Eucalyptus nitens (Deane & Maiden) Maiden

The germination and morphology of progeny from interspecific and intraspecific controlled pollinations on Eucalyptus nitens mothers were examined. All interspecific hybrids were morphologically intermediate overall with respect to parental controls, as determined by discriminant function analyses. Single univariate characters displayed additive inherit- ance on 72% of the 154 occasions where differences amongst hybrids and parents were significant. The degree of dominance of characters is discussed. Compared with outcrossing, self-fertilisation resulted in lower seed viability and a higher incidence of abnormality and mortality in developing E. nitens seedlings. Outcrossed progeny were generally distinctly different from appropriate parental controls. Reciprocal crosses were very similar, indicating no observable maternal effects.

Character Number and the Multivariate Analysis of Simple Patterns of Geographic Variation: Categorical or "Stepped Clinal" Variation

Computer selection of random sets of real characters was used to elucidate the relationship between character number and the reliability of multivariate patterns of geographic variation. The simple pattern of geographic variation was a distinct pair of parapatric races (categorical or clinal variation) in the grass snake (Natrix natrix) in Europe. The characters used were 71 significant characters of low within-group correlation drawn from six different character systems (e.g., scalation, color pattern and internal morphology). The pattern was assessed by principal coordinate analysis, and the congruence was taken as the absolute correlation between the principal coordinates. The investigation was based on two procedural models: (A) the congruence between com- pletely independent character sets using from 1 to 35 characters; and (B) the congruence be- tween the analysis based on the total 71 characters and analyses based on from 1 to 65 characters. The relationship between congruence and character number is expressed by one of two math- ematical models depending on the procedural model employed. Congruence is clearly asymp- totic with respect to character number. This indicates the existence of a stable, overall pattern of racial variation that, once established, is unlikely to be influenced by the addition of further characters. The asymptotes are reached at an early stage and, between 8 to 10 characters, reveal the distinct patterns of racial variation with at least 90% confidence, depending upon whether one is characterizing patterns on the basis of a geographic transect or a scatter on the first two principal coordinates. It does not appear to be cost effective to use more than 18 significant characters, because each additional character increases the minimum congruence by very little beyond this point. Univariate characters, and those patterns based on too few characters, can misrepresent this stable pattern. The observed failure of univariate/conventional studies to reveal this pattern, or to agree with one another, is related to the low probability of selecting the appropriate individual characters, even though they occur. (Geographic variation; races; character number; congruence; predictivity; multivariate morphometrics; stepped cline.)

Temporal variation in habitat structure and shrubsteppe bird dynamics.

We investigate the role of temporal variation in habitat physiognomy in influencing the dynamics of shrubsteppe bird populations and communities. During a 3-y (1977-1979) study of 14 sites in the northern Great Basin of North America, annual precipitation varied substantially, with one of the driest years on record followed by one of the wettest. This resulted in significant physiognomic variation (increasing height and coverage of vegetation, decreasing horizontal patchiness), mediated largely by changes in the annual elements of the flora, particularly forbs and grasses. Shrub species coverage values, on the other hand, demonstrated no statistically detectable year-to-year changes, nor were they correlated with any physiognomic variation. Despite large scale physiognomic changes, no bird species' abundance varied in a statistically significant fashion; neither could variation in bird abundances be correlated with variation in either physiognomy or shrub species coverages.Multivariate analyses revealed essentially the same patterns as the univariate analyses: substantial changes in physiognomy, few changes in shrub species coverages or bird species abundances, and little correlation of temporal variation among the three data sets. Calculation of the Euclidean distances that sites "moved" in multivariate physiognomic, bird species, or shrub species hyperspaces yields synthetic gradients of annual "turnover" of sites with respect to those data sets. Sites identified as demonstrating high physiognomic turnover were characterized by high coverage of grass and forbs, while low turnover sites had greater coverage of shrubs and higher shrub species diversity. Relatively high bird turnover sites had greater numbers of Western Meadowlarks and Black-throated Sparrows, while more stable sites had high numbers of Brewer's Sparrows. Physiognomically, high bird turnover sites were grassier and had greater total vegetation coverage, while low bird turnover sites had more bare ground and higher horizontal patchiness. A site's position on the avifauna turnover axis, however, was uncorrelated with its position on the physiognomic turnover axis. Shrub species showed virtually no annual turnover.Reanalysis of a previous Principal Components Analysis (PCA) of these same data sets that was applied without regard to year of sampling revealed that the first physiognomic component (41% of the total physiognomic variability) did in fact have a strong temporal element, and that this element was consistent with the changes in univariate characters noted above. No other physiognomic component could be associated with annual variation, nor could any components of parallel bird abundance or shrub species coverage PCA's.Regional patterns indicate that sites tended to be very consistent from year to year in their relationships to one another as defined by their relative locations in either physiognomic or shrub species hyperspaces, but varied independently of one another with respect to their bird species abundances and composition. Examination of the temporal consistency of site relationships between "bird space" and "vegetation space" reveals that bird communities are to a large degree independent of a site's physiognomic position, but instead are strongly associated with its position in shrub species hyperspace.The overall patterns that emerge from these analyses are consistent with the so-called "checkerboard effect" that results from the apparently random annual redistribution of individual birds, and leads to the conclusion that populations of shrubsteppe birds are not existing at maximum density or "carrying capacity." Such observations are consistent with contentions that these populations lack close biological coupling with coexisting species and that interactions among these species (e.g. competition) are likely to play little if any role in the organization of their communities.