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.     

Times Varying Spectral Coherence Investigation of Cardiovascular Signals Based on Energy Concentration in Healthy Young and Elderly Subjects by the Adaptive Continuous Morlet Wavelet Transform

Objective

The aims of this study, to investigate the interaction among heart rate variability (HRV), respiratory, systolic arterial blood pressure variability (SABPV) and systolic arterial pressure interval variability (APIV) signals for understanding of cardiovascular control.

Forest carbon storage along the north-south transect of eastern China: Spatial patterns,allocation, and influencing factors

Forests play an important role in sequestrating atmospheric CO₂; therefore, understanding the spatial variations and controlling mechanisms of forest carbon (C) storage is important. In this study, we collected data on forest C storage along a north-south transect of eastern China from literature published between 2004 and 2014. The collected data, which were from over 2000 plots, allowed us to explore the latitudinal patterns in forest C storage. The results showed that vegetation C storage decreased with increasing latitude, while soil C storage increased. This spatial pattern of vegetation C storage was more apparent for mature forests (forest age > 80 years). Furthermore, latitudinal patterns in forest C storage, both in vegetation and in soil, became stronger with increasing statistical scale, increasing from plot scale to latitudinal scale (2–5°). However, total forest C storage (vegetation + soil) had no apparent latitudinal pattern. Interestingly, the allocation ratios of forest C storage between vegetation and soil had a negative logarithmic relationship with latitude. These results suggest that in eastern China, climatic factors control latitudinal patterns in the forest C storage of vegetation and soil, albeit in different ways (positive for vegetation and negative for soil), and also control the allocation ratios of forest C storage between vegetation and soil. Furthermore, the latitudinal patterns of forest C storage were opposite for vegetation and soil, resulting from the different climatic controlling mechanism.     

Comparison of the muscle activation pattern for the vastus lateralis before and after an 8-week resistance training program

The purpose of this investigation was to use wavelet analyses and pattern classification techniques to examine potential changes in the joint time–frequency distribution of surface electromyographic (EMG) signals due to an 8-week resistance training program. Thirteen untrained men (mean ± S.D. age = 22.2 ± 4.0 yrs) performed eight separate submaximal isometric muscle actions of the dominant leg extensors in 10% increments from 10 to 80% of the maximum voluntary contraction (MVC). During each muscle action, a monopolar surface EMG signal was detected from the vastus lateralis. All signals were then analyzed with a wavelet analysis designed specifically for EMG signals, and the resulting intensity patterns were classified using pattern classification techniques into their respective pre-training versus post-training categories. The results showed accuracy rates (% of correctly classified patterns) that ranged from approximately 62 to 92%, but these rates did not change consistently with increases in force. In addition, for five of the eight submaximal force levels, the classification was considered to be significantly different from random. Thus, although the differences between the pre- and post-training EMG intensity patterns were not always consistent, our findings did suggest that there is the potential for wavelet analyses and pattern classification techniques to be used to examine neuromuscular adaptations during resistance training.     

Investigating the Effect of Flickering Frequency Pair and Mother Wavelet Selection in Steady-State Visually-Evoked Potentials on Two-Command Brain-Computer Interfaces

IntroductionSteady-state visually evoked potentials (SSVEPs) have become popular in brain-computer interface (BCI) applications in addition to many other applications on clinical neuroscience (neurodegenerative disorders, schizophrenia, epilepsy, etc.), cognitive (visual attention, working memory, brain rhythms, etc.), and use of engineering researches. Among available methods to measure brain activities, SSVEPs have advantages like higher information transfer rate, simplicity in structure, and short training time. SSVEP-based BCIs use flickering stimuli at different frequencies to discriminate distinct commands in real life. Some features are extracted from the SSVEP signals before these commands are classified. The wavelet transform (WT) has attracted researchers among feature extraction methods since it utilizes the non-stationary signals well. In the WT, a sample function (named mother wavelet) represents the SSVEP signal in both time and frequency domains. Unfortunately, there is no universal mother wavelet function that fits all the signals. Therefore, choosing an appropriate mother wavelet function may be a challenge in WT-related studies. Although there are such studies in three- and seven-command SSVEP-based studies, there is no study for two-command systems in our knowledge.Materials and MethodsIn this study, two user commands flickered at the combinations of seven different frequencies were tested to determine which frequency pairs give the highest performance. For this purpose, three well-known wavelet features (energy, entropy, and variance) were calculated for each of derived EEG frequency bands from the discrete WT coefficients of SSVEP signals. The WT was repeated for six different mother wavelet functions (Haar, Db4, Sym4, Coif1, Bior3.5, and Rbior2.8). Then, four feature sets (every three features, and all together) were applied to seven commonly-used machine learning algorithms (Decision Tree, Discriminant Analysis, Logistic Regression, Naive Bayes, Support Vector Machines, Nearest Neighbors, and Ensemble Classifiers).Results and DiscussionWe achieved 100% accuracies among these 3,528 runs (7 classifiers x 4 feature sets x 6 mother wavelets x 21 flickering frequency pairs) using the mother wavelet function of Haar and the Ensemble Learner classifier. The highest classifier performances are 100% when two commands have the flickering frequency pairs of (6.0 and 10 Hz), (6.5 and 8.2 Hz), or (6.5 and 10.0 Hz).ConclusionWe obtained three main outcomes from this study. First, the most representative mother wavelet function was Haar, while the worst one was Symlet 4. Second, the Ensemble Learner classifier gave the maximum classifier performance in a two-command SSVEP-based BCI system. Besides, two user commands from SSVEP should be one of the frequency pairs of (6.0 and 10.0 Hz), (6.5 and 8.2 Hz), and (6.5 and 10.0 Hz) to achieve the maximum accuracy.     

Traversing the Center: The Politics of Language Use in a Catholic Religious Education Program for Immigrant Mexican Children

This article examines the implementation of educational policy in a religious education program at a Los Angeles Catholic parish. It charts the elimination of Spanish-based classes (doctrina) for Mexican immigrant children in favor of "English-only" instruction. The article offers insights into the politics of language use in everyday practice and examines the resulting educational policy decisions.     

A fluorometric method for the discrimination of harmful algal bloom species developed by wavelet analysis

An in vivo 3D fluorescence discrimination technique for ten harmful algal bloom (HAB) species that belong to eight genera of four divisions was developed by wavelet analysis. Daubechies-7 (db7) was employed as the mother wavelet. The fifth scale domains were selected as the discriminant characteristic spectra (DCS). Based on the DCS, The phytoplankton species at different growth stages were classified correctly at both the division and the genus level by Bayesian discriminant analysis (BDA). Based on the reference spectra of the DCS, the discrimination method of the phytoplankton species was established by the nonnegative least squares (NNLS) method. The correct discrimination ratios (CDRs) for samples of the single species were 96.1% with 0% blank noise and 93.3% with 10% noise at the genus level, while the CDRs were both 100% with 0% or 10% blank noise at the division level. When blank noise was up to 20%, the CDRs were down to 85.2% at the genus level and 98.0% at the division level. For the mixture samples, the CDRs of the dominant species were 98.3% and 96.3%, respectively, at the division level and at the genus level. As dominant species, Prorocentrum minimum (Pm), Gymnodinium simplex (Gs), Scrippsiella trochoidea (Sc), Skeletonema costatuma (Sk), Chaetoceros (Cu and De), Phaeocystis globosa (Cg) and Chlorella pynnoidosa (Ch) can be correctly discriminated at both the division level and the genus level.     

Discordant patterns of geographic variation between mitochondrial and microsatellite markers in the Mexican black iguana (Ctenosaura pectinata) in a contact zone

Aim To delimit the distribution of matrilines of the black iguana (Ctenosaura pectinata), detect potential contact zones between them, and test the hypothesis of geographic concordance in the structuring of matrilines with respect to genetic structuring across the nuclear genome. Location Pacific coast of Mexico in the states of Nayarit, Jalisco, Colima, Michoacán in the lowlands adjacent to the western end of the Mexican Volcanic Belt. Methods Tissue samples were obtained every 10–20 km along a transect across the range of three previously described mitochondrial DNA (mtDNA) clades of C. pectinata. Iguanas were genotyped with 11 nuclear microsatellites and maternal lineages were inferred based on mtDNA sequences. Geographic structure and geographic concordance between biparentally and maternally inherited markers were analysed with clustering methods, F_ST and N_ST indexes as well as haplotype networks. Results Geographic structure was evident for both markers and the existence of contact zones confirmed. Nevertheless, the distribution of nuclear and mtDNA genetic variation is not geographically concordant. Four matrilines exist in the area, whereas only two nuclear clusters occur. A contact zone between nuclear clusters extends along a distance of c. 60 km, and introgression is evident in individuals from several localities. Main conclusions High levels of genetic diversity were detected on the western coast of Mexico. Historical and contemporaneous processes seem to shape the distribution of genetic variation in C. pectinata. There are no evident geographic, environmental or ecological barriers that coincide with genetic subdivisions, and the observed mtDNA structure is likely to be the result of past climatic changes. The less structured distribution of nuclear genetic variation is consistent with the homogenizing effect of male‐biased dispersal. Our findings have implications for the taxonomy and conservation strategies for this threatened species, and highlight the fact that geographic analyses of both cytoplasmic and nuclear genetic variation are important for the meaningful inference of evolutionary and demographic histories.     

A New Testing Approach for Comparing the Overall Homogeneity of Survival Curves

The assessment of overall homogeneity of time‐to‐event curves is a key element in survival analysis. The currently commonly used methods, e.g., log‐rank and Wilcoxon tests, may have a significant loss of statistical testing power under certain circumstances. In this paper a new statistical testing approach is developed to compare the overall homogeneity of survival curves. The proposed new method has greater power than the commonly used tests to detect overall differences between crossing survival curves. The small‐sample performance of the new test is investigated under a variety of situations by means of Monte Carlo simulations. Furthermore, the applicability of the proposed testing approach is illustrated by a real data example from a kidney dialysis trial. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Winter bird communities in the northern Negev: species dispersal patterns, habitat use and implications for habitat conservation

Bird habitat conservation may require different management strategies for different seasonal bird assemblages. We studied habitat use by winter birds in forest and scrubland habitat patches in the northern Negev, Israel. Our goal was to assess whether differences in responses to landscape and habitat structure between breeding and non-breeding seasons require changes in future conservation plans that have been suggested for the Negev breeding bird community. We evaluated habitat and area effects on bird abundance and distribution and tested whether species habitat use during winter involves niche shifts. Compared with breeding birds, a larger proportion of winter bird species occupied both scrubland and forest. As in summer, forest bird species responded to habitat structure, whereas scrubland species were associated with both habitat structure and area. Resident birds disperse into habitats in which they were not present during summer. Consequently, for several species, the correlation between bird densities and environmental factors showed a better fit at the landscape rather than at the habitat scale. In addition, rather than niche shift, birds actually extended their niche breadth. Nest site selection may constrain bird distribution into a realized niche, smaller than their fundamental niche. Despite the scale differences in habitat use, the similar species diversity patterns between seasons suggest that both winter and summer birds would benefit from conservation of scrub patches larger than 50 ha, and enrichment of foliage layers within the planted forests.     

The use of inverse sine transformations in the analysis of non-metric cranial data

In recent years osteologists have frequently used non-metric (dichotomous) cranial data to measure biological distance between skeletal samples of Homo sapiens. Applying methods used earlier by biologists, these workers begin by attempting to stabilize the variance of the measures used by transforming the observed trait frequencies using some type of inverse sine transformation. The frequently used Grewal-Smith transformation doesn't work well for small samples of the size often considered by osteologists. As a consequence the mean measure of divergence between populations determined by this method is strongly influenced by a bias which depends on sample size. This paper compares several transformations in terms of how close the actual variance of the transformed frequency corresponds to its nominal value. It is suggested that the traditional (Grewal-Smith) inverse sine transformation not be used, and several alternatives are considered.     

水生态空间红线概念、划定方法及实证研究

我国面临着多方面、复杂的水生态问题:洪涝、干旱、水质污染、水生生境丧失以及人水关系日益疏远等等。解决这些问题,不能依赖单一目标的灰色工程方法,而必须从维护和保育水生态系统的完整性出发,来系统地解决问题。为此,如何定义一个相对完整的水生态系统的边界、划定维护其安全和健康的底线,即水生态空间红线,是用生态方法综合解决水问题的基础性的工作。研究提出了以保护水生态系统的综合生态服务为核心的水生态空间红线概念;提出了以水生态安全格局构建为基础的水生态空间红线划定方法和"水生态问题分析-水生态过程模拟和评价-水生态安全等级划分-水生态安全格局判定-水生态空间红线的划定"技术流程,分别划定水资源供给保护、水文调节保护、水生命支持和水文化保护四种类型的水生态保护空间红线,在此基础上,整合为综合的水生态空间红线,它呈现为对水生态过程具有关键意义的点、线、面和空间联系所构成的空间格局,并以雁栖湖流域为例进行了实证研究。     

Effects of quadrat size and data measurement on the detection of boundaries

Abstract. With sampled field data, the accuracy of delineation of ecotones is directly related to the resolution of the data (i.e. spatial and measurement type) and to the edge detection algorithm used. In the present study the reliability is investigated of an edge detection algorithm (lattice-wombling) to delimit vegetation boundaries when different spatial resolutions (quadrat sizes) are used. To quantify whether the edge detection algorithm is robust, it was applied to data from woody species in a second-growth woodland measured at different spatial resolutions with different data types. Boundaries were found at similar locations using any reasonable quadrat size (ca. 200 m²) but there were some slight differences when using different vegetation measures (density versus presence/absence data).     

The effect of zoo visitors on the behaviour and faecal cortisol of the Mexican wolf (Canis lupus baileyi)

The effect of zoo visitors on the behaviour and physiological responses of the Mexican wolf has not been documented but is worthy of investigation since it is a critically endangered native species and most of the population live in zoos. The effect of the number of visitors was assessed in 12 wolves (five males and seven females) in three zoos of central Mexico. Each wolf was observed for a total of 72 h on Saturdays, Sundays, Mondays and Tuesdays (6 h/day) during a three-week period. Scan sampling was used to obtain individual time budgets. A faecal sample was collected on the following morning of each observation day from 10 wolves to determine cortisol level (RIA). A repeated measures analysis of variance revealed that there was an effect of day on the proportion of time lying (P < 0.01), eating (P < 0.01) and in locomotion (P < 0.01). Wolves spent less time lying on Saturdays and Sundays (0.2980 ± 0.012 and 0.3266 ± 0.012, respectively) than on Mondays and Tuesdays (0.3821 ± 0.012 and 0.4075 ± 0.012, respectively), as well as less time eating on weekend days (Saturdays 0.1214 ± 0.015, Sundays 0.0556 ± 0.015) than in the other 2 days (Mondays 0.816 ± 0.015 and Tuesdays 0.0915 ± 0.015). Mean faecal cortisol was 203.7 ng/g of DM and ranged from 113.10 to 314.48 ng/g. There was an effect of day on the faecal cortisol response (P < 0.01) with wolves having higher cortisol response on Sundays (242.50 ng/g ± 8.48) compared to the other 3 days (Saturdays 192.71 ± 8.48, Mondays 170.73 ng/g ± 7.80, Tuesdays 183.82 ng/g ± 8.48). This is the first study that measures faecal cortisol of Mexican wolves. These results indicate that the amount of visitors in zoos influence the behaviour and adrenal activity of these animals which could be undesirable for ex situ conservation efforts of this endangered species.     

Refining the standardized growth change method for pointer year detection: Accounting for statistical bias and estimating the deflection period

Detecting pointer years in tree-ring data is a central aspect of dendroecology. Pointer years are usually represented by extraordinary secondary tree growth, which is often interpreted as a response to abnormal environmental conditions such as late-frosts or droughts. Objectively identifying pointer years in larger tree-ring networks and relating those to specific climatic conditions will allow for refining our understanding of how trees perform under extreme climate and consequently, under anticipated climate change. Recently, Buras et al. (2020) demonstrated that frequently used pointer-year detection methods were either too sensitive or insensitive for such large scale analyses. In their study, Buras et al. (2020) proposed a novel approach for detecting pointer years – the standardized growth change (SGC) method which outperformed other pointer-year detection methods in pseudopopulation trials. Yet, the authors concluded that SGC could be improved further to account for the inability to detect pointer years following successive growth decline. Under this framework, we here present a refined version of the SGC-method – the bias-adjusted standardized growth change method (BSGC). The methodological adjustment to the SGC approach comprises conflated probabilities derived from standardized growth changes with probabilities derived from a time-step specific global standardization of growth changes. In addition, BSGC allows for estimating the length of the deflection period, i.e. the period before extraordinary growth values have reached normal levels. Application of BSGC to simulated and measured tree-ring data indicated an improved performance in comparison to SGC which allows for the identification of pointer years following years of successive growth decline. Also, deflection period lengths were estimated well and revealed plausible results for an existing tree-ring data set. Based on these validations, BSGC can be considered a further refinement of pointer-year detection, allowing for a more accurate identification and consequently better understanding of the radial growth response of trees to extreme events.     

Historical biogeographical patterns of the species of Bursera (Burseraceae) and their taxonomic implications

Aim The plant genus Bursera, with 104 species of trees and shrubs, has been used as a model for biogeographical analyses because of its high species richness and large number of endemic species. The biogeographical patterns of Bursera and their implications for its phylogenetic classification are reviewed in order that some hypotheses on the historical biogeography of tropical Mexico can be proposed. Location Bursera is found in the south‐western USA, most of Mexico, mainly below 1700 m elevation in tropical forests, with some species in xeric shrublands, diversifying along the Pacific slope, Central America, and north‐western South America. A few species occur on the Galapagos and Revillagigedo archipelagos, some of which are endemics, whereas in the Antilles species are distributed extensively, with several endemics in the Bahamas, Cuba, Jamaica, and Hispaniola. Methods Data from specimens in herbaria and the literature were used to construct a matrix of 104 species in 160 areas. Distributional patterns of the species of Bursera were inferred applying track analysis, parsimony analysis of endemicity (PAE), and Brooks parsimony analysis (BPA). Results Track analysis revealed four individual tracks: (1) a circum‐Caribbean track, comprising species of the Bursera simaruba species group; (2) an Antillean track, including species that have been transferred to Commiphora based on their pollen traits; (3) a Mexican Pacific track, including species of the B. fragilis, B. microphylla, and B. fagaroides species groups, called ‘cuajiotes’; and (4) a Neotropical Pacific track, including the two species groups assigned to section Bullockia, in which the individual track of the Bursera copallifera species group is nested within the track of the B. glabrifolia species group. The four tracks overlap in a node in the Mexican Pacific slope, where they are highly diversified. PAE allowed us to identify 22 areas of endemism: 12 in Mexico (11 along the Mexican Pacific slope), six in the Antilles, two in Central America, one in South America, and one in the Galapagos. The general area cladogram obtained by BPA has two main clades: one includes the greater Antilles; and the other, 12 Mexican areas of endemism. Main conclusions Bursera fragilis, B. microphylla, and B. fagaroides species groups can be treated together as a new section within Bursera, sect. Quaxiotea, because they are segregated from the other groups of sect. Bursera based on morphological, anatomical, molecular and geographical evidence.     

The extraordinary journey of Peperomia subgenus Tildenia (Piperaceae): insights into diversification and colonization patterns from its cradle in Peru to the Trans‐Mexican Volcanic Belt

Aim Peperomia subgenus Tildenia consists of c. 60 species growing in seasonal habitats of Neotropical mountain areas from Mexico to Argentina. The subgenus can be split geographically, with almost equal diversity in the Northern Hemisphere (centred in Mexico and Guatemala) and in the Southern Hemisphere (centred in Peru and Bolivia). Only a few species are known from a limited number of localities between these two hotspots. As such, Tildenia is an ideal candidate with which to test time, direction and mode of migration of high mountain taxa against the background of the ‘Great American Biotic Interchange’. Location The Andes with focus on the Central Andes, and the Mexican mountain chains, especially the Trans‐Mexican Volcanic Belt. Methods To elucidate the spatio‐temporal origin, subsequent colonization and radiation of Tildenia, we combine Bayesian phylogenetics based on the chloroplast trnK–matK–psbA region, georeferenced distribution data, and fossil calibrated molecular dating approaches using both penalized likelihood and relaxed phylogenetics. Reconstruction of the ancestral distribution area was performed using dispersal–vicariance analysis and dispersal–extinction–cladogenesis. Results Peperomia subgenus Tildenia is subdivided into six Andean clades and one Mexican and Central American clade originating from a north/central Peruvian ancestor. Molecular dating approaches converge on a stem age of c. 38 Ma for Tildenia and a mostly Miocene diversification and colonization. Main conclusions We detect a strong correlation between diversification of Tildenia and orogenetic events in the respective distribution centres. In the Andes, distribution was influenced by the Altiplano–Eastern Cordillera System as well as the Amotape‐Huancabamba Zone, where the latter serves as both migration barrier and migration bridge for different clades. In contrast to most studies of high‐elevation taxa, we provide support for a south–north colonization towards Central America and Mexico, and provide additional, independent evidence for the latest view on the timing of the Great American Biotic Interchange. In Mexico, the Trans‐Mexican Volcanic Belt has played a major role in more recent radiations together with climatic oscillation and the formation of refugia.