Testing Pairwise Association between Spatially Autocorrelated Variables: A New Approach Using Surrogate Lattice Data

International audienceBackground: Independence between observations is a standard prerequisite of traditional statistical tests of association. This condition is, however, violated when autocorrelation is present within the data. In the case of variables that are regularly sampled in space (i.e. lattice data or images), such as those provided by remote-sensing or geographical databases, this problem is particularly acute. Because analytic derivation of the null probability distribution of the test statistic (e.g. Pearson's r) is not always possible when autocorrelation is present, we propose instead the use of a Monte Carlo simulation with surrogate data. Methodology/Principal Findings: The null hypothesis that two observed mapped variables are the result of independent pattern generating processes is tested here by generating sets of random image data while preserving the autocorrelation function of the original images. Surrogates are generated by matching the dual-tree complex wavelet spectra (and hence the autocorrelation functions) of white noise images with the spectra of the original images. The generated images can then be used to build the probability distribution function of any statistic of association under the null hypothesis. We demonstrate the validity of a statistical test of association based on these surrogates with both actual and synthetic data and compare it with a corrected parametric test and three existing methods that generate surrogates (randomization, random rotations and shifts, and iterative amplitude adjusted Fourier transform). Type I error control was excellent, even with strong and long-range autocorrelation, which is not the case for alternative methods. Conclusions/Significance: The wavelet-based surrogates are particularly appropriate in cases where autocorrelation appears at all scales or is direction-dependent (anisotropy). We explore the potential of the method for association tests involving a lattice of binary data and discuss its potential for validation of species distribution models. An implementation of the method in Java for the generation of wavelet-based surrogates is available online as supporting material

Self-organized vegetation pattern modulation in arid climates

À l’échelle macroscopique, à savoir celle du paysage, la couverture végétale des milieux arides apparaît comme fortement hétérogène. Cette organisation spatiale des peuplements est habituellement attribuée aux processus de facilitation et de compétition qui opèrent à l’échelle microscopique des individus végétaux. Le qualificatif d’auto-organisées fut donc attribué à ces végétations qui se structurent en l’absence d’hétérogénéité préexistante du milieu physique. L’auto-organisation de la végétation fut particulièrement bien étudiée dans le cas des structures périodiques connues dès les années '50 sous le nom de brousses tigrées. Depuis les années '90, un pas en avant dans la compréhension de ce phénomène fut accompli grâce au développement de modèles mécanistes de la dynamique de la phytomasse et des ressources, émanant du cadre théorique de l'auto-organisation des structures dissipatives. Ces modèles se rejoignent sur un ensemble de prédictions robustes et vérifiables concernant la formation, le maintien et la modulation par l'environnement des structures macroscopiques. Durant le même laps de temps, notre niveau d’analyse a connu une expansion sans précédent, à la fois dans le temps et dans l’espace, grâce au développement de l’imagerie satellitaire et des outils d’analyse spatiale. Nous nous trouvons dès lors à un moment charnière pour la validation macroscopique des théories d’auto-organisation des végétations en milieu aride.Le présent travail s'articule en quatre études, chacune traitant d'une prédiction différente. Nous avons mis en évidence les principales variables responsables de la formation des structures et de leur modulation en termes d’échelle et de géométrie. Enfin avons démontré la mobilité des structures sous l’effet d’une pente de terrain.Doctorat en Sciencesinfo:eu-repo/semantics/nonPublishe

Hymenophyllum senterreanum Dubuisson & Deblauwe, sp. nov. (Hymenophyllaceae) and its relatives in western Central Africa

International audienceThe fern genus Hymenophyllum (Hymenophyllaceae) so far encompassed not more than five species in western Central Africa. New investigations into BRLU and P collections on Hymenophyllaceae specimens collected in western Central Africa allowed us to identify a new species for the area. The species Hymenophyllum senterreanum sp. nov. displays indusia with an original and particular campanulate-like shape, usually observed in the distinct trichomanoid lineage. It seems endemic to sub-montane rainforests of coastal west-south Cameroon and Equatorial Guinea, and is currently known only from four localities. The novelty is considered as Endangered according to IUCN Categories and Criteria. An updated key is proposed for the genus Hymenophyllum for the region

Case Study of Self-Organized Vegetation Patterning in Dryland Regions of Central Africa

International audienceA growing body of empirical evidence supporting or opposing the mechanistic hypotheses and predictions of self-organization models exist which have been applied to the case of spatially periodic vegetation patterns found in semi-arid and arid areas around hot deserts in Africa. Overall, remarkable qualitative – and sometimes quantitative – agreement is found and presented here between the rich theoretical framework and predictions of self-organization models and the results of field and remotely sensed investigations for dryland areas in Niger, Morocco and Suda

Hymenophyllum senterreanum Dubuisson & Deblauwe, sp. nov. (Hymenophyllaceae) and its relatives in western Central Africa

The fern genus Hymenophyllum (Hymenophyllaceae) so far encompassed not more than five species in western Central Africa. New investigations into BRLU and P collections on Hymenophyllaceae specimens collected in western Central Africa allowed us to identify a new species for the area. The species Hymenophyllum senterreanum sp. nov. displays indusia with an original and particular campanulate-like shape, usually observed in the distinct trichomanoid lineage. It seems endemic to sub-montane rainforests of coastal west-south Cameroon and Equatorial Guinea, and is currently known only from four localities. The novelty is considered as Endangered according to IUCN Categories and Criteria. An updated key is proposed for the genus Hymenophyllum for the region.SCOPUS: ar.jinfo:eu-repo/semantics/publishe

Data from: Determinants and dynamics of banded vegetation pattern migration in arid climates

Dense vegetation bands aligned parallel to contour levels and alternating at regular intervals with relatively barren interbands have been reported at the margins of all tropical deserts. Since their discovery in the 1950s, it has been suspected that these vegetation bands migrate upslope, forming a space-time cyclic pattern. Evidence to date has been relatively sparse and indirect, and observations have remained conflicting. Unequivocal photographic evidence of upslope migration (a few dm yr-1) is provided here for three independent dryland areas exhibiting periodic banded pattern the U.S. northeastern Chihuahuan Desert (1), the Somalian Haud (2), and the Mediterranean steppes of eastern Morocco (3). Migration speeds, averaged through time and space using Fourier cross-spectral analysis, are shown to be directly proportional to pattern scale (wavelength). An aerial photography sequence of (1) showed that migration was not continuous but intermittent in response to fluctuating weather regimes. The rates at which bands expanded upslope and contracted downslope were better predicted by the change in annual rainfall than by its average level. However, migration of banded pattern cannot be considered as systematic because observations are reported from three other banded systems located in the Somalian Haud, central Australia, and western New South Wales in which migration was undetectable at the available image resolution. In each of the six sites under study, the modal value of band orientation axes was verified to be approximately orthogonal to the steepest slope. Our results underscore the importance of taking both the spatial structure and the past climate sequence into account for understanding vegetation dynamics in arid to semi-arid ecosystems. In addition, we show how Fourier spectral analysis applied to historical series of optical images can serve to quantify landscape dynamics at a decadal time scale

NCD_time_series

Data for Fig. 5 & Fig. 6. Projection and datum of geotiff files are UTM Zone 13 N, NAD 1983

Examples of surrogates for images with increasing degree of autocorrelation.

<p>The first row features particular simulations of fractal patterns (fractional Brownian field) generated by Fourier synthesis <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0048766#pone.0048766-Keitt2" target="_blank">[27]</a> for four degrees of autocorrelation (from short- to long-ranged as indirectly quantified by the <i>β</i> parameter). The following rows (2 to 5) display one particular random realization (i.e. re-simulation) of each of these fractal patterns according to four surrogate producing methods (random reassignments, random shifts, iterative amplitude adjusted Fourier transform (IAAFT) and wavelet-based energy synthesis, respectively).</p