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Exponential Curve (exponential + curve)
Selected AbstractsTidal estuary width convergence: Theory and form in North Australian estuariesEARTH SURFACE PROCESSES AND LANDFORMS, Issue 7 2010Gareth Davies Abstract In order to better understand the relations between tidal estuary shape and geomorphic processes, the width profiles of 79 tidal channels from within 30 estuaries in northern Australia have been extracted from LANDSAT 5 imagery using GIS. Statistics describing the shape and width convergence of individual channels and entire estuaries (which can contain several channels) are analysed along with proxies for the tidal range and fluvial inputs of the estuaries in question. The width profiles of most individual channels can be reasonably approximated with an exponential curve, and this is also true of the width profiles of estuaries. However, the shape of this exponential width profile is strongly related to the mouth width of the system. Channels and estuaries with larger mouths generally exhibit a more pronounced ,funnel shape' than those with narrower mouths, reflecting the hydrodynamic importance of the distance over which the channel or estuarine width converges. At the estuarine scale, this ,convergence length' also tends to be higher in estuaries which have larger catchments relative to their size. No clear relation between the estuarine width convergence length and tidal range could be discerned within the Northern Australian estuaries although, when these data are combined with data from other studies, a weak relationship emerges. Copyright © 2010 John Wiley & Sons, Ltd. [source] Threshold changes in vegetation along a grazing gradient in Mongolian rangelandsJOURNAL OF ECOLOGY, Issue 1 2008Takehiro Sasaki Summary 1The concept of threshold has become important in ecology, but the nature of potential threshold responses of vegetation to grazing in rangeland ecosystems remains poorly understood. We aimed to identify ecological thresholds in vegetation changes along a grazing gradient and to examine whether threshold changes were expressed similarly at a variety of ecological sites. 2To accomplish this, we surveyed the vegetation along grazing gradients at 10 ecological sites, each located at different landscape positions in Mongolia's central and southern rangelands. Evidence for a threshold in changes in floristic composition along the grazing gradient was examined by comparing linear models of the data with nonlinear models fitted using an exponential curve, an inverse curve, a piecewise regression and a sigmoid logistic curve. 3Three nonlinear models (piecewise, exponential and sigmoid) provided a much better fit to the data than the linear models, highlighting the presence of a discontinuity in vegetation changes along the grazing gradient. The shapes of the best-fit models and their fit to the data were generally similar across sites, indicating that the changes in floristic composition were relatively constant below a threshold level of grazing, after which the curve changed sharply. 4Except for two sites, the best-fit models had relatively narrow bootstrap confidence intervals (95% CI), especially around threshold points or zones where the rate of change accelerated, emphasizing that our results were robust and conclusive. 5Synthesis. Our study provided strong evidence for the existence of ecological thresholds in vegetation change along a grazing gradient across all ecological sites. This suggests that vegetation responses to grazing in the study areas are essentially nonlinear. The recognition that real threshold changes exist in real grazing gradients will help land managers to prevent the occurrence of undesirable states and promote the occurrence of desirable states, and will therefore permit a major step forward in the sustainable management of rangeland ecosystems. [source] The circadian and homeostatic modulation of sleep pressure during wakefulness differs between morning and evening chronotypesJOURNAL OF SLEEP RESEARCH, Issue 4 2003Jacques Taillard Summary The purpose of this study was to evaluate homeostatic and circadian sleep process in ,larks' and ,owls' under daily life conditions. Core body temperature, subjective sleepiness and waking electroencephalogram (EEG) theta,alpha activity (6.25,9 Hz) were assessed in 18 healthy men (nine morning and nine evening chronotypes, 21.4 ± 1.9 years) during a 36-h constant routine that followed a week of a normal ,working' sleep,wake schedule (bedtime: 23.30 h, wake time: 07.30 h). The phase of the circadian rhythm of temperature and sleepiness occurred respectively, 1.5 h (P = 0.01) and 2 h (P = 0.009) later in evening- than in morning-type subjects. Only morning-type subjects showed a bimodal rhythm of sleep,wake propensity. The buildup of subjective sleepiness, as quantified by linear regression, was slower in evening than in morning types (P = 0.04). The time course of EEG theta,alpha activity of both chronotypes could be closely fitted by an exponential curve. The time constant of evening types was longer than that of morning types (P = 0.03), indicating a slower increase in sleep pressure during extended wakefulness. These results suggest that both the circadian signal and the kinetics of sleep pressure buildup differ between the two chronotypes even under prior naturalistic conditions mimicking the usual working day. [source] HOW DID LIFE BECOME SO DIVERSE?PALAEONTOLOGY, Issue 1 2007THE DYNAMICS OF DIVERSIFICATION ACCORDING TO THE FOSSIL RECORD AND MOLECULAR PHYLOGENETICS Abstract:, The long-term diversification of life probably cannot be modelled as a simple equilibrial process: the time scales are too long, the potential for exploring new ecospace is too large and it is unlikely that ecological controls can act at global scales. The sum of many clade expansions and reductions, each of which happens according to its own dynamic, probably approximates more a damped exponential curve when translated into a global-scale species diversification curve. Unfortunately, it is not possible to plot such a meaningful global-scale species diversification curve through time, but curves at higher taxonomic levels have been produced. These curves are subject to the vagaries of the fossil record, but it is unlikely that the sources of error entirely overwhelm the biological signal. Clades radiate when the external and internal conditions are right: a new territory or ecospace becomes available, and the lineage has acquired a number of characters that open up a new diet or mode of life. Modern high levels of diversity in certain speciose clades may depend on such ancient opportunities taken. Dramatic climatic changes through the Quaternary must have driven extinctions and originations, but many species responded simply by moving to more favourable locations. Ecological communities appear to be no more than merely chance associations of species, but there may be real interactions among species. Ironically, high species diversity may lead to more speciation, not, as had been assumed, less: more species create more opportunities and selective pressures for other species to respond to, rather than capping diversity at a fixed equilibrium level. Studies from the scale of modern ecosystems to global long-term patterns in the fossil record support a model for the exponential diversification of life, and one explanation for a pattern of exponential diversification is that as diversity increases, new forms become ever more refinements of existing forms. In a sense the world becomes increasingly divided into finer niche space. Organisms have a propensity to speciate freely, species richness within ecosystems appears to generate opportunities for more speciation, clades show all kinds of patterns from sluggish speciation rates and constant diversity through time to apparently explosive speciation, and there is no evidence that rapidly speciating clades have reached a limit, nor that they are driving other clades to extinction. A corollary of this view is that current biodiversity must be higher than it has ever been. Limits to infinite growth are clearly local, regional, and global turnover and extinction events, when climate change and physical catastrophes knock out species and whole clades, and push the rising exponential curve down a notch or two. [source] Temporal changes in retinal thickness after removal of the epiretinal membraneACTA OPHTHALMOLOGICA, Issue 4 2009Hitoshi Aso Abstract. Purpose:, We aimed to study the temporal aspects of the postoperative reduction of retinal thickness in eyes with epiretinal membrane after vitrectomy with peeling of the epiretinal membrane and internal limiting membrane. Methods:, In a retrospective study performed as a non-comparative, interventional case series, 16 eyes from 15 patients with idiopathic epiretinal membrane who underwent vitrectomy and removal of the epiretinal membrane were followed up using optical coherence tomography measurements. Retinal thickness in the macular area was assessed by the foveal thickness and macular volume in a circle 6 mm in diameter. Results:, Scattergrams of the foveal thickness and macular volume were best fitted with exponential curves. The average time constants of the exponential curve for foveal thickness and macular volume changes were 31 days (range 4,109 days) and 36 days (range 5,100 days), respectively. The average expected final values for foveal thickness and macular volume were 334 ,m (range 206,408 ,m) and 7.53 mm3 (range 6.57,8.66 mm3), respectively, which were significantly greater than those in normal controls (p < 0.0001, t -test). Conclusions:, Retinal thickness decreases rapidly immediately after surgical removal of the epiretinal membrane and the reduction rate gradually slows thereafter. Approximation of the exponential curve provides an estimation of final retinal thickness after surgical removal of the epiretinal membrane; final thickness is expected to be greater than in normal eyes. [source] | |||||||||||||