The form of the species richness-productivity relationship (SRPR) is both theoretically important and contentious. In an effort to distill general patterns, ecologists have undertaken meta-analyses, within which each SRPR data set is first classified into one of five alternative forms: positive, humped (unimodal), negative, U-shaped (unimodal), and no relationship. Herein, I first provide a critique of this approach, based on 68 plant data sets/studies used in three meta-analyses published in Ecology. The meta-analyses are shown to have resulted in highly divergent outcomes, inconsistent and often highly inappropriate classification of data sets, and the introduction and multiplication of errors from one meta-analysis to the next. I therefore call on the ecological community at large to adopt a far more rigorous and critical attitude to the use of meta-analysis. Second, I develop the argument that the literature on the SRPR continues to be bedeviled by a common failing to appreciate the fundamental importance of the scale of analysis, beginning with the confusion evident between concepts of grain, focus, and extent. I postulate that variation in the form of the SRPR at fine scales of analysis owes much to artifacts of the sampling regime adopted. An improved understanding may emerge from combining sampling theory with an understanding of the factors controlling the form of species abundance distributions and species accumulation curves.
Abstract A non-linear poroelastic finite element model of the lumbar spine was developed to investigate spinal response during daily dynamic physiological activities. Swelling was simulated by imposing a boundary pore pressure of 0.25 MPa at all external surfaces. Partial saturation of the disc was introduced to circumvent the negative pressures otherwise computed upon unloading. The loading conditions represented a pre-conditioning full day followed by another day of loading: 8 h rest under a constant compressive load of 350 N, followed by 16 h loading phase under constant or cyclic compressive load varying in between 1000 and 1600 N. In addition, the effect of one or two short resting periods in the latter loading phase was studied. The model yielded fairly good agreement with in-vivo and in-vitro measurements. Taking the partial saturation of the disc into account, no negative pore pressures were generated during unloading and recovery phase. Recovery phase was faster than the loading period with equilibrium reached in only ∼3 h. With time and during the day, the axial displacement, fluid loss, axial stress and disc radial strain increased whereas the pore pressure and disc collagen fiber strains decreased. The fluid pressurization and collagen fiber stiffening were noticeable early in the morning, which gave way to greater compression stresses and radial strains in the annulus bulk as time went by. The rest periods dampened foregoing differences between the early morning and late in the afternoon periods. The forgoing diurnal variations have profound effects on lumbar spine biomechanics and risk of injury.