A Revision of the Traditional Analysis Method of Allometry to Allow Extension of the Normality-Borne Complexity of Error Structure: Examining the Adequacy of a Normal-Mixture Distribution-Driven Error Term.

Huxley's model of simple allometry provides a parsimonious scheme for examining scaling relationships in scientific research, resource management, and species conservation endeavors. Factors including biological error, analysis method, sample size, and overall data quality can undermine the reliability of a fit of Huxley's model. Customary amendments enhance the complexity of the power function-conveyed systematic term while keeping the usual normality-borne error structure. The resulting protocols bear multiple-parameter complex allometry forms that could pose interpretative shortcomings and parameter estimation difficulties, and even being empirically pertinent, they could potentially bear overfitting. A subsequent heavy-tailed Q-Q normal spread often remains undetected since the adequacy of a normally distributed error term remains unexplored. Previously, we promoted the advantages of keeping Huxley's model-driven systematic part while switching to a logistically distributed error term to improve fit quality. Here, we analyzed eelgrass leaf biomass and area data exhibiting a marked size-related heterogeneity, perhaps explaining a lack of systematization at data gathering. Overdispersion precluded adequacy of the logistically adapted protocol, thereby suggesting processing data through a median absolute deviation scheme aimed to remove unduly replicates. Nevertheless, achieving regularity to Huxley's power function-like trend required the removal of many replicates, thereby questioning the integrity of a data cleaning approach. But, we managed to adapt the complexity of the error term to reliably identify Huxley's model-like systematic part masked by variability in data. Achieving this relied on an error term conforming to a normal mixture distribution which successfully managed overdispersion in data. Compared to normal-complex allometry and data cleaning composites present arrangement delivered a coherent Q-Q normal mixture spread and a remarkable reproducibility strength of derived proxies. By keeping the analysis within Huxley's original theory, the present approach enables substantiating nondestructive allometric proxies aimed at eelgrass conservation. The viewpoint endorsed here could also make data cleaning unnecessary.

Assessment of a Takagi-Sugeno-Kang fuzzy model assembly for examination of polyphasic loglinear allometry.

BACKGROUND: The traditional allometric analysis relies on log- transformation to contemplate linear regression in geometrical space then retransforming to get Huxley's model of simple allometry. Views assert this induces bias endorsing multi-parameter complex allometry forms and nonlinear regression in arithmetical scales. Defenders of traditional approach deem it necessary since generally organismal growth is essentially multiplicative. Then keeping allometry as originally envisioned by Huxley requires a paradigm of polyphasic loglinear allometry. A Takagi-Sugeno-Kang fuzzy model assembles a mixture of weighted sub models. This allows direct identification of break points for transition between phases. Then, this paradigm is seamlessly appropriate for efficient allometric examination of polyphasic loglinear allometry patterns. Here, we explore its suitability. METHODS: Present fuzzy model embraces firing strength weights from Gaussian membership functions and linear consequents. Weights are identified by subtractive clustering and consequents through recursive least squares or maximum likelihood. Intersection of firing strength factors set criterion to estimate breakpoints. A multi-parameter complex allometry model follows by adapting firing strengths by composite membership functions and linear consequents in arithmetical space. RESULTS: Takagi-Sugeno-Kang surrogates adapted complexity depending on analyzed data set. Retransformation results conveyed reproducibility strength of similar proxies identified in arithmetical space. Breakpoints were straightforwardly identified. Retransformed form implies complex allometry as a generalization of Huxley's power model involving covariate depending parameters. Huxley reported a breakpoint in the log-log plot of chela mass vs. body mass of fiddler crabs (Uca pugnax), attributed to a sudden change in relative growth of the chela approximately when crabs reach sexual maturity. G.C. Packard implied this breakpoint as putative. However, according to present fuzzy methods existence of a break point in Huxley's data could be validated. CONCLUSIONS: Offered scheme bears reliable analysis of zero intercept allometries based on geometrical space protocols. Endorsed affine structure accommodates either polyphasic or simple allometry if whatever turns required. Interpretation of break points characterizing heterogeneity is intuitive. Analysis can be achieved in an interactive way. This could not have been obtained by relying on customary approaches. Besides, identification of break points in arithmetical scale is straightforward. Present Takagi-Sugeno-Kang arrangement offers a way to overcome the controversy between a school considering a log-transformation necessary and their critics claiming that consistent results can be only obtained through complex allometry models fitted by direct nonlinear regression in the original scales.

Examination of the Effects of Curvature in Geometrical Space on Accuracy of Scaling Derived Projections of Plant Biomass Units: Applications to the Assessment of Average Leaf Biomass in Eelgrass Shoots.

Conservation of eelgrass relies on transplants and evaluation of success depends on nondestructive measurements of average leaf biomass in shoots among other variables. Allometric proxies offer a convenient way to assessments. Identifying surrogates via log transformation and linear regression can set biased results. Views conceive this approach to be meaningful, asserting that curvature in geometrical space explains bias. Inappropriateness of correction factor of retransformation bias could also explain inconsistencies. Accounting for nonlinearity of the log transformed response relied on a generalized allometric model. Scaling parameters depend continuously on the descriptor. Joining correction factor is conceived as the partial sum of series expansion of mean retransformed residuals leading to highest reproducibility strength. Fits of particular characterizations of the generalized curvature model conveyed outstanding reproducibility of average eelgrass leaf biomass in shoots. Although nonlinear heteroscedastic regression resulted also to be suitable, only log transformation approaches can unmask a size related differentiation in growth form of the leaf. Generally, whenever structure of regression error is undetermined, choosing a suitable form of retransformation correction factor becomes elusive. Compared to customary nonparametric characterizations of this correction factor, present form proved more efficient. We expect that offered generalized allometric model along with proposed correction factor form provides a suitable analytical arrangement for the general settings of allometric examination.

On the suitability of an allometric proxy for nondestructive estimation of average leaf dry weight in eelgrass shoots I: sensitivity analysis and examination of the influences of data quality, analysis method, and sample size on precision.

BACKGROUND: The effects of current anthropogenic influences on eelgrass (Zostera marina) meadows are noticeable. Eelgrass ecological services grant important benefits for mankind. Preservation of eelgrass meadows include several transplantation methods. Evaluation of establishing success relies on the estimation of standing stock and productivity. Average leaf biomass in shoots is a fundamental component of standing stock. Existing methods of leaf biomass measurement are destructive and time consuming. These assessments could alter shoot density in developing transplants. Allometric methods offer convenient indirect assessments of individual leaf biomass. Aggregation of single leaf projections produce surrogates for average leaf biomass in shoots. Involved parameters are time invariant, then derived proxies yield simplified nondestructive approximations. On spite of time invariance local factors induce relative variability of parameter estimates. This influences accuracy of surrogates. And factors like analysis method, sample size and data quality also impact precision. Besides, scaling projections are sensitive to parameter fluctuation. Thus the suitability of the addressed allometric approximations requires clarification. RESULTS: The considered proxies produced accurate indirect assessments of observed values. Only parameter estimates fitted from raw data using nonlinear regression, produced robust approximations. Data quality influenced sensitivity and sample size for an optimal precision. CONCLUSIONS: Allometric surrogates of average leaf biomass in eelgrass shoots offer convenient nondestructive assessments. But analysis method and sample size can influence accuracy in a direct manner. Standardized routines for data quality are crucial on granting cost-effectiveness of the method.

The effect of parameter variability in the allometric projection of leaf growth rates for eelgrass (Zostera marina L.) II: the importance of data quality control procedures in bias reduction.

BACKGROUND: Eelgrass grants important ecological benefits including a nursery for waterfowl and fish species, shoreline stabilization, nutrient recycling and carbon sequestration. Upon the exacerbation of deleterious anthropogenic influences, re-establishment of eelgrass beds has mainly depended on transplantation. Productivity estimations provide valuable information for the appraisal of the restoration of ecological functions of natural populations. Assessments over early stages of transplants should preferably be nondestructive. Allometric scaling of eelgrass leaf biomass in terms of matching length provides a proxy that reduces leaf biomass and productivity estimations to simple measurements of leaf length and its elongation over a period. We examine how parameter variability impacts the accuracy of the considered proxy and the extent on what data quality and sample size influence the uncertainties of the involved allometric parameters. METHODS: We adapted a Median Absolute Deviation data quality control procedure to remove inconsistencies in the crude data. For evaluating the effect of parametric uncertainty we performed both a formal exploration and an analysis of the sensitivity of the allometric projection method to parameter changes. We used parameter estimates obtained by means of nonlinear regression from crude as well as processed data. RESULTS: We obtained reference leaf growth rates by allometric projection using parameter estimates produced by the crude data, and then considered changes in fitted parameters bounded by the modulus of the vector of the linked standard errors, we found absolute deviations up to 10% of reference values. After data quality control, the equivalent maximum deviation was under 7% of corresponding reference rates. Therefore, the addressed allometric method is robust. Even the smaller sized samples in the quality controlled dataset produced better accuracy levels than the whole set of crude data. CONCLUSIONS: We propose quality control of data as a highly recommended step in the overall procedure that leads to reliable allometric surrogates of eelgrass leaf growth rates. The proliferation of inconsistent replicates in the crude data points towards the importance of discarding incomplete leaves. We also recommend avoiding errors in estimating the biomass of small leaves for which precision of the used analytical scale might be an issue.

Surface aggregation patterns of LDL receptors near coated pits III: potential effects of combined retrograde membrane flow-diffusion and a polarized-insertion mechanism.

Although the process of endocytosis of the low density lipoprotein (LDL) macromolecule and its receptor have been the subject of intense experimental research and modeling, there are still conflicting hypotheses and even conflicting data regarding the way receptors are transported to coated pits, the manner by which receptors are inserted before they aggregate in coated pits, and the display of receptors on the cell surface. At first it was considered that LDL receptors in human fibroblasts are inserted at random locations and then transported by diffusion toward coated pits. But experiments have not ruled out the possibility that the true rate of accumulation of LDL receptors in coated pits might be faster than predicted on the basis of pure diffusion and uniform reinsertion over the entire cell surface. It has been claimed that recycled LDL receptors are inserted preferentially in regions where coated pits form, with display occurring predominantly as groups of loosely associated units. Another mechanism that has been proposed by experimental cell biologists which might affect the accumulation of receptors in coated pits is a retrograde membrane flow. This is essentially linked to a polarized receptor insertion mode and also to the capping phenomenon, characterized by the formation of large patches of proteins that passively flow away from the regions of membrane exocytosis. In this contribution we calculate the mean travel time of LDL receptors to coated pits as determined by the ratio of flow strength to diffusion-coefficient, as well as by polarized-receptor insertion. We also project the resulting display of unbound receptors on the cell membrane. We found forms of polarized insertion that could potentially reduce the mean capture time of LDL receptors by coated pits which is controlled by diffusion and uniform insertion. Our results show that, in spite of its efficiency as a possible device for enhancement of the rate of receptor trapping, polarized insertion nevertheless fails to induce the formation of steady-state clusters of receptor on the cell membrane. Moreover, for appropriate values of the flow strength-diffusion ratio, the predicted steady-state distribution of receptors on the surface was found to be consistent with the phenomenon of capping.

A method for calculating the area of Zostera marina leaves from digital images with noise induced by humidity content.

Despite the ecological importance of eelgrass, nowadays anthropogenic influences have produced deleterious effects in many meadows worldwide. Transplantation plots are commonly used as a feasible remediation scheme. The characterization of eelgrass biomass and its dynamics is an important input for the assessment of the overall status of both natural and transplanted populations. Particularly, in restoration plots it is desirable to obtain nondestructive assessments of these variables. Allometric models allow the expression of above ground biomass and productivity of eelgrass in terms of leaf area, which provides cost effective and nondestructive assessments. Leaf area in eelgrass can be conveniently obtained by the product of associated length and width. Although these variables can be directly measured on most sampled leaves, digital image methods could be adapted in order to simplify measurements. Nonetheless, since width to length ratios in eelgrass leaves could be even negligible, noise induced by leaf humidity content could produce misidentification of pixels along the peripheral contour of leaves images. In this paper, we present a procedure aimed to produce consistent estimations of eelgrass leaf area in the presence of the aforementioned noise effects. Our results show that digital image procedures can provide reliable, nondestructive estimations of eelgrass leaf area.

Using the value of Lin's concordance correlation coefficient as a criterion for efficient estimation of areas of leaves of eelgrass from noisy digital images.

BACKGROUND: Eelgrass is a cosmopolitan seagrass species that provides important ecological services in coastal and near-shore environments. Despite its relevance, loss of eelgrass habitats is noted worldwide. Restoration by replanting plays an important role, and accurate measurements of the standing crop and productivity of transplants are important for evaluating restoration of the ecological functions of natural populations. Traditional assessments are destructive, and although they do not harm natural populations, in transplants the destruction of shoots might cause undesirable alterations. Non-destructive assessments of the aforementioned variables are obtained through allometric proxies expressed in terms of measurements of the lengths or areas of leaves. Digital imagery could produce measurements of leaf attributes without the removal of shoots, but sediment attachments, damage infringed by drag forces or humidity contents induce noise-effects, reducing precision. Available techniques for dealing with noise caused by humidity contents on leaves use the concepts of adjacency, vicinity, connectivity and tolerance of similarity between pixels. Selection of an interval of tolerance of similarity for efficient measurements requires extended computational routines with tied statistical inferences making concomitant tasks complicated and time consuming. The present approach proposes a simplified and cost-effective alternative, and also a general tool aimed to deal with any sort of noise modifying eelgrass leaves images. Moreover, this selection criterion relies only on a single statistics; the calculation of the maximum value of the Concordance Correlation Coefficient for reproducibility of observed areas of leaves through proxies obtained from digital images. RESULTS: Available data reveals that the present method delivers simplified, consistent estimations of areas of eelgrass leaves taken from noisy digital images. Moreover, the proposed procedure is robust because both the optimal interval of tolerance of similarity and the reproducibility of observed leaf areas through digital image surrogates were independent of sample size. CONCLUSION: The present method provides simplified, unbiased and non-destructive measurements of eelgrass leaf area. These measurements, in conjunction with allometric methods, can predict the dynamics of eelgrass biomass and leaf growth through indirect techniques, reducing the destructive effect of sampling, fundamental to the evaluation of eelgrass restoration projects thereby contributing to the conservation of this important seagrass species.

Using allometric procedures to substantiate the plastochrone method for eelgrass leaf growth assessments.

Estimation of leaf productivity in eelgrass (Zostera marina L.) is crucial for evaluating the ecological role of this important seagrass species. Although leaf marking techniques are widely used to obtain estimates of leaf productivity, the accuracy of these assessments, has been questioned mainly because these fail to account for leaf growth below the reference mark and also because they apparently disregard the contribution of mature leaf tissues to the growth rate of leaves. On the other hand, the plastochrone method is a simpler technique that has been considered to effectively capture growth in a more realistic way, thereby providing more accurate assessments of both above- and below-ground productivities. But since the actual values of eelgrass growth rates are difficult to obtain, the worth of the plastochrone method has been largely vindicated because it produces assessments that overestimate productivity as compared to estimates obtained by leaf marking. Additionally, whenever eelgrass leaf biomass can be allometrically scaled in terms of matching leaf length in a consistent way, the associated leaf growth rates can be also projected allometrically. In this contribution, we used that approach to derive an authentication of the plastochrone method and formally demonstrate that, as has been claimed to occur for leaf marking approaches, the plastochrone method itself underestimates actual values of eelgrass leaf growth rates. We also show that this unavoidable bias is mainly due to the inadequacy of single-leaf biomass assessments in providing a proxy for the growth of all leaf tissue in a shoot over a given interval. Moreover, the derived formulae give conditions under which assessments of leaf growth rates using the plastochrone method would systematically underestimate matching values obtained by leaf marking procedures. And, assessments of leaf growth rates obtained by using the present data show that plastochrone method estimations underestimated corresponding proxies obtained allometrically (27%), or through leaf marking (35%). Allometric projection is recommended as a simpler and more effective procedure to reduce the bias in eelgrass leaf productivity estimations that associates to the use of plastochrone methods.

An evaluation of leaf biomass : length ratio as a tool for nondestructive assessment in eelgrass (Zostera marina L.).

The characterization of biomass and its dynamics provides valuable information for the assessment of natural and transplanted eelgrass populations. The need for simple, nondestructive assessments has led to the use of the leaf biomass-to-length ratio for converting leaf-length measurements, which can be easily obtained, to leaf growth rates through the plastochrone method. Using data on leaf biomass and length collected in three natural eelgrass populations and a mesocosm, we evaluated the suitability of a leaf weight-to-length ratio for nondestructive assessments. For the data sets considered, the isometric scaling that sustains the weight-to-length proxy always produced inconsistent fittings, and for leaf-lengths greater than a threshold value, the conversion of leaf length to biomass generated biased estimations. In contrast, an allometric scaling of leaf biomass and length was highly consistent in all the cases considered. And these nondestructive assessments generated reliable levels of reproducibility in leaf biomass for all the ranges of variability in leaf lengths. We argue that the use of allometric scaling for the representation of leaf biomass in terms of length provides a more reliable approach for estimating eelgrass biomass.

Surface aggregation patterns of LDL receptors near coated pits II. The retrograde membrane flow-diffusion and generalized plaque-form insertion mechanism.

This study presents a theoretical exploration of the effects of mechanisms that, in addition to diffusion, may influence the surface dynamics and display of unbound receptors in the low-density lipoprotein (LDL) endocytic cycle in human fibroblasts. The factors considered here are a transverse membrane flow and a generalized plaque-form insertion mode. The proposed model permits estimations of aggregation rates of unbound receptors in coated pits as well as pictorial representations of their expected steady-state display on the cell surface. Our findings show that this display is determined in a fundamental way by the ratio of the strength of the flow to the diffusion coefficient. For measured values of the diffusion coefficient and the estimated value of the flow rate strength (and independent of the receptor insertion mode), the display predicted by our model is consistent with the capping phenomenon, i.e., a gradated clustering in the direction of flow streamlines. There could be suitable characterizations of the receptor reinsertion mode that would produce a substantial reduction in the mean capture time of LDL receptors by coated pits. In any event, our results show that the existence of a transverse membrane flow precludes the display of steady-state plaque-form surface clusters.

An allometric method for the projection of eelgrass leaf biomass production rates.

We demonstrate that an allometric model for eelgrass leaf-growth rates can be derived from data on leaf architecture and growth form. Using this construct, we produced indirect assessments of growth rates of leaves that we call projections, which can be easily obtained in terms of allometric parameters and proxy values for leaf area, expressed as the product of leaf length and width. These projections of leaf-growth rates displayed a high level of correspondence with values observed in our data, as well as with other sets of reference data. A comparison with growth rates obtained by using the plastochrone index method showed that our model provides more accurate estimations while using a simpler methodology. Our results also show that whenever allometric parameters for the scaling of eelgrass leaf dry weight in terms of leaf area are available, the proposed model provides an accurate, cost-effective and non-destructive alternative to assessments based on traditional or plastochrone methods.

An economical non-destructive method for estimating eelgrass, Zostera marina (Potamogetonaceae) leaf growth rates: formal development and use in northwestern Baja California

Seagrass beds provide much of the primary production in estuaries; host many fishes and fish larvae, and abate erosion. The present study presents original analytical methods for estimating mean leaf-growth rates of eelgrass (Zostera marina). The method was calibrated by using data collected in a Z. marina meadow at Punta Banda estuary in Baja California, Mexico. The analytical assessments were based on measurements of leaf length and standard regression procedures. We present a detailed explanation of the formal procedures involved in the derivation of these analytical methods. The measured daily leaf-growth rate was 10.9 mm d-1 leaf-1. The corresponding value projected by our method was 10.2 mm d-1 leaf-1. The associated standard errors were of 0.53 and 0.56 mm d-1 leaf-1 respectively. The method was validated by projecting leaf-growth rates from an independent data set, which gave consistent results. The use of the method to obtain the mean leaf growth rate of a transplanted plot is also illustrated. Comparison of our leaf-growth data with previously reported assessments show the significant forcing of sea-surface temperature on eelgrass leaf dynamics. The formal constructs provided here are of general scope and can be applied to equivalent eelgrass data sets in a straightforward manner. Rev. Biol. Trop. 56 (3): 1003-1013. Epub 2008 September 30.

Las praderas de pastos marinos abaten la erosión y aportan gran parte de la productividad primaria de los esteros y son refugio de muchos peces y sus larvas. El presente trabajo introduce métodos analíticos para estimar las tasas medias de crecimiento foliar de Zostera marina L. y sus varianzas. La calibración del método se llevó a cabo utilizando datos de una pradera de esta fanerógama en el Estero de Punta Banda Baja California, México. Las referidas estimaciones analíticas, se basan en medias de longitud foliar y en procedimientos estandarizados de regresión. Dichas determinaciones son por ende no-destructivas. Se proporciona una explicación detallada de los aspectos formales de la derivación del método. El valor promedio observado de la tasa media diaria de crecimiento foliar fue de 10.9 mm d-1 leaf-1. El valor correspondiente proyectado mediante nuestro método fue de 10.2 mm d-1 leaf-1. Los errores estándar asociados fueron 0.53 y 0.56 mm d-1 leaf-1 respectivamente. Valores proyectados de la tasa media de crecimiento foliar diario utilizando datos de longitudes foliares publicadas por otros autores dieron también resultados consistentes. Se ilustra también el uso del método para proyectar la media de crecimiento foliar de una parcela transplantada de Zostera marina. La comparación de los resultados de este estudio con equivalentes reportados previamente nos permite concluir que las diferencias observadas pueden ser explicadas en función de la variabilidad de la temperatura superficial del mar en virtud del control de esta variable sobre la dinámica foliar de Z. marina. Las herramientas de estimación indirecta presentadas en este trabajo pueden aplicarse fácilmente a datos equivalentes de Z. marina.

Mortality rate estimation for eelgrass Zostera marina (Potamogetonaceae) using projections from Leslie matrices

The main goal of this study is to provide estimations of mean mortality rate of vegetative shoots of the seagrass Zostera marina in a meadow near Ensenada Baja California, using a technique that minimizes destructive sampling. Using cohorts and Leslie matrices, three life tables were constructed, each representing a season within the period of monthly sampling (April 1999 to April 2000). Ages for the cohorts were established in terms of Plastochrone Interval (PI). The matrices were projected through time to estimate the mean total number of individuals at time t, n(t) as well as mortality. We found no statistical differences between observed and predicted mean values for these variables (t=-0.11, p=0.92 for n(t) and t=0.69, p=0.5 for mean rate of mortality). We found high correlation coefficient values between observed and projected values for monthly number of individuals (r=0.70, p=0.007) and monthly mortality rates (r=0.81, p=0.001). If at a certain time t a sudden environmental change occurs, and as long as the perturbation does not provoke the killing of all the individuals of a given age i for 0 ≤ i ≤ x - 1, there will be a prevailing number of individuals of age or stage x at a time t+1. This nondestructive technique reduces the number of field visits and samples needed for the demographic analysis of Z. marina, and therefore decreases the disturbance caused by researches to the ecosystem. Rev. Biol. Trop. 56 (3): 1015-1022. Epub 2008 September 30.

El propósito principal de este estudio es el de proveer estimaciones de tasas promedio de mortalidad de tallos vegetativos de Zostera marina en una pradera cercana a Ensenada Baja California, utilizando una técnica que minimiza los muestreos destructivos para estos pastos marinos. Mediante la utilización de cohortes y matrices de Leslie, se construyeron tres tablas de vida, cada una representando a una estación dentro de período anual de muestreos mensuales (Abril 1999 a Abril 2000). Las edades de los cohortes fueron estimadas en términos de Intervalos de Plastocrono (IP). Las matrices de Leslie fueron proyectadas a través del tiempo para estimar el número total de individuos a un tiempo t, n(t) así como las tasas de mortalidad. No se encontraron diferencias significativas entre los valores medios observados y proyectados para estas variables (t=0.11, p=0.92 para n(t) y t=0.69, p=0.5 para la tasa media de mortalidad). Se encontraron altas correlaciones los valores observados y proyectados tanto en el número de individuos (r=0.70, p=0.007) como las tasas mensuales de mortalidad (r=0.81, p=0.001). Si a cierto tiempo t ocurre un cambio ambiental repentino, de tal manera que la perturbación no provoque la muerte de todos los individuos de una edad i para 0 ≤ i ≤ x-1, prevalecerá un número de individuos de edad o estadio x al tiempo t+1. Esta técnica no destructiva reduce el número de visitas al campo y de muestras necesarias para un análisis demográfico de Z. marina y por lo tanto decrece el disturbio causado al ecosistema.

An economical non-destructive method for estimating eelgrass, Zostera marina (Potamogetonaceae) leaf growth rates: formal development and use in northwestern Baja California.

Seagrass beds provide much of the primary production in estuaries; host many fishes and fish larvae, and abate erosion. The present study presents original analytical methods for estimating mean leaf-growth rates of eelgrass (Zostera marina). The method was calibrated by using data collected in a Z. marina meadow at Punta Banda estuary in Baja California, Mexico. The analytical assessments were based on measurements of leaf length and standard regression procedures. We present a detailed explanation of the formal procedures involved in the derivation of these analytical methods. The measured daily leaf-growth rate was 10.9 mm d(-1) leaf(-1). The corresponding value projected by our method was 10.2 mm d(-1) leaf(-). The associated standard errors were of 0.53 and 0.56 mm d(-1) leaf(-1) respectively. The method was validated by projecting leaf-growth rates from an independent data set, which gave consistent results. The use of the method to obtain the mean leaf growth rate of a transplanted plot is also illustrated. Comparison of our leaf-growth data with previously reported assessments show the significant forcing of sea-surface temperature on eelgrass leaf dynamics. The formal constructs provided here are of general scope and can be applied to equivalent eelgrass data sets in a straightforward manner.

Mortality rate estimation for eelgrass Zostera marina (Potamogetonaceae) using projections from Leslie matrices.

The main goal of this study is to provide estimations of mean mortality rate of vegetative shoots of the seagrass Zostera marina in a meadow near Ensenada Baja California, using a technique that minimizes destructive sampling. Using cohorts and Leslie matrices, three life tables were constructed, each representing a season within the period of monthly sampling (April 1999 to April 2000). Ages for the cohorts were established in terms of Plastochrone Interval (PI). The matrices were projected through time to estimate the mean total number of individuals at time t, n(t) as well as mortality. We found no statistical differences between observed and predicted mean values for these variables (t = -0.11, p = 0.92 for n(t) and t = 0.69, p = 0.5 for mean rate of mortality). We found high correlation coefficient values between observed and projected values for monthly number of individuals (r = 0.70, p = 0.007) and monthly mortality rates (r = 0.81, p = 0.001). If at a certain time t a sudden environmental change occurs, and as long as the perturbation does not provoke the killing of all the individuals of a given age i for 0 < or = i < or = x - 1, there will be a prevailing number of individuals of age or stage x at a time t+1. This nondestructive technique reduces the number of field visits and samples needed for the demographic analysis of Z. marina, and therefore decreases the disturbance caused by researches to the ecosystem.

A functionally diverse population growth model.

The present work deals with a single species population growth model, exhibiting diverse functional modes. The model is based on the principle of limiting factors for population growth. This paradigm was adapted from the law of the minimum, and the law of the tolerance. In the framework presented here, rates of natality and mortality are controlled by extreme values of limiting factors. The formal expression of these ideas corresponds to what we call a functionally diverse model. This model permits the identification of thresholds of viability, starvation, intraspecific cooperation and competition. The performance of the model is evaluated using data for populations growing under experimental or natural conditions.

Improved leaf area index based biomass estimations for Zostera marina L.

The application of special scanning technologies in plant population studies makes it now possible to offer reliable indirect estimations of Leaf Area Index (LAI). This has stimulated the adaptation of related biomass assessment methods and has provided a way to simplify tedious laboratory procedures whilst avoiding destructive sampling. Particularly, above-ground biomass for Zostera marina L. has been expressed depending linearly on Leaf Area Index. Nevertheless, we demonstrate that this approach produces biased estimations. It is also shown that expressing leaf dry weight by means of an allometric function of length and width can eliminate bias. Furthermore, the dominant term of the associated power series expansion becomes the aforementioned linear representation in terms of Leaf Area Index. The consistency of the estimation methods derived from the allometric model was tested using data from a Z. marina meadow. Consequently, the improved method is expected to become a valuable tool for the reduction of the uncertainty associated with the estimation of above-ground biomass through the use of Leaf Area Index.

An upgraded method to relocate marked shoots of the seagrass Zostera marina

This paper presents a new method for the recovery of marked seagrass blades. The introduction of a plastic belt surrounding the marked shoot at a sediment level provided a relocation arrangement which was unloosed by drag forces or grazing. The relocation method was tested on Zostera marina L. It proved to have the advantage of increasing dramatically the number of marked shoots recovered up to 100 while reducing the cost of the procedure to a minimum. An allometric model indicated that the introduced relocation method has no impact on the development of the plant.