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.

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The rate of production of leaf biomass in eelgrass (Zostera marina L.) is an indicator variable for environmental influences on the growth of this important seagrass species. The efforts to restore eelgrass meadows from the harmful human influences make the use of nondestructive evaluations essential. We present, here, an indirect procedure for the estimation of the growth rates of eelgrass leaves by using easily obtained measurements of leaf length and increases in leaf length, and allometric parameters linked to the scaling of leaf biomass and leaf length. This allometric method includes criteria that allow the estimation of leaf growth rates even when the sizes of some of the leaves cannot be determined because of herbivory or other environmental factors. To validate the proposed method, we performed simulation studies and analyzed data from two natural eelgrass populations in the East Pacific (México). These allometric projections of leaf growth rates displayed a high level of correspondence with observed values. We show that whenever the allometric parameters for the scaling of eelgrass leaf dry weight in terms of leaf length have been previously fitted, the method proposed here can provide an alternative for estimating biomass production that is both accurate and nondestructive and uses easily obtained data on leaf length and increases in leaf length between the sampling periods.

ABSTRACT. Restoration of eelgrass Zostera marina meadows from harmful anthropogenic influences has made it essential to evaluate these efforts by using non-destructive assessments. Allometric methods provide a convenient framework for the derivation of reliable indirect assessments of leaf biomass and leaf growth of eelgrass. Invariance of the involved parameters could grant truly nondestructive assessments because previously fitted values could be used to produce consistent estimations. In order to explore this property we analyzed data from two natural eelgrass populations in the East Pacific (México), as well as populations in the West Pacific (two natural in Korea and one mesocosm in Japan). When we compared observed leaf growth rates with those projected allometrically by using parameter values fitted at different sites, we found that only parameter values fitted at sites within the same geographical region can produce consistent results. Therefore if this restriction holds previously fitted parameters can indeed be used to produce reliable non-destructive assessments of eelgrass leaf growth rates. Keywords: Zostera marina, foliar growth, eelgrass meadow, allometric modeling, restoration evaluation.Efectos de la variabilidad paramétrica en la obtención de tasas de crecimiento foliar en Zostera marina L. mediante métodos alométricos RESUMEN. La restauración de praderas de Zostera marina que han sido dañadas por influencia antropogénica, ha hecho necesaria la evaluación de estos esfuerzos mediante métodos no destructivos. Las metodologías alométricas proporcionan un marco formal que favorece la obtención de estimaciones indirectas de biomasa y tasas de crecimiento foliar. La invariancia de los parámetros asociados asegura la obtención de técnicas de estimación no destructiva de gran confiabilidad, puesto que, parámetros previamente ajustados podrían usarse para producir estimaciones consistentes. Para investigar la existencia de esta propiedad se analizan datos provenientes de dos poblaciones naturales de Z. marina en el Pacífico oriental (México) así como también poblaciones en el Pacífico occidental (dos naturales en Corea y una cultivada en laboratorio en Japón). Al comparar valores observados de tasas de crecimiento foliar con aquellos obtenidos alométricamente, utilizando parámetros ajustados en sitios indistintos, se observó que únicamente cuando los parámetros provienen de una región geográfica equivalente se pueden producir resultados consistentes. Por lo tanto, tomando en cuenta esta restricción parámetros alométricos previamente ajustados pueden, en efecto, producir evaluaciones no destructivas y fiables de tasas de crecimiento de las hojas de Z. marina.

(1) Background: We previously demonstrated that customary regression protocols for curvature in geometrical space all derive from a generalized model of complex allometry combining scaling parameters expressing as continuous functions of covariate. Results highlighted the relevance of addressing suitable complexity in enhancing the accuracy of allometric surrogates of plant biomass units. Nevertheless, examination was circumscribed to particular characterizations of the generalized model. Here we address the general identification problem. (2) Methods: We first suggest a log-scales protocol composing a mixture of linear models weighted by exponential powers. Alternatively, adopting an operating regime-based modeling slant we offer mixture regression or Takagi–Sugeno–Kang arrangements. This last approach allows polyphasic identification in direct scales. A derived index measures the extent on what complexity in arithmetic space drives curvature in arithmetical space. (3) Results: Fits on real and simulated data produced proxies of outstanding reproducibility strength indistinctly of data scales. (4) Conclusions: Presented analytical constructs are expected to grant efficient allometric projection of plant biomass units and also for the general settings of allometric examination. A traditional perspective deems log-transformation and allometry inseparable. Recent views assert that this leads to biased results. The present examination suggests this controversy can be resolved by addressing adequately the complexity of geometrical space protocols

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BackgroundEelgrass 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.MethodsWe 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.ResultsWe 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.ConclusionsWe 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.

BackgroundThe 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.ResultsThe 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.ConclusionsAllometric 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.