Evaluation of self-thinning models and estimation methods in multilayered sessile animal populations

23 pages, 5 figures, 5 tables, 3 appendix.-- This is an open-access article distributed under the terms of the Creative Commons Attribution License

Self-thinning (ST) models have been widely used in the last decades to describe population dynamics under intraspecific competition in plant and animal communities. Nevertheless, their applicability in animal populations is subjected to the appropriate inclusion of space occupancy and energy requirements. Specifically, the disposition of gregarious sessile animals in complex matrices hampers the application of classical ST models. This paper reviews the self-thinning models, regression methods (central tendency and frontier techniques) and discrimination criteria currently applied for gregarious sessile species through application to the analysis of mussel populations (Mytilus galloprovincialis) grown in suspended culture. In addition, we propose to model the temporal evolution of site occupancy in the stochastic frontier function (SFF). Our results confirm that the number of layers should be included in the classical bidimensional ST model for the analysis of multilayered populations. The estimated parameters obtained by the different fitting techniques depended on the measurement method of the variables in the model. This, together with the proximity between the space and food self-thinning theoretical exponents (SST and FST, respectively) highlights the difficulty in discriminating the competition limiting factor (space/food) from the self-thinning exponent. On the other hand, the SFF provided congruent results for biomass and individual mass analysis, in contrast to the lack of robustness observed for the central tendency regression methods. Furthermore, the SFF approach allowed a dynamic interpretation of the ST process providing insight into the temporal evolution of site occupancy. These results highlight the suitability of the stochastic frontier approach in the analysis of self-thinning dynamics in sessile animal populations

This study was supported by the contract-project PROINSA Mussel Farm, Codes CSIC 20061089 and 0704101100001, and Xunta de Galicia PGIDIT06RMA018E and PGIDIT09MMA038E. A. M. Cubillo was funded by a CSIC-I3P-PC 2008 contract, financed by the European Social Fund, and a CSIC 201030E071 contract to carry out this work

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