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

Abstract

Abstract. 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 selfthinning 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.

A bioeconomic approach to optimize mussel culture production

“…indicated an underuse of the available resources. The relative efficiency of 1150 ind m À1 , which suffered the strongest competition effects on mussel growth and survivorship (Cubillo et al 2012a;Fuentes-Santos et al 2014), indicates that this density exceeded the carrying capacity of the rope, with the subsequent economic losses. Mussel mortality also implies a higher organic loading beneath culture leases that may alter the physical and chemical conditions of the bottom sediments and affect benthic biodiversity (Callier et al 2009;Soto 2009;Ysebaert et al 2009).…”

Dynamic self‐thinning model for sessile animal populations with multilayered distribution

“…We tested the validity of the dynamic self-thinning model and compared this approach with the traditional ST model through the analysis of multilayered mussel populations grown in suspended culture. Firstly, for each density treatment, the traditional ST model (eqn 1) was fitted using the regression methods applied in Cubillo et al (2012b). We tested whether the traditional model can detect different competition patterns among densities.…”

“…We tested whether the traditional model can detect different competition patterns among densities. To discriminate the competition limiting factor, the estimated exponents were compared with the theoretical food self-thinning (FST) exponent (b FST = À1.33) and the space self-thinning (SST) exponent obtained using image analysis (b SST = À1.23; Cubillo et al 2012b).…”

“…We extended the dynamic model proposed by Roderick and Barnes (2004) for the analysis of self-thinning in plants to the study of multilayered sessile animal populations. For this purpose, we substituted the density or number of individuals per unit area (N) by the effective density (N e ) defined in the self-thinning model (Guiñez & Castilla 1999;Cubillo et al 2012b).…”

“…Thus, while self-thinning has been formally recognized as a dynamic process, the current models are not dynamic, failing to include the time effect. Cubillo et al (2012b) partially overcame this problem fitting the traditional ST model using frontier analysis, which provides a dynamic interpretation of the ST process through the temporal evolution of site occupancy. On the other hand, Roderick and Barnes (2004) proposed a new formulation of self-thinning as a dynamic problem.…”