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Estimation of density-dependent mortality of juvenile bivalves in the Wadden Sea.

Andresen H, Strasser M, van der Meer J - PLoS ONE (2014)

Bottom Line: We analyzed count data from three years of temporal sampling during the first months after bivalve settlement at ten transects in the Sylt-Rømø-Bay in the northern German Wadden Sea.Measurement error was estimated by bootstrapping, and residual deviances were adjusted by adding process error.With simulations the effect of these two types of error on the estimate of the density-dependent mortality coefficient was investigated.

View Article: PubMed Central - PubMed

Affiliation: Department of Marine Ecology, Royal Netherlands Institute for Sea Research, Den Burg, The Netherlands.

ABSTRACT
We investigated density-dependent mortality within the early months of life of the bivalves Macoma balthica (Baltic tellin) and Cerastoderma edule (common cockle) in the Wadden Sea. Mortality is thought to be density-dependent in juvenile bivalves, because there is no proportional relationship between the size of the reproductive adult stocks and the numbers of recruits for both species. It is not known however, when exactly density dependence in the pre-recruitment phase occurs and how prevalent it is. The magnitude of recruitment determines year class strength in bivalves. Thus, understanding pre-recruit mortality will improve the understanding of population dynamics. We analyzed count data from three years of temporal sampling during the first months after bivalve settlement at ten transects in the Sylt-Rømø-Bay in the northern German Wadden Sea. Analyses of density dependence are sensitive to bias through measurement error. Measurement error was estimated by bootstrapping, and residual deviances were adjusted by adding process error. With simulations the effect of these two types of error on the estimate of the density-dependent mortality coefficient was investigated. In three out of eight time intervals density dependence was detected for M. balthica, and in zero out of six time intervals for C. edule. Biological or environmental stochastic processes dominated over density dependence at the investigated scale.

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Illustration of the steps within the analysis of density dependence.A: regression through observed data of Macoma balthica for the time interval May to June 1997. B: preset slope forced through observed data (in this example slope = 1 for density independence). C: deterministic data calculated from observed data to lie on hypothetical regression line from previous step. D: regression after measurement error, estimated by bootstrapping, was added to deterministic data, one example of 10000 simulations. E: additionally, before adding measurement error, process error was added to logDt+1, to arrive at observed residual deviance from first step, one example of 10000 simulations. F: modelled slope values with prediction intervals for various preset slopes, simulated with observed measurement error alone (white line for slope values and grey bootstrap interval) and observed process error additionally (black dots and whiskers). The dashed line gives the observed slope from step A. In this case the observed slope falls within the modelled prediction interval, whatever the preset slope (i.e. assumed true slope) is.
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pone-0102491-g002: Illustration of the steps within the analysis of density dependence.A: regression through observed data of Macoma balthica for the time interval May to June 1997. B: preset slope forced through observed data (in this example slope = 1 for density independence). C: deterministic data calculated from observed data to lie on hypothetical regression line from previous step. D: regression after measurement error, estimated by bootstrapping, was added to deterministic data, one example of 10000 simulations. E: additionally, before adding measurement error, process error was added to logDt+1, to arrive at observed residual deviance from first step, one example of 10000 simulations. F: modelled slope values with prediction intervals for various preset slopes, simulated with observed measurement error alone (white line for slope values and grey bootstrap interval) and observed process error additionally (black dots and whiskers). The dashed line gives the observed slope from step A. In this case the observed slope falls within the modelled prediction interval, whatever the preset slope (i.e. assumed true slope) is.

Mentions: In the data analysis procedure, first, a linear regression was fit of the log counts+1 in the ten transects at the end of a time step on the log counts+1 at the beginning of the time interval (example Fig. 2A). The regression was done as a GLM (Generalized linear model) with the quasipoisson family to allow for overdispersion, while the associated log link suits the exponential nature of mortality and implicates that density dependence is modeled as a function of log density. Sampling areas were changed over time and this was accounted for by using an offset, namely the log of the ratio of the sampling areas at the end and at the beginning of a time interval. For both species a regression model was fitted for every period. The observed slope was subsequently compared to the outcomes of simulations. The statistical question to be answered is, which hypothetical true slopes may lead to the observed slope under the observed measurement error? For this, a density-independent model (slope = 1) and models with different predefined levels of density dependence (slopes<1) were forced through the observed data (example Fig. 2B). The preset slopes and the respective resulting intercepts were then used to calculate deterministic data without error (Fig. 2C) from the observed data. Next, error was added by generating random deviates with the observed measurement error (details on quantification of measurement error below). Through these simulated data, a regression was fit again (example Fig. 2D). Adding the error and fitting the regression was repeated 10000 times per preset slope, and the average resulting slopes with 95% prediction intervals (white line and grey area in example Fig. 2F) plotted against the preset slopes to compare it with the slope calculated from the observed field data (dashed line in Fig. 2F).


Estimation of density-dependent mortality of juvenile bivalves in the Wadden Sea.

Andresen H, Strasser M, van der Meer J - PLoS ONE (2014)

Illustration of the steps within the analysis of density dependence.A: regression through observed data of Macoma balthica for the time interval May to June 1997. B: preset slope forced through observed data (in this example slope = 1 for density independence). C: deterministic data calculated from observed data to lie on hypothetical regression line from previous step. D: regression after measurement error, estimated by bootstrapping, was added to deterministic data, one example of 10000 simulations. E: additionally, before adding measurement error, process error was added to logDt+1, to arrive at observed residual deviance from first step, one example of 10000 simulations. F: modelled slope values with prediction intervals for various preset slopes, simulated with observed measurement error alone (white line for slope values and grey bootstrap interval) and observed process error additionally (black dots and whiskers). The dashed line gives the observed slope from step A. In this case the observed slope falls within the modelled prediction interval, whatever the preset slope (i.e. assumed true slope) is.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4126668&req=5

pone-0102491-g002: Illustration of the steps within the analysis of density dependence.A: regression through observed data of Macoma balthica for the time interval May to June 1997. B: preset slope forced through observed data (in this example slope = 1 for density independence). C: deterministic data calculated from observed data to lie on hypothetical regression line from previous step. D: regression after measurement error, estimated by bootstrapping, was added to deterministic data, one example of 10000 simulations. E: additionally, before adding measurement error, process error was added to logDt+1, to arrive at observed residual deviance from first step, one example of 10000 simulations. F: modelled slope values with prediction intervals for various preset slopes, simulated with observed measurement error alone (white line for slope values and grey bootstrap interval) and observed process error additionally (black dots and whiskers). The dashed line gives the observed slope from step A. In this case the observed slope falls within the modelled prediction interval, whatever the preset slope (i.e. assumed true slope) is.
Mentions: In the data analysis procedure, first, a linear regression was fit of the log counts+1 in the ten transects at the end of a time step on the log counts+1 at the beginning of the time interval (example Fig. 2A). The regression was done as a GLM (Generalized linear model) with the quasipoisson family to allow for overdispersion, while the associated log link suits the exponential nature of mortality and implicates that density dependence is modeled as a function of log density. Sampling areas were changed over time and this was accounted for by using an offset, namely the log of the ratio of the sampling areas at the end and at the beginning of a time interval. For both species a regression model was fitted for every period. The observed slope was subsequently compared to the outcomes of simulations. The statistical question to be answered is, which hypothetical true slopes may lead to the observed slope under the observed measurement error? For this, a density-independent model (slope = 1) and models with different predefined levels of density dependence (slopes<1) were forced through the observed data (example Fig. 2B). The preset slopes and the respective resulting intercepts were then used to calculate deterministic data without error (Fig. 2C) from the observed data. Next, error was added by generating random deviates with the observed measurement error (details on quantification of measurement error below). Through these simulated data, a regression was fit again (example Fig. 2D). Adding the error and fitting the regression was repeated 10000 times per preset slope, and the average resulting slopes with 95% prediction intervals (white line and grey area in example Fig. 2F) plotted against the preset slopes to compare it with the slope calculated from the observed field data (dashed line in Fig. 2F).

Bottom Line: We analyzed count data from three years of temporal sampling during the first months after bivalve settlement at ten transects in the Sylt-Rømø-Bay in the northern German Wadden Sea.Measurement error was estimated by bootstrapping, and residual deviances were adjusted by adding process error.With simulations the effect of these two types of error on the estimate of the density-dependent mortality coefficient was investigated.

View Article: PubMed Central - PubMed

Affiliation: Department of Marine Ecology, Royal Netherlands Institute for Sea Research, Den Burg, The Netherlands.

ABSTRACT
We investigated density-dependent mortality within the early months of life of the bivalves Macoma balthica (Baltic tellin) and Cerastoderma edule (common cockle) in the Wadden Sea. Mortality is thought to be density-dependent in juvenile bivalves, because there is no proportional relationship between the size of the reproductive adult stocks and the numbers of recruits for both species. It is not known however, when exactly density dependence in the pre-recruitment phase occurs and how prevalent it is. The magnitude of recruitment determines year class strength in bivalves. Thus, understanding pre-recruit mortality will improve the understanding of population dynamics. We analyzed count data from three years of temporal sampling during the first months after bivalve settlement at ten transects in the Sylt-Rømø-Bay in the northern German Wadden Sea. Analyses of density dependence are sensitive to bias through measurement error. Measurement error was estimated by bootstrapping, and residual deviances were adjusted by adding process error. With simulations the effect of these two types of error on the estimate of the density-dependent mortality coefficient was investigated. In three out of eight time intervals density dependence was detected for M. balthica, and in zero out of six time intervals for C. edule. Biological or environmental stochastic processes dominated over density dependence at the investigated scale.

Show MeSH
Related in: MedlinePlus