Lake Jyväsjärvi (62° 14′ N, 25° 46′ E) is a moderately eutrophic (total phosphorus concentration around 35–40 µg L−1) urban lake in central Finland with an area of 3.4 km2. Jyväsjärvi is recovering from earlier severe pollution by municipal and industrial waste waters and recent restoration methods have included mass removals of small fish. Perch and roach analysed for this study were collected from these fish removal catches in 2005 and 2006 allowing a random sampling of 202 perch (mean ± SD total length 124±32 mm, range 57–212 mm) and 173 roach (171±73 mm, 57–275 mm) individuals for SIA. A small muscle sample was dissected from each fish, dried in an oven at 60 °C and ground into homogenous powder using a mortar and pestle. A small subsample (0.6 mg) was then accurately weighed into a tin cup for the analysis of δ13C and δ15N in a FlashEA 1112 elemental analyzer coupled to a Thermo Finnigan DELTAplus Advantage mass spectrometer (Thermo Electron Corporation, Waltham, MA, U.S.A.) at the University of Jyväskylä following standard protocols.
Reliable testing for the influence of increasing sample size on the TA, SEA and SEAc in a δ13C–δ15N biplot requires extensive data sets, which are not often available in published ecological stable isotope studies. The 202 perch and 173 roach individuals from Jyväsjärvi were assumed to sufficiently reflect the statistical distributions for the δ13C and δ15N values of these populations and, therefore, could be used for analysing the effect of sample size on TA, SEA and SEAc by bootstrapping (resampling). 5000 random samples of n individuals were drawn from the dataset with replacement and all three metrics were calculated for each draw. The minimum n was set to 5 and maximum to 80 (<50 % of the number of individuals in the original datasets). The same procedure was repeated for the simulated data sets, which were generated for both perch and roach such that sample sizes matched the true data sets. Their sample means were the same as those obtained from the true datasets and the covariance structures of the generated δ13C and δ15N values were the same as in the original data, but the observations followed a multivariate normal distribution.
The metric areas were calculated using a recently published Stable Isotope Bayesian Ellipses in R (SIBER) package [18] (link) for R v.2.10.1 [23] . The original script was modified to include bootstrapping of 5000 isotopic niche areas for each sample size n, which were then stored and their distributions examined using percentile values. The simulated data sets were generated with Multivariate Normal and t Distributions (mvtnorm) package in R.
Reliable testing for the influence of increasing sample size on the TA, SEA and SEAc in a δ13C–δ15N biplot requires extensive data sets, which are not often available in published ecological stable isotope studies. The 202 perch and 173 roach individuals from Jyväsjärvi were assumed to sufficiently reflect the statistical distributions for the δ13C and δ15N values of these populations and, therefore, could be used for analysing the effect of sample size on TA, SEA and SEAc by bootstrapping (resampling). 5000 random samples of n individuals were drawn from the dataset with replacement and all three metrics were calculated for each draw. The minimum n was set to 5 and maximum to 80 (<50 % of the number of individuals in the original datasets). The same procedure was repeated for the simulated data sets, which were generated for both perch and roach such that sample sizes matched the true data sets. Their sample means were the same as those obtained from the true datasets and the covariance structures of the generated δ13C and δ15N values were the same as in the original data, but the observations followed a multivariate normal distribution.
The metric areas were calculated using a recently published Stable Isotope Bayesian Ellipses in R (SIBER) package [18] (link) for R v.2.10.1 [23] . The original script was modified to include bootstrapping of 5000 isotopic niche areas for each sample size n, which were then stored and their distributions examined using percentile values. The simulated data sets were generated with Multivariate Normal and t Distributions (mvtnorm) package in R.
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