Ecological Archives A025081A2
Margot L. HessingLewis, Sally D. Hacker, Bruce A. Menge, SeaOh McConville, and Jeremy Henderson. 2015. Are large macroalgal blooms necessarily bad? nutrient impacts on seagrass in upwellinginfluenced estuaries. Ecological Applications 25:1330–1347. http://dx.doi.org/10.1890/140548.1
Appendix B. Model structures for experiment response metrics.
Model structures for all response metrics used in AIC (Akaike Information Criteria)based model selection for field and mesocosm experiments (implemented in the nlme R package using the lme (linear mixed effects) function). Prior to model structure formulation, the fit of nonGaussian data (using the glm (generalized linear model)) function was assessed visually. Gaussian distributions were used for all response variables, including count data, because alternative distributions (i.e., Poisson and negative binomial) did not improve the model fit. Fixed effects for most variables included macroalgal (M) and nutrient (N) factors, as well as their interaction with time when applicable. Dates of repeated measurements (Time) and number of measurements per time step are indicated. Dates are ordered chronologically and converted to continuous numeric variables in all the models; time represents fixed intervals between all measurement dates. For the random effect, models considered included both random intercept and slope models for hierarchically nested grouping factors (field experiment random effects included: replicate block; mesocosm experiment random effects included: bucket nested within replicate). The specification of random effects considers the spatial nonindependence between observations nested in these factorial experiments through induced correlation structures (intraclass correlation). In R’s nlme package, random effects in the model structure are designated as: random = ~ random effects model  grouping structure, with the random effects formula repeated for all levels of grouping specified by the “ / ” sign. Inclusion of alternative variance structures were also evaluated based on AIC and visual inspection of model fit; they were employed in the model structure to improve equality of residual variance for the treatment factors. In R, the variance structure is specified as: weights = variance structure (form = ~ variance covariate  grouping factor for the coefficients). The varIdent structure, representing a constant variance structure, was commonly used to improve model fit where the variance covariate = 1, and the grouping factor Macroalgae × Nutrient (M × N) specifies that both factors that are allowed to have different variances. Alternatives variance structures available in R and grouping factors were also considered. To account for nonindependence of residuals between repeated measurements though time, correlation structures were considered that specified dependence between observations. These were implemented in the model structure if they improved model fit. In R, correlation structures are specified as: correlation = corStruct(form = ~ time covariate  grouping factor). The correlation structure applies to the observations within the same grouping level. We compared both corAR1 (autocorrelation of order 1, i.e., variation between measurements closer in time are most similar) and corCompSymm (compound symmetry corresponding to constant/uniform correlation structures, i.e., variation between all dates are the same) in terms of their improvement to model fit. Treatment manipulations were replicated 3 times at the plot level for the field experiment, and 3 times at the tank level for the mesocosm experiment (with buckets nested within tanks).
Table B1.

Response metric 
Full Model Fixed Effects 
Random Effects 
Variance Structure

Correlation Structure 
A. Field experiment 
Macroalgal volume (mL rep^{1}) 
N × M × Time
Time = Jun.20, Jul.05, Jul.24, Aug.22, Sep.17, Oct.10 
Random intercept (Rep) and slope (Time) R: TimeRep 
YES R: varIdent (form = ~1N × M) 
YES R: corAR1 (form = ~1Rep) 

Eelgrass density (% change in shoots rep^{1}) per central quadrat (0.25 m²) 
N × M
Jun.09  Sep.17

Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1N × M) 
NO 

Eelgrass density (% change in shoots rep^{1}) per haphazard quadrat (0.0625 m²) 
N × M
Jul.24  Oct.10

Random intercept (Rep) R: 1Rep 
NO 
NO 

Final eelgrass biomass rep^{1})

N × M Oct.10 
Random intercept (Rep) R: 1 Rep 
YES R: varIdent (form = ~1N × M) 
NO 

Eelgrass shoot length (% change in cm rep^{1})

N × M × Time
Time = Jun.22  Jul.23, Jul.23  Aug.20, Aug.20  Sep.16, Sep.16  Oct.7 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1N) 
YES R: corAR1 (form = ~1Rep) 

Eelgrass sheath length

N × M × Time
Time = Jul.05  Aug.22, Aug.22  Oct.10 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1N × M) 
YES R: corAR1 (form = ~1Rep) 

Redox potential (mV rep^{1})

N × M × Time
Time = Jun.09, Aug.22, Sep.17, Oct.10 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1 N) 
NO 

PPFD (μmol photon m2 s^{1} rep^{1})

M
Time = Aug.1822, Sep. 17^{1}9 
Random intercept (Time) R: 1Time 
YES R: varIdent (form = ~1M) 
NO 
B. Mesocosm experiment 
Macroalgal volume (mL rep^{1}) 
N × Time
Time = Aug.14, Sep.01, Oct.22 
Random intercept (Rep) R: 1 Rep

YES R: varIdent (form = ~1 N) 
NO 

Eelgrass density (% change shoots bucket^{1} rep^{1}) 
N × M
Jul.12  Sep.29 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1M) 
NO 

Final eelgrass biomass (g dry wt shoot^{1} rep^{1}) 
N × M
Oct. 22 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1N) 
NO 

Eelgrass shoot length (% change in cm rep^{1} bucket^{1}) 
N × M × Time
Time = Jul.16  Sep.01, Sep.01Sep.29 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1M) 
NO 

Eelgrass sheath length (% change in cm rep^{1} bucket^{1}) 
N × M × Time
Time = Jul.12 – Sep. 01, Sep.01 Sep.29 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1N × M) 
YES R: corAR1 (form = ~1Rep/Bucket) 

Trimmed eelgrass biomass (g dry wt rep^{1}) 
N × M × Time
Time = Jun. (25, 29), Jul. (04, 11, 16, 23, 29), Aug. (05, 11, 17, 24, 31), Sep. (08, 15, 24)

Random intercept (Rep) and slope (Time) R: Time Rep

NO 
YES R: corAR1 (form = ~1Rep) 

Sloughed eelgrass biomass (g dry wt rep^{1}) 
N × M × Time
Time = Jun. (16, 25, 29), Jul. (04, 11, 16, 23, 29), Aug. (05, 11, 17, 24, 31), Sep. (08, 15, 24, 27), Oct. (03, 18) 
Random intercept (Rep) R: 1 Rep

YES R: varIdent (form = ~1N × M) 
YES R: corAR1 (form = ~1Rep) 

Redox potential (mV rep^{1})

N × M × Time
Time = Jul.12, Aug.14, Sep.01, Sep.29, Oct.22 
Random intercept (Rep) and slope (Time) R: TimeRep 
YES R: varIdent (form = ~1N × M) 
YES R: corAR1 (form = ~1Rep/Bucket) 

Total light attenuation (μmol photon m2 s^{1} rep^{1})

N × M × Time
Time = Jul. prealgae (n = 2), Jul. postalgae (n = 3), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) 
Random intercept (Rep) R: 1Rep 
YES R: varIdent (form = ~1M) 
YES R: corAR1 (form = ~1Rep) 

Temperature (°C rep^{1}) 
N × M
Time = Jul. (n = 5), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) 
Random intercept (Rep) and slope (Time) R: TimeRep 
YES R: varIdent (form = ~1M) 
YES R: corAR1 (form = ~1Rep) 

Salinity (ppt rep^{1}) 
N × M
Time = Jul. (n = 5), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) 
Random intercept (Rep) and slope (Time) R: TimeRep 
NO 
YES R: corAR1 (form = ~1Rep) 

Dissolved Oxygen (mgL^{1} rep^{1}) 
N × M
Time = Jul. (n = 5), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) 
Random intercept (Rep) and slope (Time) R: TimeRep 
YES R: varIdent (form = ~1M) 
YES R: corAR1 (form = ~1Rep) 

pH (rep^{1}) 
N × M
Time = Jul. (n = 5), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) 
Random (Rep) R: 1Rep 
YES R: varIdent (form = ~1N × M) 
YES R: corAR1 (form = ~1Rep) 