Ecological Archives A025-081-A2
Margot L. Hessing-Lewis, Sally D. Hacker, Bruce A. Menge, Sea-Oh McConville, and Jeremy Henderson. 2015. Are large macroalgal blooms necessarily bad? nutrient impacts on seagrass in upwelling-influenced estuaries. Ecological Applications 25:1330–1347. http://dx.doi.org/10.1890/14-0548.1
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 non-Gaussian 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 non-independence 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 non-independence 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: Time|Rep |
YES R: varIdent (form = ~1|N × M) |
YES R: corAR1 (form = ~1|Rep) |
|
Eelgrass density (% change in shoots rep-1) per central quadrat (0.25 m²) |
N × M
Jun.09 - Sep.17
|
Random intercept (Rep) R: 1|Rep |
YES R: varIdent (form = ~1|N × 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: 1|Rep |
NO |
NO |
|
Final eelgrass biomass rep-1)
|
N × M Oct.10 |
Random intercept (Rep) R: 1| Rep |
YES R: varIdent (form = ~1|N × 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: 1|Rep |
YES R: varIdent (form = ~1|N) |
YES R: corAR1 (form = ~1|Rep) |
|
Eelgrass sheath length
|
N × M × Time
Time = Jul.05 - Aug.22, Aug.22 - Oct.10 |
Random intercept (Rep) R: 1|Rep |
YES R: varIdent (form = ~1|N × M) |
YES R: corAR1 (form = ~1|Rep) |
|
Redox potential (mV rep-1)
|
N × M × Time
Time = Jun.09, Aug.22, Sep.17, Oct.10 |
Random intercept (Rep) R: 1|Rep |
YES R: varIdent (form = ~1| N) |
NO |
|
PPFD (μmol photon m-2 s-1 rep-1)
|
M
Time = Aug.18-22, Sep. 17-19 |
Random intercept (Time) R: 1|Time |
YES R: varIdent (form = ~1|M) |
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: 1|Rep |
YES R: varIdent (form = ~1|M) |
NO |
|
Final eelgrass biomass (g dry wt shoot-1 rep-1) |
N × M
Oct. 22 |
Random intercept (Rep) R: 1|Rep |
YES R: varIdent (form = ~1|N) |
NO |
|
Eelgrass shoot length (% change in cm rep-1 bucket-1) |
N × M × Time
Time = Jul.16 - Sep.01, Sep.01-Sep.29 |
Random intercept (Rep) R: 1|Rep |
YES R: varIdent (form = ~1|M) |
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: 1|Rep |
YES R: varIdent (form = ~1|N × M) |
YES R: corAR1 (form = ~1|Rep/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 = ~1|Rep) |
|
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 = ~1|N × M) |
YES R: corAR1 (form = ~1|Rep) |
|
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: Time|Rep |
YES R: varIdent (form = ~1|N × M) |
YES R: corAR1 (form = ~1|Rep/Bucket) |
|
Total light attenuation (μmol photon m-2 s-1 rep-1)
|
N × M × Time
Time = Jul. pre-algae (n = 2), Jul. post-algae (n = 3), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) |
Random intercept (Rep) R: 1|Rep |
YES R: varIdent (form = ~1|M) |
YES R: corAR1 (form = ~1|Rep) |
|
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: Time|Rep |
YES R: varIdent (form = ~1|M) |
YES R: corAR1 (form = ~1|Rep) |
|
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: Time|Rep |
NO |
YES R: corAR1 (form = ~1|Rep) |
|
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: Time|Rep |
YES R: varIdent (form = ~1|M) |
YES R: corAR1 (form = ~1|Rep) |
|
pH (rep-1) |
N × M
Time = Jul. (n = 5), Aug. (n = 6), Sep. (n = 1), Oct. (n = 1) |
Random (Rep) R: 1|Rep |
YES R: varIdent (form = ~1|N × M) |
YES R: corAR1 (form = ~1|Rep) |