Overwintering aggregation patterns of European catfish Silurus glanis

Table 2 Results of the Cox model corresponding to the event “Leaving the aggregation”

	Log-likelihood	Chi2	df	p value
a
NULL	− 139,012
Temperature	− 137,329	3365.39	1	< 0.001
Fish size	− 137,322	14.64	2	< 0.001
Time of day	− 136,845	954.25	3	< 0.001
b
Model without random effects: Log-likelihood = − 137,257; Concordance = 0.641; Wald statistic = 3421 (df = 6, p < 0.001) Comparison between model with and without random effects (deviance analysis): Chi2 = 825.04 df = 1 p < 0.001

	Coef	Exp(coef)	z	p
c
Temperature	0.21	1.23 [1.22; 1.24]	46.70	< 0.001
Large/small	0.37	1.44 [1.11; 1.87]	2.77	0.006
Large/medium	0.44	1.55 [1.26; 1.90]	4.14	< 0.001
Dusk/day	0.68	1.98 [1.88; 2.10]	25.07	< 0.001
Night/dusk	− 0.21	0.81 [0.78; 0.85]	− 9.28	< 0.001
Dawn/night	− 0.45	0.64 [0.61; 0.68]	− 16.24	< 0.001

Contrast	Ratio	df	z ratio	p
d
Small/medium	1.07	Inf	0.61	0.817
Small/large	0.69	Inf	− 2.77	0.016
Medium/large	0.65	Inf	− 4.14	< 0.001
Dawn/day	1.03	Inf	0.89	0.811
Dawn/dusk	0.52	Inf	− 20.35	< 0.001
Dawn/night	0.64	Inf	− 16.24	< 0.001
Day/dusk	0.50	Inf	− 25.07	< 0.001
Day/night	1.23	Inf	− 21.81	< 0.001
Dusk/night	1.23	Inf	9.28	< 0.001

The model equation is the following: Survival(Start, Stop, “Leaving the aggregation”) ~ TEMPERATURE + FISH SIZE + TIME OF DAY + (1|Fish identity). Part a gives the statistics and associated p value of each covariate. Part b compares this model with the same model without random effects and gives the goodness-of-fit of this latter model which is not accessible for the mixed model; the Wald test tests the null hypothesis that the coefficients of the covariates are null; the Concordance should be greater than 0.5 for the model to be informative. Part c shows the covariate coefficients of the mixed Cox model; the exponentiated coefficients are multiplicative effects on the hazard: for continuous covariates, as Temperature, exp(coef) = 1.23 means that when temperature rises by 1 °C, the probability to leave the aggregation increases by 23%. For categorical covariates, for example the coefficient of large fish in reference to small fish, exp(coef) = 1.44 means that the probability for large fish to leave the aggregation is 44% higher than that of small fish. Coefficients are shown only for significant contrasts in part d and, for time of day, only between consecutive classes in the diel cycle (Day/Dawn, Dusk/Day, Night/Dusk and Dawn/Night)

ISSN: 2051-3933