Ecological Archives E093-150-A3

Salvador Herrando-Pérez, Steven Delean, Barry W. Brook, and Corey J. A. Bradshaw. 2012. Decoupling of component and ensemble density feedbacks in birds and mammals. Ecology 93:1728–1740. http://dx.doi.org/10.1890/11-1415.1

Appendix C. Model metrics correlating strength of component and ensemble density feedbacks across magnitudes of statistical support for ensemble (EREN) and component (ERCF) feedback.

Table C1. Ensemble feedback strength (EN) fitted as a function of sample size in the time series (q, years), body size (BL = body length, mm), and component feedback strength (CF) in birds and mammals. N is the number of demographic rates included in each model contrast, wAICc are model probabilities (shown only top-ranked models in a set*), and DE is % deviance explained (total and broken down by predictors). Model fits were done using all demographic rates, split by fertility or survival rates; and all types of component feedback (ERCF > 1), split by compensatory or depensatory feedbacks. Included demographic rates from populations with strongest AICc evidence ratio for ensemble feedback (EREN > 4).

Rates N Component
feedback type
Top-ranked
models
wAICc DEtotal DEq DEBL DECF
All 137 All EN ~ q + BL 0.70 8.1 2.1 6.0 -
Fertility 68 EN ~ q + BL 0.40 7.1 1.2 5.9 -
Survival 69 EN ~ q + BL + CF 0.69 18.7 2.7 11.0 5.0
All 87 Compensatory EN ~ 1 0.36 0.0 - - -
Fertility 38 EN ~ 1 0.45 0.0 - - -
Survival 49 EN ~ q + BL + CF 0.59 17.3 1.4 6.1 9.8
All 50 Depensatory EN ~ q + BL 0.69 17.5 3.7 13.7 -
Fertility 30 EN ~ 1 0.56 - - - -
Survival 20 EN ~ q + BL 0.46 34.0 7.1 26.9 -

Note: See Table 3 in the main text for when EREN > 1 and ERCF > 1, and Table C2 for when EREN > 4 and ERCF > 4
* Response: EN = Strength of (Gompertz-logistic) ensemble density feedback (square root-transformed)
Predictors: q = number of annual time steps in the paired time series of abundance and demographic rates;
BL = Body length for each species from tip of nose/beak to end of tail;
CF = Strength of linear component feedback.
All predictors were log-transformed.
Model set: EN ~ 1; EN ~ q; EN ~ q + BL; EN ~ q + BL + CF

 

Table C2. Ensemble feedback strength (EN) fitted as a function of sample size in the time series (q in years), body size (BL = body length in mm), and component feedback strength (CF) in birds and mammals. N is the number of demographic rates included in the contrast of each model set, wAICc are model probabilities (shown only top-ranked models in a set*), and DE is % deviance explained (total and broken down by predictors). Model fits were done using all demographic rates having strong support for component feedback (ERCF > 4), split by fertility or survival rates; and all types of component feedback, split compensatory or depensatory feedbacks. Included demographic rates from populations with strongest AICc evidence ratio for ensemble feedback (EREN > 4).

Rates N Component
feedback type
Top-ranked
models
wAICc DEtotal DEq DEBL DECF
All 57 All EN ~ 1 0.57 0.0 - - -
Fertility 31 EN ~ 1 0.45 0.0 - - -
Survival 26 EN ~ 1 0.51 0.0 - - -
All 38 Compensatory EN ~ 1 0.69 0.0 - - -
Fertility 17 EN ~ 1 0.62 0.0 - - -
Survival 21 EN ~ 1 0.51 0.0 - - -
All 19 Depensatory EN ~ q + BL 0.58 37.1 15.6 21.5 -
Fertility 14 EN ~ q 0.51 32.8 32.8 - -
Survival 5 EN ~ q + BL + CF 1.00 74.3 11.0 58.9 4.4

Note: See Table 3 in the main text for when EREN > 1 and ERCF > 1, and Table C1 for when EREN > 4 and ERCF > 1
* Response: EN = Strength of (Gompertz-logistic) ensemble density feedback (square root-transformed)
Predictors: q = number of annual time steps in the paired time series of abundance and demographic rates;
BL = Body length for each species from tip of nose/beak to end of tail;
CF = Strength of linear component feedback.
All predictors are log-transformed.
Model set: EN ~ 1; EN ~ q; EN ~ q + BL; EN ~ q + BL + CF


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