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Table 2 Summary of the results for the exponential decay regression, generalized additive model (GAM), and segmented and linear regression models, ordered according to their second-order Akaike information criterion (AICc) score and the absolute value of ΔAICc

From: Aedes albopictus abundance and phenology along an altitudinal gradient in Lazio region (central Italy)

Model

Formula

df (edf)

AICc

|ΔAICc|

Estimated intercept (± SE)

Intercept P-value

Adj. R2

Exponential decay

Altitude ~ 1015.00 × e(−0.003 × MEggs)

42

583.48

0

1015.00 (± 52.27)

< 2e−16

NA

GAM

Altitude ~ s(MEggs, k = 4, sp = 0.1)

2.22·

587.16

3.68

987.65 (± 26.86)

< 2e−16

0.72

Segmented regression

segmented.lm[lm, seg.Z = ~ MEggs, control = seg.control (n.boot = 10)]

40

588.26

4.78

1010.13 (± 55.36)

< 2e−16

0.72

Linear model (lm)

Altitude ~ − 1.46 × MEggs + 904.29

42

593.75

10.27

904.29 (± 46.33)

< 2e−16

0.66

  1. The predicted values of altitude where the weekly maximum number of eggs laid (MEggs) by Aedes albopictus dropped to zero are reported as an estimated intercept. The GAM function was set with four basis functions (k = 4); the smooth function (s) was used to imply a flexible relation between Altitude and MEggs and the smoothing parameter (sp) was set to 0.1. The results of the gam.check function indicated that the number of basis functions was appropriate since P-value of GAM was 0.36 and k-index was close to 1 (0.97), with k’ = 3 [46]. The effective df (edf) of the GAM model indicated that the relation between Altitude and MEggs was similar to a quadratic curve (namely where edf = 2). The Estimated break-point (± SE) from segmented regression was 206 (± 56.29) and the slopes (± SE) of the two resulting linear regressions were − 2.66 (± 0.57) and − 0.76 (± 0.29)
  2. e Euler's number (~ 2.71828); seg.Z the continuous covariate (MEggs in this formula), which is understood to have a piecewise-linear relationship with response (Altitude); n.boot number of bootstrap samples used in the bootstrap restarting algorithm; Adj. adjusted