Beech tree masting explains the inter-annual variation in the fall and spring peaks of Ixodes ricinus ticks with different time lags

Table 5 Model selection results are shown for the generalized additive model (GAM) with negative binomial errors of the density of I. ricinus nymphs (DON) at the four elevation sites on Chaumont Mountain over 14 years (2004 to 2017)

Rank	Model structure	df	logLik	AICc	ΔAICc	Weight1 (%)	Weight2 (%)	r² (%)
1	S + P + B_2.1 + Y + S:Y + P:B_2.1	40	−2197.872	4483.411	0.000	25.63	25.63	68.78
2	S + P + B_2.1 + Y + S:Y	39	−2199.014	4483.632	0.221	22.95	48.58	68.52
3	S + P + B_2.1 + Y + S:Y + S:B_2.1	42	−2195.501	4483.645	0.234	22.80	71.39	68.53
4	S + P + B_2.1 + Y + S:B_2.1 + P:B_2.1 + S:Y	43	−2194.543	4483.844	0.433	20.64	92.03	68.93
5	S + P + B_2.1 + Y + S:P + P:B_2.1 + S:Y	43	−2196.813	4488.264	4.853	2.26	94.29	68.64
6	S + P + B_2.1 + Y + S:P + S:B_2.1 + S:Y	45	−2194.473	4488.622	5.211	1.89	96.19	68.39
7	S + P + B_2.1 + Y + S:Y + S:P	42	−2198.053	4488.631	5.220	1.88	98.07	68.39
8	S + P + B_2.1 + Y + S:P + S:B_2.1 + P:B_2.1 + S:Y	46	−2193.434	4488.697	5.286	1.82	99.89	68.78
9	S × P × B_2.1 + Y + S:Y	49	−2192.736	4494.377	10.966	0.11	100.00	68.53
10	S + P + B_1.1 + Y + S:Y + P:B_1.1	39	−2221.763	4529.831	46.419	0.00	100.00	63.90
11	S + P + B_1.1 + Y + S:B_1.1 + P:B_1.1 + S:Y	42	−2220.213	4533.738	50.327	0.00	100.00	63.97
12	S + P + B_1.1 + Y + S:P + P:B_1.1 + S:Y	42	−2220.971	4535.077	51.666	0.00	100.00	63.71

The explanatory variables were elevation site (S), nymphal peak (P), beech masting index (B), and year (Y). There are three different beech masting indices, B_2.2, B_1.1, and B_2.1, which reflect the different time lags for the spring peak and fall peak. Interactions are indicated with a full colon; for example, the interaction between site and year is represented with ‘S:Y’. To model the bimodal phenology of the DON, a site-specific smoother function was applied to the calendar day, s(day, by = S); this site-specific smoother function is common to all the models and is therefore not shown in the model structure. The models are ranked according to their corrected Akaike information criterion (AICc). Shown for each model are the model rank (Rank), model structure, model degrees of freedom (df), log-likelihood (logLik), AICc, difference in the AICc value from the top model (ΔAICc), model weight (Weight1), cumulative model weight (Weight2), and adjusted r-squared value (r²)

ISSN: 1756-3305