Table 2.

Multi-model selection approach: models, formulas and parameters, responses, and expectations

Model	Equations and parameters	Responses	Expectations
1	$\frac{M\#}{1+e^a}$	Uniform	Null hypothesis
2	$\frac{M}{1+e^{a+b-x}}$	Linear	Abundance or infection correlates linearly with forest cover values
3	$\frac{M}{\left(1,+,e^{a+b\ast x}\right)\ast (1+e^c)}$	Linear with Plateau
4	$\frac{M}{\left(1,+,e^{a+b-x}\right)\ast (1+e^{c-b-x})}$	Unimodal	Abundance or infection has a unimodal correlation with forest cover values
5	$\frac{M}{\left(1,+,e^{a+b\ast x}\right)\ast (1+e^{c-d\ast x})}$	Asymmetric Unimodal
6	$\frac{M}{\left(1,+,e^{a+b\ast x}\right)\ast (1+e^{c-b\ast x})}+\frac{M}{\left(1,+,e^{a+b\ast (x-d)}\right)\ast (1+e^{c-d\ast (x-d)})}$	Bimodal	Abundance or infection has a bimodal correlation with forest cover values
7	$\frac{M}{\left(1,+,e^{a+b\ast x}\right)\ast (1+e^{c-b\ast x})}+\frac{M}{\left(1,+,e^{a+b\ast (x-d)}\right)\ast (1+e^{c-f\ast (x-d)})}$	Asymmetric Bimodal

Models were assumed having Poisson errors–Poisson regressions were worked out

^#M is the maximum abundance or infection value which is within the positive integer set (1, 2, 3,…, n) for Poisson data. Model variables a–d and f are optimized in the process of model fitting [46]