Comparing six mathematical link function models of the antifeedant activity of lesser grain borer exposed to sub-lethal concentrations of some extracts from calotropis procera

Figures & data

Table 1. Feeding deterrence index (FDI) of R. dominica exposed to C. procera extracts-treated food at sub-lethal concentrations, t = 3 days.

Concentrations (mg/mL)	0.313	0.625	1.250	2.500	3.750	5.000
Latex protein	0.102	0.305	0.561	0.859	0.930	1.000
Crude flavonoids	0.086	0.204	0.390	0.592	0.726	0.862
Quercetin-3-O-rutinoside	0.050	0.091	0.185	0.322	0.420	0.533
Kaempferol-3-O-rutinoside	0.000	0.088	0.185	0.284	0.405	0.491
Isorhamnetin-3-O-rutinoside	0.000	0.035	0.097	0.215	0.331	0.429

Table 2. (a): Observed and predicted FDI against extracts concentrations using Probit, Logit, Log-log, Clog-log, Cauchy, Fractional, and Optimal models, t = 3 days. (b): Observed and predicted FDI against extracts concentrations using Probit, Logit, Log-log, Clog-log, Fractional, Cauchy and Optimal models, t = 3 days.

Extractions	Concentrations	0.313	0.625	1.250	2.500	3.750	5.000
(a)
Latex protein	Observed	0.102	0.305	0.561	0.859	0.930	1.000
	Probit	0.100	0.301	0.594	0.841	0.925	0.961
	Logit	0.103	0.293	0.598	0.843	0.919	0.951
	Log-log	0.074	0.343	0.644	0.835	0.898	0.929
	Clog-log	0.116	0.265	0.539	0.855	0.963	0.992
	Cauchy	0.114	0.234	0.638	0.854	0.896	0.914
	Fractional	0.136	0.295	0.498	0.762	0.958	1.000
	Optimal	0.102	0.301	0.567	0.855	0.925	1.000
Crude flavonoids	Observed	0.086	0.204	0.390	0.592	0.726	0.862
	Probit	0.079	0.203	0.403	0.632	0.752	0.822
	Logit	0.083	0.196	0.395	0.637	0.757	0.825
	Log-log	0.053	0.216	0.450	0.660	0.753	0.806
	Clog-log	0.095	0.189	0.356	0.602	0.759	0.855
	Cauchy	0.098	0.154	0.314	0.668	0.793	0.841
	Fractional	0.089	0.211	0.368	0.579	0.740	0.878
	Optimal	0.086	0.203	0.395	0.591	0.740	0.867
Quercetin-3-O-rutinoside with Log transformation	Observed	0.050	0.091	0.185	0.322	0.420	0.533
	Probit	0.043	0.099	0.196	0.335	0.430	0.501
	Logit	0.047	0.096	0.186	0.328	0.433	0.512
	Log-log	0.036	0.103	0.213	0.348	0.430	0.487
	Clog-log	0.050	0.095	0.177	0.318	0.433	0.528
	Cauchy	0.058	0.079	0.125	0.269	0.501	0.680
	Fractional	0.039	0.105	0.194	0.320	0.421	0.512
	Optimal	0.050	0.095	0.186	0.320	0.421	0.528
Quercetin-3-O-rutinoside without Log transformation	Observed	0.050	0.091	0.185	0.322	0.420	0.533
	Probit	0.079	0.096	0.138	0.257	0.414	0.587
	Logit	0.079	0.094	0.132	0.246	0.412	0.601
	Log-log	0.075	0.096	0.147	0.276	0.421	0.560
	Clog-log	0.080	0.094	0.129	0.235	0.406	0.636
	Cauchy	0.076	0.083	0.100	0.168	0.393	0.753
	Fractional	0.084	0.102	0.143	0.248	0.401	0.648
	Optimal	0.075	0.089	0.147	0.276	0.421	0.560
(b)
Kaempferol-3-O-rutinoside	Observed	0.000	0.088	0.185	0.284	0.405	0.491
	Probit	0.034	0.083	0.174	0.310	0.406	0.479
	Logit	0.044	0.088	0.171	0.305	0.406	0.483
	Log-log	0.020	0.075	0.180	0.320	0.409	0.470
	Clog -log	0.051	0.094	0.170	0.298	0.402	0.489
	Cauchy	0.087	0.114	0.163	0.269	0.388	0.502
	Fractional	0.011	0.075	0.163	0.295	0.408	0.514
	Optimal	0.011	0.088	0.180	0.282	0.406	0.489
Isorhamnetin-3-O-rutinoside with Log transformation	Observed	0.000	0.035	0.097	0.215	0.331	0.429
	Probit	0.007	0.030	0.094	0.225	0.336	0.424
	Logit	0.014	0.037	0.093	0.217	0.331	0.428
	Log-log	0.002	0.021	0.094	0.238	0.341	0.417
	Clog -log	0.017	0.041	0.094	0.211	0.326	0.432
	Cauchy	0.044	0.058	0.085	0.154	0.270	0.450
	Fractional	0.000	0.041	0.110	0.218	0.316	0.413
	Optimal	0.000	0.034	0.094	0.214	0.331	0.428
Isorhamnetin-3-O-rutinoside without Log transformation	Observed	0.000	0.035	0.097	0.215	0.331	0.429
	Probit	0.052	0.064	0.094	0.181	0.308	0.464
	Logit	0.057	0.067	0.094	0.175	0.303	0.472
	Log-log	0.043	0.057	0.092	0.191	0.317	0.450
	Clog -log	0.061	0.071	0.096	0.172	0.298	0.484
	Cauchy	0.065	0.070	0.083	0.127	0.252	0.622
	Fractional	0.063	0.076	0.105	0.181	0.296	0.487
	Optimal	0.043	0.057	0.096	0.191	0.317	0.450

Table 3. ε and $L_2$ for all used extracts with Probit, Logit, Log-log, Clog-log, Cauchy and fractional models.

Extract	Model	Probit	Logit	Cauchy	Clog-log	Log-log	Fractional	Optimal
Latex protein	ε	0.0440	0.0580	0.1354	0.0967	0.0045	0.0001	-
	$L_2$	0.0005	0.0007	0.0053	0.0040	0.0011	0.0101	0.0000
Crude flavonoids	ε	-	-	-	-	-	-	-
	$L_2$	0.0023	0.0025	0.0106	0.0074	0.0015	0.0006	0.0001
Quercetin with Log transformation	ε	-	-	-	-	-	-	-
	$L_2$	0.0025	0.0011	0.0571	0.0066	0.0005	0.0014	0.0001
Quercetin without Log transformation	ε	-	-	-	-	-	-	-
	$L_2$	0.0166	0.0230	0.1328	0.0091	0.0369	0.0364	0.0091
Kaempferol-3-O-rutinoside	ε	0.0320	0.0428	0.0995	0.0178	0.0514	0.0001	-
	$L_2$	0.0018	0.0003	0.0036	0.0037	0.0009	0.0028	0.0003
Isorhamnetin with Log transformation	ε	0.0064	0.0143	0.0656	0.0009	0.0190	0.0001	-
	$L_2$	0.0005	0.0001	0.0253	0.0028	0.0003	0.0022	0.0000
Isorhamnetin without Log transformation	ε	0.0730	0.0858	0.0545	0.0545	0.0991	0.1011	-
	$L_2$	0.0116	0.0170	0.1679	0.0053	0.0241	0.0249	0.0043
The sum of $L_2$		0.0358	0.0447	0.4026	0.0389	0.0653	0.0784	0.0139
The order of models		Second	Fourth	Seventh	Third	Fifth	Sixth	First

Table 4. The parameters a, b for Probit, Logit, Log-log, Clog-log, Cauchy and fractional models.

Extract	Parameters	Probit	Logit	Log-log	Clog-log	Cauchy	Fractional
Latex protein	a	0.3061	−7.9182	−4.9567	−6.2157	−9.7138	−0.3984
	b	2.5234	4.2561	2.9569	3.0481	5.2076	0.3848
Crude flavonoids	a	0.9580	−6.8345	−4.0127	−5.6315	−8.7543	−0.3173
	b	1.9423	3.2789	2.1689	2.4608	4.1408	0.2944
Quercetin with Log transformation	a	1.3589	−6.4324	−2.9222	−6.0069	−12.274	−0.1789
	b	1.4250	2.5346	1.2717	2.2379	5.0502	0.1594
Quercetin without Log transformation	a	3.4770	−2.6445	−1.0496	−2.6448	−4.4544	0.0577
	b	0.0048	0.0085	0.0044	0.0074	0.0152	0.0005
Kaempferol-3-O-rutinoside	a	1.1801	−6.4819	−3.2103	−5.8361	−7.5916	−0.2187
	b	1.4737	2.5090	1.3660	2.1272	2.9719	0.1698
Isorhamnetin with Log transformation	a	0.0296	−8.7116	−4.0866	−7.9584	−14.941	−0.1978
	b	1.8697	3.2945	1.6511	2.8903	5.7822	0.1412
Isorhamnetin without Log transformation	a	3.2718	−2.9883	−1.2359	−2.9202	−5.1599	0.0432
	b	0.0045	0.0080	0.0041	0.0070	0.0155	0.0004

Table 5. Concentrations corresponding to 25%, 50% and 75% FDI using Probit, Logit, Log-log, Clog-log, and Cauchy models.

Extract	Percent	Probit	Logit	Log-log	Clog-log	Cauchy
Latex protein	25%	0.5439	0.5559	0.5111	0.5931	0.6546
	50%	1.0064	1.0072	0.8769	1.1525	1.0185
	75%	1.8624	1.8250	1.7392	1.9456	1.5849
Crude flavonoids	25%	0.7524	0.7798	0.6954	0.8411	1.0359
	50%	1.6739	1.6868	1.4515	1.9151	1.8064
	75%	3.7237	3.6484	3.6920	3.6632	3.1500
Quercetin-3-O-rutinoside	25%	1.6770	1.7663	1.5264	1.8626	2.3720
	50%	4.9872	4.7918	5.3546	4.6034	3.7422
	75%	14.831	12.999	26.317	9.3931	5.9038
Kaempferol-3-O-rutinoside	25%	1.8924	1.9419	1.7938	1.9977	2.2943
	50%	5.4285	5.3222	5.7708	5.1754	4.9789
	75%	15.572	14.586	25.412	10.960	10.805
Isorhamnetin-3-O-rutinoside	25%	2.7565	2.8410	2.6294	2.9183	3.5783
	50%	6.3258	6.1227	6.9128	5.8801	5.3287
	75%	14.517	13.195	23.564	10.214	7.9353

Figure 1. Observed FDI for various concentrations of all extracts.

Figure 2. Observed and predicted FDI for various concentrations of Latex protein using Probit, Logit and Cauchy models.

Figure 3. Observed and predicted FDI for various concentrations of Crude flavonoids using Probit, Clog-log Cauchy and Fractional models.

Figure 4. Observed and predicted FDI for various concentrations of Quercetin-3-O-rutinoside using Probit, Clog-log, Cauchy and Fractional models.

Figure 5. Observed and predicted FDI for various concentrations of Kaempferol-3-O-rutinoside using Probit, Clog-log and Cauchy models.

Figure 6. Observed and predicted FDI for various concentrations of Isorhamnetin-3-O-rutinoside using Probit, Logit and Cauchy models.

Figure 7. Observed FDI, predicted FDI for minimum $L_2$ and predicted FDI with $\epsilon =0.0001$, $\epsilon =0.01$ for various concentrations of Latex protein using Probit models.

Figure 8. Observed FDI, predicted FDI for minimum $L_2$and predicted FDI with $\epsilon =0.0001$ and $\epsilon =0.01$ for various concentrations of Kaempferol-3-O-rutinoside using Logit models.

Figure 9. Observed FDI, predicted FDI for minimum $L_2$and predicted FDI with $\epsilon$ =0.0001 and $\epsilon =0.01$ for various concentrations of Isorhamnetin-3-O-rutinoside using Clog-log models.

Figure 10. $L_2$ against ε for Latex protein, Kaempferol-3-O-rutinoside and Isorhamnetin-3-O-rutinoside using Probit models.

Figure 11. Observed and predicted latex protein concentrations corresponding to FDI using Probit, Logit and Cauchy models.

Figure 12. Observed and predicted isorhamnetin-3-O-rutinoside concentrations corresponding to FDI using Probit, Logit and Cauchy models.

Figure 13. Observed and predicted FDI for various concentrations of latex protein using Logit, Log-log, and Clog-log models.