Correction: Jafari et al. Modeling Thermal Developmental Trajectories and Thermal Requirements of the Ladybird Stethorus gilvifrons. Insects 2023, 14, 11

Maryam Jafari; Shila Goldasteh; Hossein Ranjbar Aghdam; Abbas Ali Zamani; Ebrahim Soleyman-Nejadian; Peter Schausberger

doi:10.3390/insects14070581

,

and

¹

Department of Entomology, College of Agriculture, Arak Branch, Islamic Azad University, Arak 6134937333, Iran

²

Iranian Research Institute of Plant Protection, Agricultural Research, Education and Extension Organization, Tehran 1475744741, Iran

³

Department of Plant Protection, College of Agriculture, Razi University, Kermanshah 6718773654, Iran

⁴

Department of Behavioral and Cognitive Biology, University of Vienna, 1030 Vienna, Austria

Insects2023, 14(7), 581;https://doi.org/10.3390/insects14070581

This article belongs to the Section Insect Physiology, Reproduction and Development

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Errors in Tables

Following the publication of [1], we detected some errors in Tables 1, 4 and 5. Table 1 reported an incorrect formula for the third-order polynomial model; Tables 4 and 5 contained a few incorrect numerical values. The corrected Table 1, Table 4 and Table 5 are given below; the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Table 1. Linear and non-linear models used to simulate the developmental rates of S. gilvifrons at various constant temperatures.

Table 4. Parameter estimates for the twenty non-linear, temperature-dependent models used for describing immature development of S. gilvifrons.

Table 5. Goodness-of-fit measures for the twenty non-linear, temperature-dependent models used for describing immature development of S. gilvifrons.

Reference

Jafari, M.; Goldasteh, S.; Aghdam, H.R.; Zamani, A.A.; Soleyman-Nejadian, E.; Schausberger, P. Modeling thermal developmental trajectories and thermal requirements of the ladybird Stethorus gilvifrons. Insects 2023, 14, 11. [Google Scholar] [CrossRef] [PubMed]

Table 1. Linear and non-linear models used to simulate the developmental rates of S. gilvifrons at various constant temperatures.

Equation	Model	References
$D (T) = a + b T$ $T_{0} = - \frac{a}{b} K = \frac{1}{b}$	Ordinary linear regression	[35]
$D T = K + t_{m i n} D$	Ikemoto & Takai	[39]
$R (T) = \frac{c}{1 + e^{(a + b . T)}}$	Sigmoid	[40]
$R (T) = Ψ \times [e^{ρ \times T} - e^{(ρ \times T_{m a x} - \frac{T_{m a x} - T}{Δ T})}]$	Logan-6	[41]
$R (T) = a \times [\frac{1}{1 + K \times e^{- ρ \times T}} - e^{(\frac{T_{m a x} - T}{Δ T})}]$	Logan-10	[41]
$R (T) = e^{ρ \times T} - e^{(ρ \times T_{m a x} - (\frac{T_{m a x} - T}{Δ T}))}$	Lactin-1	[42]
$R (T) = e^{ρ \times T} - e^{(ρ \times T_{m a x} - (\frac{T_{m a x} - T}{Δ T})) + λ}$	Lactin-2	[42]
$R (T) = a \times T (T - T_{0}) \times \sqrt{T_{m a x} - T}$	Briere-1	[43]
$R (T) = a \times T (T - T_{0}) \times \sqrt[m]{T_{m a x} - T}$	Briere-2	[43]
$R (T) = a {(T - T_{a})}^{n} \times {(T_{m a x} - T)}^{m}$	Analytis	[44,45]
$R (T) = a x^{3} + b x^{2} + c x + d$	Polynomial 3rd order	[46]
$R (T) = a {(T - T_{a})}^{2} (T_{m a x} - T)$	Kontodimas-16	[37]
$D (T) = \frac{2}{D_{m i n} (e^{k (T - T_{o p t})} + e^{- λ (T - T_{o p t})})}$	Janisch	[47]
$D (T) = R_{m}^{e (- a s \times {(\frac{T - T_{m}}{T_{a}})}^{a})}$	Taylor	[48]
$R (T) = \frac{c}{1 + e^{a + b \times T}} f o r T \leq T_{o p t}$ $R (T) = \frac{c}{1 + e^{a_{1} + b_{1} (2 \times T_{o p t} - T)}} f o r T > T_{o p t}$	Stinner	[49]
$R (T) = Ψ [\frac{(T - T_{0})^{2}}{{(T - T_{0})}^{2} + D^{2}} - e^{(- \frac{T_{m a x - (T - T_{0})}}{Δ})}]$	Hilbert & Logan, or Holling III	[50,51]
$R (T) = R_{m} \times e x p [- 0.05 {(\frac{T - T_{o p t}}{T_{0}})}^{2}] f o r T \leq T_{o p t}$ $R (T) = R_{m} \times e x p [- 0.05 {(\frac{T - T_{o p t}}{T_{m a x}})}^{2}] f o r T > T_{o p t}$	Lamb	[52]
$\frac{1}{D} = a {(T - t_{m i n})}^{2} (t_{m a x} - T)$	Equation-16	[37]
$\frac{1}{D} = (a + b \times T) \times [e (- (c + d \times T))]$	Enkegaard	[53]
$\frac{1}{D} = [a (T - x_{m a x})] - [b^{(T - x_{m i n})}]$	Bieri-1	[54]
$\frac{1}{D} = a (\frac{(T - x_{m i n})}{b^{(T - x_{m i n})}})$	Bieri-2	[54]
$R (T) = \frac{φ \frac{T}{T_{1}} e x p [\frac{Δ H_{A}}{R} (\frac{1}{T_{1}} - \frac{1}{T})]}{1 + e x p [\frac{Δ H_{L}}{R} (\frac{1}{T_{L}} - \frac{1}{T})] + e x p [\frac{Δ H_{H}}{R} (\frac{1}{T_{H}} - \frac{1}{T})]}$	Sharpe & DeMichele	[55]

Table 4. Parameter estimates for the twenty non-linear, temperature-dependent models used for describing immature development of S. gilvifrons.

Model	Parameters	Egg	Larva	Pupa	Total Development
Briere-1	a	30.51 × 10⁻⁵	17.50 × 10⁻⁵	35.61 × 10⁻⁵	7.86 × 10⁻⁵
	t_min	13.48	14.38	13.64	13.00
	t_opt	29.75	29.75	29.75	29.75
	t_max	35.00	35.00	35.00	35.00
Briere-2	a	3.55 × 10⁻⁴	1.67 × 10⁻⁶	1.82 × 10⁻⁴	6.30 × 10⁻⁹
	m	3.09	0.64	1.68	0.358
	t_min	11.17	12.20	11.24	11.96
	t_opt	31.00	35.75	31.50	32.00
	t_max	34.93	57.80	38.80	67.48
Logan-6	$φ$	−0.047	1.066	−0.045	0.570
	$ρ$	0.185	0.166	0.167	0.151
	$Δ$	6.83	5.59	6.09	6.41
	t_opt	30.75	32.50	31.75	31.75
	t_max	36.22	38.68	37.55	38.21
Logan-10	$α$	0.466	0.517	0.419	0.105
	$ρ$	0.236	0.176	0.315	0.291
	$Δ$	3.71	7.60	4.67	6.49
	k	249.56	138.09	847.63	586.62
	T_L	38.66	44.05	44.05	44.04
	t_opt	33.75	34.25	31.00	32.75
	t_max	38.43	44.03	36.97	44.03
Lactin-1	$Δ$	5.4453	6.1696	6.0314	6.5082
	$ρ$	0.1834	0.1619	0.1654	0.1535
	t_opt	31.00	33.00	31.09	32.00
	t_max	36.3378	38.7646	37.5502	38.2170
Lactin-2	$Δ$	2.70	9.87	5.01	26.62
	$ρ$	0.01	0.011	0.018	0.017
	e	1.21	1.13	1.24	0.86
	T_L	39.87	59.56	44.67	70.78
	t_min	12.50	12.48	12.09	13.04
	t_opt	30.75	34.00	31.50	32.25
	t_max	36.50	47.27	36.62	46.73
Sigmoid	a	7.6721	5.8402	6.5996	6.2261
	b	−0.3775	−0.2714	−0.3224	−0.3167
	c	0.3105	0.1824	0.3772	0.0842
Hilbert & Logan, or Holling III	$φ$	0.8069	1.1954	2.6544	1.4284
	T₀	5.1643	−0.0286	2.2864	−5.4646
	d	2.6455	34.8905	10.2500	62.5963
	T_L	33.6489	71.6097	46.7278	75.7471
	$Δ$	17.1084	20.7993	20.0060	19.6420
	t_min	6.18	7.3623	11.2824	12.4085
	t_opt	31.00	36.11	31.18	33.00
	t_max	38.21	67.99	45.91	66.11
Stinner (T > T_opt)	a	−2.9618	−1.7579	−2.4292	−2.6428
	b	0.1898	0.1355	0.1612	0.1583
	c	0.3102	0.1824	0.3772	0.0842
	t_opt	-	-	-	-
Polynomial 3rd order	a	1.5108	0.0316	0.9548	0.8113
	b	−0.2282	−0.0137	−0.1512	−0.1118
	c	0.0112	0.0011	0.0079	5.02 × 10⁻³
	d	−1.65 × 10⁻⁴	−1.90 × 10⁻⁵	−1.18 × 10⁻⁴	−6.97 × 10⁻⁵
	t_opt	30.00	34.25	31.42	32.50
	t_max	38.00	47.47	40.57	37.69
Equation-16	a	8.9669 × 10⁻⁵	2.2398 × 10⁻⁵	6.9155 × 10⁻⁵	1.2974 × 10⁻⁵
	t_min	10.7196	8.7399	9.2019	8.0642
	t_opt	30.00	34.00	31.40	32.00
	t_max	39.6390	46.5227	42.4350	43.4616
Kontodimas-16	a	8.9669 × 10⁻⁵	2.2398 × 10⁻⁵	6.9155 × 10 ⁻⁵	1.2973 × 10⁻⁵
	t_min	10.7196	8.7399	9.2019	8.0643
	t_opt	30.00	34.01	31.19	31.90
	t_max	39.6390	46.5227	42.3350	43.4615
Lamb (T > T_opt)	R_m	0.3245	0.1780	0.3782	0.0852
	t_m (=t_opt)	29.6197	33.1083	30.8630	31.2873
	T₀	7.4244	9.7908	8.6507	9.5089
Analytis	a	1.3038 × 10⁻¹⁵	1.1464 × 10⁻¹⁵	1.3474 × 10⁻¹⁴	2.2536 × 10⁻¹⁷
	n	7.6175	6.1802	5.3244	5.8251
	m	2.1428	2.5713	3.9925	4.7378
	t_min	−9.4633	−17.2948	−0.3747	−1.9163
	t_opt	30.10	37.40	31.02	31.00
	t_max	41.1822	60.0903	54.5616	57.4548
Enkegaard	a	0.0248	0.0178	0.0407	0.0122
	b	−68.3956 × 10⁻⁵	−46.1022 × 10⁻⁵	−10.8593 × 10⁻⁴	−31.9438 × 10⁻⁵
	c	1.1245	1.1075	1.1075	1.1075
	d	−0.1835	−0.1620	−0.1656	−0.1535
	t_opt	31.11	33.00	31.90	32.01
	t_max	36.66	38.76	37.55	38.21
Taylor	R_m	0.3245	0.1780	0.3782	0.0852
	t_m (=t_opt)	29.6197	33.1083	30.8630	31.2874
	$T_{σ}$	7.4244	9.7909	8.6509	9.5093
Janisch	D_min	3.0985	5.6899	3.6422	12.3639
	k	−0.1834	−0.1414	−0.2354	−0.1547
	$λ$	0.1221	−0.0975	−0.0364	−0.0785
	t_opt	28.0868	30.7786	23.6969	27.90
Sharpe & DeMichele	a	5.1991	−10.5143	−5.2836	−8.4871
	b	−322.3149	−1502.5915	−259.0272	−1360.8376
	c	7.9817	−6.6145	−2.8555	−4.5433
	d	−365.7124	−1536.7211	−304.9700	−1403.3453
	f	17.7782	0.1576	3.076	0.1380
	g	−38.2689	−1276.7436	−108.8371	−1252.6541
	t_opt	30.00	32.23	31.00	32.05
Bieri-1	a	0.0209	0.103	0.0249	0.0177
	b	1.5436	1.3103	1.274	1.0288
	x_max	12.5366	12.4235	12.2484	−6.9928
	x_min	37.99	45.5230	40.99	49.43
	t_min	12.69	12.52	12.32	12.96
	t_opt	31.01	33.50	32.00	33.04
	t_max	36.33	41.03	39.38	49.76
Bieri-2	a	−0.1749	−0.0813	−0.1801	−0.0373
	b	0.8323	0.8504	0.8473	0.8575
	x_min	36.33	38.76	37.55	38.21
	t_opt	31.00	33.00	31.53	32.00
	t_max	36.33	38.76	37.55	38.21

Table 5. Goodness-of-fit measures for the twenty non-linear, temperature-dependent models used for describing immature development of S. gilvifrons.

Model	Parameters	Egg	Larva	Pupa	Total Development
Briere-1	R²	0.9177	0.6358	0.8053	0.7871
	R²_adj	0.8628	0.3930	0.6755	0.6451
	AIC	−35.69	−35.49	−28.75	−46.31
	RSS (10⁻⁴)	57.63	83.13	183.13	72.60
Briere-2	R²	0.9773	0.9716	0.9627	0.9923
	R²_adj	0.9432	0.9290	0.9069	0.9807
	AIC	−42.72	−47.75	−38.04	−65.33
	RSS (10⁻⁴)	12.79	5.53	27.90	0.29
Logan-6	R²	0.9634	0.9444	0.9447	0.9493
	R²_adj	0.9085	0.8661	0.8617	0.8732
	AIC	−39.55	−44.16	−35.46	−54.10
	RSS (10⁻⁴)	21.70	10.05	42.90	1.92
Logan-10	R²	0.9903	0.9757	0.9785	0.9956
	R²_adj	0.9515	0.8785	0.8925	0.9780
	AIC	−47.67	−49.33	−41.12	−69.08
	RSS (10⁻⁴)	5.60	4.25	16.69	1.34
Lactin-1	R²	0.9735	0.9696	0.9586	0.9919
	R²_adj	0.9559	0.9494	0.9311	0.9154
	AIC	−43.52	−46.19	−37.45	−56.10
	RSS (10⁻⁴)	15.61	9.99	42.90	1.91
Lactin-2	R²	0.9576	0.9648	0.9587	0.9776
	R²_adj	0.8940	0.9120	0.8967	0.9440
	AIC	−31.02	−47.04	−37.41	−57.99
	RSS (10⁻⁴)	89.97	6.22	30.98	0.61
Sigmoid	R²	0.9362	0.9777	0.9731	0.9969
	R²_adj	0.8936	0.9629	0.9552	0.9948
	AIC	−38.03	−51.85	−41.50	−73.20
	RSS (10⁻⁴)	38.96	3.89	21.85	0.11
Hilbert & Logan, or Holling III	R²	0.9792	0.9737	0.9697	0.9937
	R²_adj	0.8963	0.8685	0.8485	0.9686
	AIC	−41.32	−46.84	−37.22	−64.80
	RSS (10⁻⁴)	11.57	4.61	22.91	0.23
Stinner (T > T_opt)	R²	0.9362	0.9777	0.9731	0.9969
	R²_adj	0.8406	0.9440	0.9329	0.9949
	AIC	−36.03	−49.85	−39.50	−71.20
	RSS (10⁻⁴)	38.96	3.89	21.85	0.11
Polynomial 3rd order	R²	0.9840	0.9714	0.9728	0.9924
	R²_adj	0.9600	0.9285	0.9321	0.9810
	AIC	−43.44	−48.35	−39.94	−65.87
	RSS (10⁻⁴)	11.34	5.01	20.34	0.27
Equation-16	R²	0.9696	0.9712	0.9661	0.9880
	R²_adj	0.9493	0.9521	0.9436	0.9801
	AIC	−43.24	−50.31	−40.54	−65.08
	RSS (10⁻⁴)	0.16	5.03	25.63	0.42
Kontodimas-16	R²	0.9723	0.9712	0.9659	0.9880
	R²_adj	0.9539	0.9521	0.9433	0.9801
	AIC	−43.24	−50.13	−40.54	−65.08
	RSS (10⁻⁴)	16.35	5.03	25.63	0.42
Lamb (T > T_opt)	R²	0.9870	0.9674	0.9735	0.9825
	R²_adj	0.9783	0.9456	0.9559	0.9708
	AIC	−35.68	−49.51	−42.08	−62.64
	RSS (10⁻⁴)	57.64	5.76	19.85	0.64
Analytis	R²	0.9878	0.9517	0.9718	0.9848
	R²_adj	0.9493	0.7587	0.8592	0.9241
	AIC	−44.37	−42.41	−37.68	−58.50
	RSS (10⁻⁴)	6.95	9.62	21.23	0.55
Enkegaard	R²	0.9735	0.9450	0.9447	0.9492
	R²_adj	0.9339	0.8625	0.8618	0.8732
	AIC	−41.52	−44.19	−35.45	−54.10
	RSS (10⁻⁴)	15.61	9.90	42.90	1.91
Taylor	R²	0.9870	0.9674	0.9735	0.9825
	R²_adj	0.9783	0.9456	0.9559	0.9708
	AIC	−47.52	−49.51	−42.08	−62.64
	RSS (10⁻⁴)	8.02	5.76	19.85	0.64
Janisch	R²	0.9928	0.9595	0.9821	0.9743
	R²_adj	0.9821	0.8988	0.9553	0.9358
	AIC	−49.55	−45.92	−42.25	−58.34
	RSS (10⁻⁴)	4.09	7.49	13.83	0.95
Sharpe & DeMichele	R²	0.9875	0.9668	0.9759	0.9939
	R²_adj	*	*	*	*
	AIC	−42.09	−45.54	−40.50	−63.08
	RSS (10⁻⁴)	7.29	5.82	18.51	0.22
Bieri-1	R²	0.9700	0.9676	0.9565	0.9915
	R²_adj	0.9250	0.9190	0.8913	0.9792
	AIC	−41.04	−47.59	−37.11	−65.24
	RSS (10⁻⁴)	16.90	5.67	32.65	0.29
Bieri-2	R²	0.9735	0.9449	0.9447	0.9492
	R²_adj	0.9559	0.9083	0.9079	0.9154
	AIC	−43.52	−49.59	−39.11	−56.10
	RSS (10⁻⁴)	15.61	9.99	42.90	1.91

* Non-calculable because the number of observations equals the number of model parameters, which results in a denominator of 0 in the equation.

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Correction: Jafari et al. Modeling Thermal Developmental Trajectories and Thermal Requirements of the Ladybird Stethorus gilvifrons. Insects 2023, 14, 11

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