Modeling Linear and Nonlinear Relationship between Temperature and Development Rate of Amblyseuis swirskii (Acari: Phytoseiidae)

doi:10.21203/rs.3.rs-2435207/v1

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Modeling Linear and Nonlinear Relationship between Temperature and Development Rate of Amblyseuis swirskii (Acari: Phytoseiidae)

https://doi.org/10.21203/rs.3.rs-2435207/v1

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In recent years, the utilization of biocontrol agents to administer agriculture pests has received more attention, which has conduce to an growth in companies generating biocontrol agents, including predators and parasitoids. Amblyseius swirskii Athias-Henriot as a part of predatory communities in greenhouses is currently used worldwide as a biocontrol agent against small insects and various mites, especially to suppress the population of the two-spotted spider mite (TSSM), Tetranychus urticae Koch. To improve mass rearing of A. swirskii and optimize its application in integrated pest management programs, its development rate was determined at seven constant temperatures ranging from 15 to 32 (±1)°C, 50±10% RH and a photoperiod of 16:8 (L:D) h under laboratory conditions. To determine the lower temperature threshold (T₀) and thermal constant (K) of different stages of the predator, two linear models (ordinary and Ikemoto) were used. In addition, 26 nonlinear models were fitted to evaluate the development rate at different temperatures. The lower temperature threshold (T₀) and thermal constant (K) of total immature stages were estimated by the ordinary (3.72°C and 133.22 DD) and Ikemoto (10.64°C and 86.51DD) linear models. Based on the Akaike information criterion (AIC), the best model for description of the temperature-dependent development rate of the egg, larval, protonymphal and dutonymphal stages was the Ratkowsky model and for the whole pre-adult stage, it was the Logan-6 model. Our results provided a detailed evaluation of the thermal requirements of A. swirskii, which can be important in improving the role of this mite in biological control programs.

Amblyseius swirskii

biological control

development rate

temperature threshold

linear and nonlinear modeling

Predicting the time of growth, reproduction and dormancy or migration are key factors in pest management programs. One of the most important factors that play a fundamental role in evaluating these factors is adaptation to the climatic changes (Nechols et al. 1999). In the discussion of integrated pest management programs, it is necessary to consider all the basic parameters of the population, such as age structure, development and survival, because the temperature of the surrounding environment is the determining factor in most of the life processes of poikilothermic arthropods (Cloutier et al. 1995; Clarke, 2003; Roy et al. 2002; Trudgill et al. 2005; Bensadia et al. 2006; Anton et al. 2007; Ding et al. 2021). Because temperature acts as a driver of arthropod bioprocesses, the rate of each process changes as temperature changes (Cossins and Bowler, 1987). Implementing a successful biological control program depends on understanding the climatic responses of biological factors, especially temperature. In these programs, the details of such responses are used to select an effective and compatible biological control agent (Rosen and Huffaker, 198; Obrycki and Kring, 1998). In order to know the relationship between temperature and arthropod development, various models have been proposed, which are used to foretell the acting and dynamics of the seasonal population of pests and their natural enemies (Logan et al. 19; Sharpe and De Michele, 1977; Wagner et al. 1984; Lamb, 1992; Lactin et al. 1995; Briere et al. 1999). Since the knowledge of the effects of temperature is an important factor and determines the suitable conditions for mass rearing and the distribution of natural enemies (Ghasemzadeh and Qureshi, 2018), these models can help determine the conditions suitable for mass rearing of natural enemies (Rodriguez-Saona and Miller, 1999). Although linear models using thermal constant (K) or degree-day approach are able to forespeak the development of insects, the use of nonlinear models is needful to assess the optimal temperature and upper thermal threshold. In this regard, it is necessary to use statistical indices to appraise the performance of these models (Mirhosseini et al. 2018).

Spider mites (Acari: Tetranychidae) are a group of pests that cause serious damage to a variegation of agricultural products (Gerlach and Sengonca, 1986; Han et al. 2003; Jung, 2005; Jung et al. 2005). Due to long-term control of these pests is not provided by current acaricides (Roy et al. 1999), effective integrated management emphasizing biological control is needed. In most of the crops, phytoseiid mites are used for the biological control of spider mites (Tanigoshi et al. 1983, Hoy, 1985; McMurtry, 1985; van de Vrie, 1985; Kogan et al. 1999).The generalist predator Amblyseius swirskii Athias-Henriot as a widespread phytoseiid (Type III phytoseiid), is one of the commercialized predatory mites that has frequently been recorded in plants infested by various species of insect (whiteflies and thrips) and spider mites (Nomikou et al. 2003; Rahimi et al. 2022).

Some research works have been carried out to determine biological parameters of A. swirskii (e.g. Yousef et al. 1982; Met wally et al. 1984; Hoda et al. 1987; El-Laithy and Fouly, 1992; Abou-Awad et al. 2014; Nomikou et al. 2001, Rahimi et al. 2022), but they involved a limited range of temperatures. The main aim of this research was to expand knowledge on the thermal requirements and temperature thresholds of A. swirskii. For this purpose, the development rate of all stages of this predatory mite was determined at seven constant temperatures ranging 15–35°C. Using the obtained data, two linear and 26 non-linear thermal models were tested in terms of accuracy in predicting the development rate as well as estimating biological parameters.

Rearing of two-spotted spider mite

The two-spotted spider mite (TSSM), Tetranychus urticae Koch individuals were originally collected from cucumber fields in Sanandaj, western Iran, in 2019. Stock cultures were initially reared on bean plants in a growth chamber at 25 ± 1°C, 75 ± 5% RH, and 16:8 h (L:D) photoperiod. Fifty kidney bean plants (Phaseolus vulgaris L.) were planted in pots contain about 30 kg of a 1:1:1 mixture of soil, sand, and peat and then infested with TSSM.

Phytoseiid rearing

A cohort of the phytoseiid predator A. swirskii used in this study was originated from specimens stocked by Koppert (Swirski-Mite plus®) in 2019. The bean leaf disk (2 × 2 cm) infested with TSSM were placed on a 9 cm diameter Petri dish, then A. swirskii individuals were introduced onto each leaf disk. The circumference of the leaves was covered with cotton to prevent predators from escaping (Walzer and Schausberger, 1999), and the cotton was soaked daily to maintain the moisture inside the Petri dishes. Kidney bean leaves with sufficient mixed stages of TSSM as prey were added to the arena three times a week. To reduce any intrinsic influence and diet effects and keep the potency of the population of the predator mite, the stock cultures were reared for two generations on TSSM as prey. The total development time from egg to emergence of adult mites was determined in an environmental chamber at temperatures 15, 17, 20, 22, 25, 27, 30, and 32°C.

Life history parameters

Data on development times were checked for normality using the Kolmogorov-Smirnov test and were found to be normally distributed. The one-way analysis of variance (ANOVA) was used to determine the statistical differences of development time among temperatures tested. Multiple comparisons among the treatments were made using Tukey's test (α = 0.05). Comparison of development time of the populations was done by the Student’s t-test. Minitab (ver. 19.2) software was used for all analyses. Excel 2016 was used for graph construction.

Model fitting and analysis

The development rate for egg, larval, protonymphal, deutonymphal and total immature stages (egg to adult) was determined by using the reciprocal of the development time. The effect of temperature on the development time was evaluated using the ordinary and Ikemoto linear models. The methods of performing linear fitting in these two methods are slightly different: the ordinary linear model uses ordinary least squares (OLS) approaches and the Ikemoto linear model uses reduced major axis (RMA) approaches for linear fitting (Campbell et al. 1974; Ikemoto and Takai, 2000). In the ordinary linear model, since the development rate, R(T) is dependent on the temperature (T), it is calculated as:

Where T is temperature and R is development rate. The lower temperature threshold (T₀) and thermal constant (K) are calculated as T₀ = -a/b and K = 1/b, respectively (Campbell et al. 1974).

To evaluate the suitability of the nonlinear models, three criteria are used: sum of squared error (SSE), adjusted coefficient of determination (R²_adj) and Akaike information criterion (AIC).

In order to describe the relationship between temperature (T) and development rate (R), the reciprocal of development time (D) of A. swirskii as a function of temperature, the ability of two linear models and 26 non-linear models (Table 1) was evaluated using ArthroThermoModel (ATM) software (Mirhosseini et al. 2017). Since data for temperatures higher than 32° did not fit the linear regression between temperature and development rate, to improve estimation of T₀ by means of the models, they were excluded from the analysis. This omission was necessary to correctly estimate the low temperature threshold (Ikemoto and Takai, 2000). The standard criteria for the best models are higher R²_adj and lower SSE (Walgama and Zalucki, 2006). Since nonlinear models differ in the number of parameters, R² and SSE are not sufficient to discriminate among models with different numbers of parameters. The ranking index of the fitted nonlinear models is the Akaike Information Criterion (AIC) so that statistically, selection of the best-fitted model for describing temperature-dependent development of A. swirskii was made based on the lowest AIC value.

If AIC_min interprets the AIC of the best model, the difference between the best model and the ith model by means of ∆ can be found as (Burnham et al. 2011):

The latest researchers also offered that models with ∆ > 7 should be discarded. Based on this reasoning, the egg models with ranks from 1 to 12, the nymph models with rank of 1–6 and total development models with rank of 1–10 are acceptable (Table 4) (Mirhosseini et al. 2018).

Life table

Development from egg to adult of A. swirskii was successful at all temperatures tested (Table 2). However, at a temperature of 15°C, even though the eggs were hatched, there was no growth beyond this stage, and this temperature was practically eliminated (Table 2). The results of the Tukey's test showed a significant difference during the incubation period between the tested temperatures, which means that the longest period was observed at 15°C (3.84 days) and the lowest at 30°C (1.24 days) (P < 0.05) (Table 1). The longest (9.33 days) and shortest (5.00 days) female pre-adult development times (from egg to adult) were recorded at 17°C and 32°C, respectively. The female development time was greatly influenced by temperature, with the longest female adult development observed at 27°C (32.13 days) and the shortest at 32°C (14.6 days) (P < 0.05).

Table 2

Different developmental stages (day) of *Amblyseius swirskii* reared on *Tetranychus urticae* at eight temperatures.
Parameter	15°C		17°C		20°C		22°C		25°C		27°C		30°C		32°C
	n	Mean ± SE	n	Mean ± SE	n	Mean ± SE	n	Mean ± SE	n	Mean ± SE	n	Mean ± SE	n	Mean ± SE	n	Mean ± SE
Egg	70	3.84 ± 0.19 a	70	2.63 ± 0.06 b	70	2.57 ± 0.06 b	70	2.46 ± 0.06 b	70	1.6 ± 0.06 c	70	1.44 ± 0.06 c	70	1.24 ± 0.05 d	70	1.3 ± 0.06 cd
Larva	3	1 ± 0.0 d	70	1.69 ± 0.06 a	65	1.43 ± 0.06 b	70	1.01 ± 0.01 d	65	1.11 ± 0.04 c	70	1 ± 0.0 d	66	1.08 ± 0.03 cd	54	1.02 ± 0.02 d
Protonymph	-	-	70	2.04 ± 0.02 b	63	2.81 ± 0.05 a	70	1.81 ± 0.05 cd	58	1.91 ± 0.04 c	70	1.79 ± 0.05 d	54	1.15 ± 0.05 e	47	1.02 ± 0.02 f
Deutonymph	-	-	70	2.94 ± 0.03 a	62	2.32 ± 0.06 b	70	1.67 ± 0.06 d	58	2.14 ± 0.08 c	70	1.73 ± 0.05 d	53	1.74 ± 0.06 d	46	1.22 ± 0.06 e
Female preadult	-	-	43	9.33 ± 0.1 b	20	9.65 ± 0.11 a	35	6.89 ± 0.07 d	34	7.32 ± 0.08 c	30	5.73 ± 0.1 e	25	5.6 ± 0.12 e	20	5.00 ± 0.00 f
Male preadult	-	-	27	9.26 ± 0.16 a	42	8.88 ± 0.06 b	35	7.03 ± 0.06 c	24	5.75 ± 0.09 e	40	6.12 ± 0.11 d	28	4.86 ± 0.08 f	26	4.15 ± 0.07 g
Female adult longevity	-	-	43	18.98 ± 0.26 d	20	21.5 ± 1.03 c	35	24.43 ± 0.43 b	34	20.03 ± 0.75 c	30	26.4 ± 0.4 a	25	15.44 ± 0.57 e	20	9.6 ± 0.65 f
Male adult longevity	-	-	27	16.96 ± 0.22 b	42	14.36 ± 0.79c	35	24.11 ± 0.3 a	24	13.38 ± 0.52 d	40	23.02 ± 0.49 a	28	8.61 ± 0.43 e	26	5.81 ± 0.46 f
Female total longevity	-	-	43	28.3 ± 0.28 b	20	31.15 ± 1 a	35	31.31 ± 0.42 a	34	27.35 ± 0.77 b	30	32.13 ± 0.37 a	25	21.04 ± 0.62 c	20	14.6 ± 0.65 d
Male total longevity	-	-	27	26.22 ± 0.23 c	42	23.24 ± 0.81c	‌35	31.14 ± 0.28 a	24	19.12 ± 0.52 e	40	29.15 ± 0.49 b	‌28	13.46 ± 0.43 f	26	9.96 ± 0.44 g
Means followed by different letters in the column of development rate in each temperatures significantly different (P < 0.05, Tukey's test)

Thermal modeling

Linear models

The lower temperature threshold (T₀) and thermal constant (K) of immature stages of A. swirskii were estimated by two linear models that are given in Table 3. The development rate of the predator was positively affected by temperature. In pre-adult stages, a lower value of T₀ and higher value of K were estimated by the ordinary linear model, which also had a higher R²_adj than the other linear model (Table 3). The linear model estimated that A. swirskii fed on T. urticae nymphs required 133.22 DD to complete development from egg to adult (total immature stages). The estimated lower temperature threshold was about 3.72 ºC for total immature stage. The R²_adj was high for all developmental stages (Table 3).

Table 3

Low-temperature threshold (T₀) and thermal constant (K) of different immature stages of *Amblyseius swirskii* reared on *Tetranychus urticae* estimated by two linear models
Stage	Method	Linear Regression			T₀(ºC)	K (DD)	P-Value
Stage	Method	Equation	R²_adj	R²	T₀(ºC)	K (DD)	P-Value
Egg	Ordinary	R = − 0.3115 + 0.03849 T	0.47594	0.47717	8.09	25.98	4.1335
Egg	Ikemoto	DT = 10.1731 + 17.5394 D	0.7278	0.72844	17.53	10.17	2.2868
Larva	Ordinary	R = 0.3922 + 0.020942 T	0.25698	0.25872	-18.73	47.75	1.3151
Larva	Ikemoto	DT = 6.3646 + 18.0554 D	0.52337	0.52448	18.05	6.36	2.8338
Protonymph	Ordinary	R = − 0.2279 + 0.035291 T	0.48888	0.49007	6.45	28.33	1.9635
Protonymph	Ikemoto	DT = 8.6153 + 18.3601 D	0.69274	0.69345	18.36	8.61	4.2191
Deutonymph	Ordinary	R = − 0.078707 + 0.027086 T	0.2977	0.29934	2.90	36.92	7.2686
Deutonymph	Ikemoto	DT = 9.1002 + 18.5709 D	0.58059	0.58157	18.57	9.1002	3.5885
Pre-Adult	Ordinary	R = − 0.02793 + 0.0075062 T	0.78823	0.78872	3.72	133.22	3.1198
Pre-Adult	Ikemoto	DT = 86.5106 + 10.6477 D	0.36882	0.37029	10.64	86.51	3.9421

Nonlinear models

All 26 nonlinear models fit the data of development rates of different predator stages well and were ranked by AIC (Table 4). The values of AIC, and R²_adj used to determine the goodness-of-fit of the models (Table 4). Based on the AIC criterion, Ratkowsky model with the highest value of R²_adj and the lowest value of AIC, was the best at describing the temperature-dependent development rates of the egg, larval, protonymphal and deutonymphal stages of A. swirskii (Table 4). The upper temperature threshold (T_u) for egg and nymphal stages of A. swirskii were 41.93 and 45, respectively, as estimated by the Ratkowsky model. Our results revealed that the Logan–6 model had the best fit to data for development of overall immature (Table 4). Furthermore, the Sharp and DE Michele model had the poorest fit to data among nonlinear models evaluated. The curves of the influence of temperature on development rate of overall immature stages of A. swirskii fitted by each model are shown in Fig. 1. The parameter values of acceptable models for each stage are given in Table 5.

Table 5

Parameter-values (with 95% confidence bounds) for selected nonlinear models fitted to developmental rates of preadult stage of *Amblyseius swirskii* reared on *Tetranychus urticae*
Model	Parameters	Egg	Larva	Protonymph	Deutonymph	Pre-Adult
Ratkowsky	K	0.2064 (-0.06334,0.4762)	0.06187 (0.04255, 0.08118)	0.1203 (0.04334, 0.1973)	0.1069 (0.09323, 0.1206)	-
	T₀(°C)	1.056e-06 (-5.903, 5.903)	3.125e-08 (-3.59, 3.59)	1.027e-10 (fixed at bound)	4.543e-11 (fixed at bound)	-
	T_U(°C)	41.93 (34.47, 49.39)	45 (fixed at bound)	45 (39.28, 50.72)	45 (fixed at bound)	-
	c	0.03336 (0.02196, 0.04476)	0.05638 (0.03902, 0.07373)	0.03559 (0.03266, 0.03851)	0.03565 (0.03402, 0.03728)	-
Lactin – 1	∆	6.974 (6.309, 7.64)	-	-	-	-
	ρ	0.142 (0.128, 0.156)	-	-	-	-
	T_U(°C)	38.92 (37.65, 40.19)	-	-	-	-
Logan – 6	∆T	4.353 (-1.271, 9.976)	-	0.1567 (-910.3, 910.6)	0.1612 (-2056, 2057)	0.1361 (-3581, 3581)
	Ψ	0.06728 (0.008951, 0.1256)	-	0.1332 (0.1077, 0.1588)	0.1826 (0.1407, 0.2245)	0.04518 (0.04146, 0.04891)
	ρ	0.09891 (0.02516, 0.1727)	-	0.06192 (0.05447, 0.06937)	0.04647 (0.03738, 0.05557)	0.04939 (0.04614, 0.05264)
	TL (ºC)	38.35 (35.46, 41.24)	-	34.18 (-1005, 1074)	34.31 (-3938, 4007)	34.21 (-5635, 5703)
Beta	T₀(°C)	-1.041e + 05 (-1.12e + 08, 1.118e + 08)	-	-	-	-
	T_U(°C)	38.92 (37.17, 40.68)	-	-	-	-
	T_Opt (ºC)	31.91 (31.16, 32.67)	-	-	-	-
	r_m	0.8946 (0.8634, 0.9258)	-	-	-	-
Analytis – 1	P	5 (-68.6, 78.6)	-	-	-	-
	T₀(°C)	-57.51 (-1128, 1013)	-	-	-	-
	TU(°C)	36.41 (21.99, 50.82)	-	-	-	-
	m	0.4227 (-2.395, 3.24)	-	-	-	-
Logan – 10	∆T	4 (-26.71, 34.71)	3.674 (2.226, 5.123)	-	-	-
	K	50 (-65.47, 165.5)	100 (fixed at bound)	-	-	-
	ρ	0.1521 (-0.008481, 0.3127)	0.3035 (0.292, 0.315)	-	-	-
	TL (ºC)	40.2 (16.13, 64.27)	45 (fixed at bound)	-	-	-
	a	1.494 (-5.183, 8.171)	1.03 (0.9895, 1.071)	-	-	-
Janisch/Kontodimonas	D_min	1.203 (0.9787, 1.428)	-	1.878 (-9.047e + 06, 9.047e + 06)	-	8.248 (-2.126e + 07, 2.126e + 07)
	K	-0.09236 (-0.1218, -0.06295)	-	-0.05916 (-0.06525, -0.05307)	-	26.06 (-2.681e + 10, 2.681e + 10)
	λ	-0.2023 (-0.4005, -0.004092)	-	-237.3 (-5.82e + 12, 5.82e + 12)	-	0.04923 (0.04584, 0.05261)
	T_Opt (ºC)	34.27 (31.41, 37.13)	-	34 (-8.144e + 07, 8.144e + 07)	-	34.05 (-5.236e + 07, 5.236e + 07)
Janisch/Rochat	C	0.8314 (0.6764, 0.9864)	-	0.5827 (0.5249, 0.6405)	-	0.13 (0.1271, 0.133)
	T_U(°C)	34.26 (31.39, 37.14)	-	34.59 (34.2, 34.98)	-	35.11 (34.96, 35.27)
	a	1.224 (0.9813, 1.466)	-	3 (0.2672, 5.733)	-	3 (fixed at bound)
	b	1.097 (1.064, 1.129)	-	1.066 (1.057, 1.075)	-	1.052 (1.049, 1.055)
Lactin – 2	∆	2.479 (0.02786, 4.931)	-	0.1781 (-306, 306.4)	0.1555 (-3553, 3553)	0.182 (-195.9, 196.2)
	λ	-1.193 (-1.321, -1.064)	-	-1.066 (-1.136, -0.9964)	-0.9592 (-1.043, -0.8751)	-1.015 (-1.025, -1.006)
	ρ	0.02487 (0.0211, 0.02865)	-	0.02151 (0.01979, 0.02323)	0.01758 (0.01529, 0.01987)	0.006437 (0.006083, 0.00679)
	T_U(°C)	39.52 (34.62, 44.42)	-	34.36 (-589.8, 658.5)	34.45 (-1.017e + 04, 1.024e + 04)	34.64 (-652, 721.3)
Analytis-1/Allahyari	P	1.458 (-0.5658, 3.481)	-	-	0.8203 (-1.664, 3.305)	0.2367 (0.2097, 0.2637)
	T₀(°C)	3 (-53.73, 59.73)	-	-	13.39 (7.636, 19.15)	3 (fixed at bound)
	T_U(°C)	38.68 (32.43, 44.94)	-	-	35 (-101.6, 171.7)	35 (32.22, 37.78)
	m	9.255 (-3.603, 22.11)	-	-	59.27 (-7866, 7984)	57.48 (-102.8, 217.8)
	n	1.599 (-3.725, 6.924)	-	-	0.466 (0.1089, 0.823)	1.054 (0.9832, 1.124)
Wang	C	-	-	-	-	0.5 (fixed at bound)
	K₁	-	-	-	-	0.002936 (-0.02929, 0.03516)
	K₂	-	-	-	-	1.5 (-1.663, 4.663)
	T₀(°C)	-	-	-	-	5 (0.09391, 9.906)
	T_U(°C)	-	-	-	-	35.21 (32.83, 37.6)
	m	-	-	-	-	2.807 (-26.43, 32.04)
Performance – 2	K₂	-	-	-	-	1 (0.1825, 1.817)
	T₀(°C)	-	-	-	-	5 (3.765, 6.235)
	T_U(°C)	-	-	-	-	35.77 (34.4, 37.15)
	m	-	-	-	-	0.008006 (0.00746, 0.008552)
Performance – 1	C	-	1.026 (0.8524, 1.199)	-	-	3.929 (-67.06, 74.92)
	K₁	-	0.2515 (0.05908, 0.444)	-	-	0.002083 (-0.03696, 0.04112)
	K₂	-	0.2898 (-1.627, 2.207)	-	-	1 (-0.3371, 2.337)
	T₀(°C)	-	13.04 (10.88, 15.2)	-	-	5.002 (-0.8603, 10.86)
	T_U(°C)	-	45 (-17.65, 107.7)	-	-	35.81 (33.72, 37.91)
SSI Model	∆HA	1.5e + 04 (1.037e + 04, 1.963e + 04)	-	-	4353 (-3621, 1.233e + 04)	9092 (7921, 1.026e + 04)
	∆HH	5.659e + 04 (1.979e + 04, 9.338e + 04)	-	-	8e + 04 (-7.791e + 05, 9.391e + 05)	8e + 04 (2.879e + 04, 1.312e + 05)
	∆HL	-8e + 04 (fixed at bound)	-	-	-8e + 04 (-2.444e + 05, 8.437e + 04)	-8e + 04 (fixed at bound)
	ρφ	0.4513 (-4.66e + 06, 4.66e + 06)	-	-	0.4944 (-4.39e + 06, 4.39e + 06)	0.1333 (-1.732e + 06, 1.732e + 06)
	T_H (ºK)	308 (305.6, 310.3)	-	-	320 (fixed at bound)	310 (308.6, 311.3)
	T_L (ºK)	275 (fixed at bound)	-	-	288.3 (286.3, 290.4)	275 (fixed at bound)
	T_φ (ºK)	293.3 (-1.133e + 08, 1.133e + 08)	-	-	290.4 (-3.018e + 08, 3.018e + 08)	294.9 (-2.32e + 08, 2.32e + 08)
Polynomial	a₀	-0.000474 (-0.0006141, -0.000334)	0.0001956 (8.652e-05, 0.0003048)	-0.0005761 (-0.0007074, -0.0004448)	0.0001901 (4.036e-05, 0.0003399)	-5.747e-05 (-7.261e-05, -4.234e-05)
	a₁	0.03525 (0.02456, 0.04593)	-0.0173 (-0.02563, -0.008976)	0.04432 (0.03431, 0.05434)	-0.01509 (-0.02651, -0.003665)	0.004267 (0.003113, 0.005422)
	a₂	-0.813 (-1.078, -0.5479)	0.507 (0.3005, 0.7135)	-1.077 (-1.326, -0.8287)	0.4124 (0.129, 0.6958)	-0.09603 (-0.1247, -0.06738)
	a₃	6.355 (4.222, 8.488)	-3.937 (-5.6, -2.275)	8.837 (6.836, 10.84)	-3.238 (-5.52, -0.9573)	0.7899 (0.5593, 1.021)
Davidsons logistic	a	-	5.816 (4.152, 7.48)	-	-	-
	b	-	0.3776 (0.282, 0.4732)	-	-	-
	k	-	0.9957 (0.9735, 1.018)	-	-	-
Analytis-3	T₀(°C)	-	15 (9.187, 20.81)	-	-	-
	T_U(°C)	-	45 (-37.02, 127)	-	-	-
	a	-	0.1589 (-1.629, 1.947)	-	-	-
	m	-	0.3558 (-2.291, 3.002)	-	-	-
	N	-	0.3248 (-0.4391, 1.089)	-	-	-
Sharpe and DeMichele	∆HA	11.17 (-5.467e + 06, 5.467e + 06)	-	-	-	-
	∆HH	0.9058 (-3.874e + 06, 3.874e + 06)	-	-	-	-
	∆HL	-5.148 (-1.06e + 08, 1.06e + 08)	-	-	-	-
	∆SH	7.331 (-3.595e + 07, 3.595e + 07)	-	-	-	-
	∆SL	2.004 (-1.967e + 07, 1.967e + 07)	-	-	-	-
	φ	-1.522 (-7.795e + 06, 7.795e + 06)	-	-	-	-
	R	1.906 (-1.228e + 07, 1.228e + 07)	-	-	-	-

This research clearly showed the effect of temperature on development time of all stages of A. swirskii by way of Lee and Gillespie (2011) and Farazmand et al. (2020) demonstrated that development time of A. swirskii is seriously related to temperature. The results obtained from the present research showed that the egg incubation period of A. swirskii at different temperatures had significant differences and varied from 1.24 to 3.84 d. At 15°C, the length of this period was 3.84 ± 0.19 days and at 30°C, the length of this period was 1.24 ± 0.06 days. Development time recorded in the present research was different from that reported by Farazmand et al. (2020) who noted that the egg incubation period of A. swirskii at 15°C was 7.29 d, in contrast, they estimated this value to be 1.51 d at 30°C, which is almost the same as the result of the current research (Table 2). Lee and Gillespie (2011) stated that the egg incubation period of A. swirskii at a temperature of 25°C is 1.7 d that slightly different from that estimated by the current study (Table 2). This discrepancy may be a repercussion of the rearing methods, experimental conditions, and diets along with differences in data analysis. In the present study, A. swirskii (fed on TSSM) had the shortest larval stage among all biological stages. Our results indicated that durations of the larval (~ 1 day) which was similar to or slightly higher than the populations obtained from the same species. This is a natural mechanism because the larvae are non-feeding and defenseless. But one of the good features of an effective and efficient biological control agent is the short maturation period, which causes the length of one generation to decrease and the efficiency of these agents to increase (Yazdanpanah et al. 2022).We observed the pre-adult duration in both sex (female and male) have significant differences. These figures are similar to those formerly performed on this predatory mite reported by Lee and Gillespie (2011) and Farazmand et al. (2020) who noted a 7-d pre-adult duration at 25°C. Furthermore, Yousef et al. (1982) estimated that this value at 30°C is 5.6 d that was similar the durations that obtained in the current study. The pre-adult duration of this predator mite that feeds on Thrips tabaci Lindeman at 25ºC (7.8 days) reported by Wimmer et al. (2008) are different from those estimated in our study at the same temperature. Since the rate of development and success of predator mites largely depends on the quality and quantity of preys provided (Gotoh and Gomi, 2003), the difference between our results and the literature may be related to this issue. One of the main factors in the success of biological control agents against pests is their development rate, and any natural enemy that has a faster development rate is more likely to be successful in pest control.

The development rate reaches its maximum at the fastest development temperature (T_fast) and in which the population fitness may not be maximum due to high mortality. Based on the results of this research, considering that the maximum development rate was recorded at 32°C among all temperatures tested, it can be considered as the fastest development temperature (T_fast). Using the Janisch/Kontodimonas model, as ranked second fitted model in the preadult stage, the fastest temperature has been seen at 34°C. Similar results have been reported for other phytoseiids mites: Neoseiulus cucumeris (Oudemans) (32°C) (Yazdanpanah et al. 2022), Typhlodromus bagdasarjani Wainstein and Arutunjan (Acari: Phytoseiidae) (34°C) (Ganjisaffar et al. 2011), Neoseiulus womersleyi (Schicha) (Acari: Phytoseiidae) (33°C) (Lee and Ahn 2000), and Phytoseius plumifer (Canestrini and Fanzago) (Acari: Phytoseiidae) (34°C) (Gorji et al. 2008). Amarasekare and Savage (2012) believe that the optimal temperature (T_opt), is the temperature at which the value of intrinsic increase (r) reaches its maximum. Accordingly, the optimal temperature of this predator is 27°C (Rahimi et al. 2022). Meanwhile, some researchers demonstrated that the optimal temperature is which the development time and the mortality are the lowest (Aghdam et al. 2009; Shi et al. 2013). In the case of this mite, it seems that 27°C is a more suitable temperature for mass rearing of this predator due to the short development period and total longevity of adults. However, in order to make a comprehensive and correct decision in this matter, more studies are needed on the optimal rearing conditions such as temperature, humidity and also different food sources. There are many reports that the temperature of 35°C and above reduces development rate of phytoseiid mites (Broufas and Koveos, 2001; Broufas et al. 2007; Ganjisaffar et al. 2011; Jafari et al. 2012; Yazdanpanah et al. 2022). Based on the results of the current research, the upper temperature threshold (T_U) for immature stages was estimated by the Beta model (45°C).

In the present study, the lower temperature threshold and thermal constant were obtained using both ordinary and Ikemoto linear models. The lower temperature threshold of the egg stage was 17.53°C as estimated by the Ikemoto linear model (Table 3). Our laboratory observations confirm this estimation because at a temperature of 17°C, all larvae of the predatory mite continued to grow, while at a lower temperature, i.e. 15°C, very few eggs hatched and no development was observed. The lower temperature threshold for the development of the egg stage of A. swirskii was 8.09°C, which was estimated by linear models. The lower temperature threshold value is different from that estimated by Frazmand et al. (2020) (11.45°C). Because the T₀ estimated by Ikemoto linear was closer to the observed results than ordinary model, the former was accepted for estimating the mentioned parameter. Based on Honek and Kocourek (1988, 1990) T₀ decreased if K increased therefore, the thermal constant estimated by the ordinary and Ikemoto model was 133.22 and 86.51 degree-day, respectively. The estimated thermal constant values of A. swirskii (86.51 DD) are different from those estimated for Phytoseiulus longipes Evans (Acari: Phytoseiidae) (28.7 DD) (Ferrero et al. 2007), Neoseiulus cucumeris (Acari: Phytoseiidae) (112.8 and 123.5 DD) (Yazdanpanah et al. 2022), N. californicus McGregor (Acari: Phytoseiidae) (90 DD) (Castagnoli and Simoni, 1999), N. womersleyi (69.36 DD), N. longispinosus (Evans) (Acari: Phytoseiidae) (61.5 DD) (Sugawara et al. 2017), and Euseius finlandicus (93.5 DD) (Broufas and Koveos, 2001). The thermal characteristics may be affected by population (Lee and Elliott, 1998), stage of development (Honek, 1996), and food source (Golizadeh et al. 2007) and the difference may be due to one or a set of the above factors. The R²_adj coefficients were higher for the Ikemoto model. This coefficient is used to fit the regression between temperature and growth rate. Although linear models only estimate the lower temperature threshold, this temperature is suitable for analyzing insect population phenology due to the simplification of the analysis (Ikemoto and Kiritani, 2019).

26 nonlinear models were fitted to describe the relationship between A. swirskii development rate and temperature. AIC is used in many studies related to the ranking of models (Zamani et al. 200; Aghdam et al. 2009; Zahiri et al. 2010; Pakyari et al. 2011), because it has the ability to adjust for the quantity of parameters of a model by giving a reprimand to models with many parameters (Akaike, 1974). Our observations showed that the development rate of the egg stage at 32°C was the lowest, i.e. 1.3 days. Based on the results of Table 5, the Beta model is ranked second in describing the temperature-dependent development rate of the egg stage and estimated − 1.041, 38.39 and 31.91°C for lower and upper temperature thresholds and optimum temperature, respectively (Table 5). Similarly, the upper temperature thresholds and optimum temperature for protonymph development were 34.59 and 34°C as estimated by Janisch/Kontodimonas model, which is the third best model based on the AIC. Among the 26 non-linear models fitted, the Ratkowsky model is ranked the first for all stages of egg, larva, protonemph and deutonemph, these results are similar to the results of Shi et al. (2016) who mentioned the Ratkowski model was the best model to describe the development rate for 10 other insect data. In contrast, Mirhosseini et al. (2018( claimed that this criterion is not biologically reliable. Mirhosseini et al. (2018) state that based on their results, more appropriate temperature for Nesidiocoris tenuis (Hemiptera: Miridae) is 28°C, while the Beta model, which ranked second in describing the temperature-dependent development rate of the egg stage, has estimated this temperature to be 34°C. Similar results are seen for y Analytis-1/Allahyari, Hilbert and Logan and Analytis-1 models. Considering that in some researches, the AIC has lacked validity in estimating the minimum temperature (Mirhosseini et al. 2018), it seems that the biological validity in the laboratory and the field as a function of temperature to choose the best model describing the development rate in addition statistical validation is needed. Some researchers have stated that among all the models that describe the development rate of arthropods, the most reliable and beneficial models are those that are designed based on physiological and biochemical mechanism (Shi et al. 2017). These contrasts indicate model selection is critical because of the significant differences between model predictions. Rebaudo and Rabhi (2018) pointed out each of the criteria for model selection has its advantages and disadvantages therefore, a combination of different methods should be used in model selection. The results of the present study provided essential information about the biology of A. swirskii which will lead to better performance of this predator as an impressive biological control agent against pests in greenhouse.

One of the key factors in pest control is knowing the interactions between temperature and development rate of pests on which predators prey are also important for pest control studies. Based on unpublished data (Farazmand et al. 2020) the lower temperature threshold and the thermal constant for the total immature stages of females of T. urticae was 8.71ºC (linear model) and 204.08 DD respectively, and the thermal constant for the total immature stages of Bemisia tabaci (Gennadius) was 390 DD (Muniz and Nombela, 2001). The lower temperature threshold and the thermal constant for total immature stages of A. swirskii females are lower than those above-mentioned. Therefore, it can be assumed that this predator is able to control both of these pests with a higher generation rate. In this study, we demonstrated that A. swirskii appears to be better adapted to higher temperatures, and has the potential to be used as biological control agent against Tetranychus species in greenhouse crops where temperatures are typically high in the summer.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Funding

Not applicate

ORCID

Mostafa Maroufpoor ID: 0000-0001-6677-7267

Amin Sadeghi ID: 0000-0001-6048-3532

Yaghoub Fathipour ID: 0000-0002-7963-5409

Credit authorship contribution statement

Farshad Moradi: Methodology, Investigation, Validation, Formal analysis.

Akram Rahimi: Methodology, Investigation, Validation, Formal analysis.

Amin Sadeghi: Methodology, Formal analysis.

Yaghoub Fathipour: Investigation, Validation, Formal analysis, review & editing,

Mostafa Maroufpoor: Investigation, Validation, Formal analysis, Writing - review & editing, Visualization.

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Tables 1 and 4 is available in the Supplementary Files section.

No competing interests reported.

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Modeling Linear and Nonlinear Relationship between Temperature and Development Rate of Amblyseuis swirskii (Acari: Phytoseiidae)

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Abstract

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Introduction

Materials And Methods

Rearing of two-spotted spider mite

Phytoseiid rearing

Life history parameters

Model fitting and analysis

Results

Life table

Thermal modeling

Linear models

Nonlinear models

Discussion

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References

Tables

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Supplementary Files

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