Effect of temperature on the biological parameters of the cabbage aphid Brevicoryne brassicae

Abstract The cabbage aphid, Brevicoryne brassicae, is a pest of many plants of the Brassicaceae family including cabbage, Brassica oleracea Linnaeus, 1753. We investigated the effect of temperature on the biological parameters of B. brassicae using different temperature‐based models incorporated in the Insect Life Cycle Modelling (ILCYM) software. Nymphs of first stage were individually placed in the incubators successively set at 10°C, 15°C, 20°C, 25°C, 30°C, and 35°C; 75 ± 5% RH; and L12: D12‐hr photoperiods. We found that first nymph reached the adult stage after 18.45 ± 0.04 days (10°C), 10.37 ± 0.26 days (15°C), 6.42 ± 0.07 days (20°C), 5.076 ± 0.09 days (25°C), and 5.05 ± 0.10 days (30°C), and failed at 35°C. The lower lethal temperatures for B. brassicae were 1.64°C, 1.57°C, 1.56°C, and 1.62°C with a thermal constant for development of 0.88, 0.87, and 0.08, 0.79 degree/day for nymphs I, II, III, and IV, respectively. The temperatures 10, 30, and 35°C were more lethal than 15, 20, and 25°C. Longevity was highest at 10°C (35.07 ± 1.38 days). Fertility was nil at 30°C and highest at 20°C (46.36 ± 1.73 nymphs/female). The stochastic simulation of the models obtained from the precedent biological parameters revealed that the life table parameters of B. brassicae were affected by the temperature. The net reproduction rate was highest at 20°C and lowest at 30°C. The average generation time decreased from 36.85 ± 1.5 days (15°C) to 6.86 ± 0.1 days (30°C); the intrinsic rate of increase and the finite rate of increase were highest at 25°C. In general, the life cycle data and mathematical functions obtained in this study clearly illustrate the effect of temperature on the biology of B. brassicae. This knowledge will contribute to predicting the changes that may occur in a population of B. Brassiace in response to temperature variation.

Aphids are ectothermic organisms; all their physiological processes largely depend on several climatic variables that include temperature (Brodeur et al., 2013). According to Campbell, Frazer, Gilbert, Gutierrez, and Mackauer (1974), the temperature is a critical abiotic factor affecting insect biology. The rise in temperature from 1.5 to 5.8°C until the end of 2,100 as predicted by many mathematical models (Govindasamy, Duffy, & Coquard, 2003;Hijmans, Cameron, Parra, Jones, & Jarvis, 2005;IPCC, 2014) is likely to increase the metabolic activity of B. brassicae. The ability of insects to modify their physiology and behavior in response to an environmental factor is termed phenotypic plasticity (Pigliucci, Murren, & Schlichting, 2006). This plasticity is controlled by several physiological mechanisms (transcription, translation, enzyme, and hormonal regulation) that produce local or systemic responses (Whitman & Agrawal, 2009). These responses can be visualized using mathematical functions called reaction norms, which plot values for a specific phenotypic trait across two or more environments or treatments (David et al., 1997). According to Fischer and Karl (2010), phenotypic plasticity is a powerful and effective mechanism used by different organisms to cope with the detrimental effects of short-term environmental changes. In the context of global warming, the primary challenge faced by ecologists is to predict variation that occurs on the biology of ectotherm organisms (Brodeur et al., 2013). Therefore, temperature-based reaction norms are essential analytical tools for evaluating, understanding, and predicting the phenotypic variation in insects (Baker, 1991;Jarvis & Baker, 2001).
There are two distinct modeling approaches Trnka et al., 2007). (a) The first approach is the inductive method, which matches the climate where an organism is usually found within a region to where it is not found using long-term meteorological data (Beaumont, Hughes, & Poulsen, 2005;Legaspi & Legaspi, 2007;Peacock & Worner, 2006;Sutherst & Maywald, 2005;Trnka et al., 2007). This modeling approach has an advantage to only depend on the presence/absence data of the species studied.
However, the critical limitation of this approach is its failure to consider the biological characteristics of the species in the modeling framework (Venette et al., 2010). (b) The second approach is deductive, which use mathematical functions (process-based climatic response) to describe the basic physiological principles of the insect species growth, namely its development, survival, and reproduction (Curry, Feldman, & Smith, 1978;Nietschke, Magarey, Borchert, Calvin, & Jones, 2007;Sporleder, Kroschel, Quispe, & Lagnaoui, 2004;Trnka et al., 2007). This approach is based on detailed laboratory experiments that produce life table parameters and allows the simulation of populations according to real or interpolated data for a given region and time (Sporleder, Simon, Juarez, & Kroschel, 2008).
Modeling process uses linear and nonlinear models. Linear models have long been used for the construction of phenological patterns of insect populations (Roltsch, Mayse, & Clausen, 1990) (Briere, Pracros, Le Roux, & Pierre, 1999;Logan, Wollkind, Hoyt, & Tanigoshi, 1976;. Their development requires knowledge of lethal temperatures (upper and lower) of insect species studied as well as data collected on each individual from birth to death (Nietschke et al., 2007). Several studies have already been conducted to evaluate the effect of temperature on the biology of B. brassicae (Abdel-Rahman et al.;2011;Akinlosotu, 1977;DeLoach, 1974;Fathipour, Hosseini, Talebi, Moharamipour, & Asgari, 2005;Gupta, 2014;Satar, Kerstng, & Ulusoy, 2005); however, these studies do not include reaction norms in their studies. Therefore, the main objective of this work was to study and visualize the effect of temperature on the biological parameters of B. brassicae using mathematical models found in the Insect Life Cycle Modelling (ILCYM) software . These models will serve as essential components to predict the distribution of B. brassicae as influenced by the temperature.

| Insect culture
The population of Brevicoryne brassicae used in this study was a clonal line of aphids (to avoid genetic divergence) collected initially in a single infested cabbage farm in Dschang (05° 26′70″N. 010° 04′09″E; Al. 1,391 m), a town situated in western Cameroon. The stock culture of aphids was cultured on the potted cabbage plants (Brassica oleracea var. Marcanta L) in an air-controlled insectary room maintained at 25 ± 1°C, 75% ± 5% RH, and 12L:12D-hr photoperiods. Aphids were reared in the insectary for 2-3 generations before individuals were harvested for the experiments (Kindlmann & Dixon, 1989

| Rearing conditions
The effect of temperature on the biological parameters of Brevicoryne brassicae was studied in cohorts of single life stages in controlled environmental chambers at six constant temperatures, that is, 10, 15, 20, 25, 30, and 35°C, of 75% ± 5% RH, and maintained on a photoperiod regime of 12L:12D-hr photoperiods. The required temperatures and hygrometry inside the incubators were regularly monitored using a standard thermo-hygrometer of HOBO trademark.

| Experimental conditions
One hundred cabbage leaves were received each two to three apterous individual of Brevicoryne brassicae from the stock culture ( Figure 1). Leaves were kept hydrated by immersing their petioles in distilled water in a glass tube (12 ml) sealed with parafilm. Each cabbage leave with aphids was transferred inside a clear plastic container covered with a lid previously perforated at the center and closed with an organza tissue to aerate the container. After 24 hr, one newly born nymph was maintained on each cabbage leaf; adult and the extra nymphs were removed. After that, a total of 100 nymphs were individually monitored at each test temperature. Development and mortality of the different nymph stages were recorded daily. When they reached the adult stage, individuals were monitored daily to count and separate newborn nymphs from checking for the reproduction data. For each experimental temperature, aphid individuals were followed until the death. To avoid the effect of age on the survivorship and reproduction, aphids were carefully transferred on new cabbage leaves every 7 days.

| Software description
To study and visualize the effect of temperature on the biological parameters of Brevicoryne brassicae, we used the Insect Life Cycle Modelling (ILCYM, version 3.0) software developed by the International Potato Centre (CIP) and freely available at the CIP website: http://www.cipotato.org . Insect Life Cycle Modelling contains three modules: the model builder, the F I G U R E 1 Cabbage aphids, Brevicoryne brassicae, Photo: Baleba Steve validation and simulation module, and the potential population distribution and risk mapping; we used the two-first modules for the present study. ILCYM's model builder is a complete modeling interface that helps to develop insect temperature-based models. It provides several nonlinear functions, which are adequate for describing the temperature dependency of the different processes in the species life history (i.e., development, survival, and reproduction). The Akaike's information criterion (AIC; Akaike, 1973), which is inbuilt in ILCYM, was used to select the best mathematical expression for each nymphal stage of B. brassicae. The validation and simulation module with the stochastic simulation tool was used to estimate life table parameters at constant temperatures based on the developed temperature-based models.

| Distribution model of development times
For estimation of the variation among individuals in developmental times of Brevicoryne brassicae, the concepts of rate summation (Curry et al., 1978) and same shape (Sharpe, Curry, DeMichele, & Cole, 1977) were included. These concepts assumed that the intrinsic distributions of insect development times at different constant temperatures have the same shape (i.e., the distributions at different temperatures will fall on top of each other when "normalized" by a selected value such as the mean or median of each distribution).
The data collected from different constant temperatures were fitted to three dichotomic models: logit, probit, and complementary log. Due to its lowest AIC value, the logit model represented by the following function was selected to depict the effect of temperature on the developmental time of the four nymphal stages of

B. brassicae.
where F(x) is the probability to complete development at time x, lnx is the natural logarithm of the days observed, a is the intercept corresponding to temperature i, and b is the common slope of the regression model.

| Temperature-dependent development rate model
Development rate was expressed by the reciprocal of the mean development times for all the four nymphal stages of Brevicoryne brassicae. The relationship between temperature and development rate was described by the nonlinear Sharpe & DeMichele 1 model  for nymph I stage; while nymph II, III, and IV stages were described by the modified Janisch 1 model (Janisch, 1932). We chose the precedent models based on their respective AIC value that was smaller compared to those of other models; their mathematical equations are respectively expressed below: where r(T) is the development rate at temperature T (°K), R is the universal gas constant (1.987 cal/degree/mol), p represents the development rate at optimum temperature T opt (°K) assuming no enzyme inactivation, ΔH A is the enthalpy of activation of the reaction catalyzed by an enzyme (cal/mol/1), ΔH L and ΔH H are the change in enthalpy at high temperature (cal/mol/1), and T H is the high temperature at which enzyme is half active. T opt is the optimum temperature for survival (°C).
For each B. brassicae immature stage, the following linear regression equation was used to evaluate the lower developmental threshold (T 0 ) and the thermal constant (K) expressed in degree days (DD) where r(T) is the rate of development at temperature T, a is the y-intercept, and b is the slope. The lower developmental threshold (T 0 ) and the degree-day (DD) requirement were estimated using the parameters: T 0 = −a∕b and DD = 1∕b

| Temperature-dependent mortality model
The mortality rate of each Brevicoryne brassicae immature stage was calculated by dividing the number of individuals that did not develop successfully to the next stage by the initial number of individuals at each stage. The effect of temperature on the mortality rate of B. brassicae was described by using polynomial 2 function for nymph Wang 1 and 7 functions (Wang, Lan, & Ding, 1982) were used to illustrate the temperature dependence of mortality in nymphs III and IV, respectively. The following equations were used: where m(T) is the rate of mortality at temperature T(°C). T opt is the optimum temperature for survival (°C). B, B l, B h , and H are the fitted parameters.
As rule of thumb, all the listed functions were chosen based on the lower value of their value.

| Longevity and fecundity
The longevity of Brevicoryne brassicae was determined using the mean survival time of an adult. The inversion of the mean longevity time allows us to calculate the senescence rate. The Stinner 4 model (Stinner, Gutierrez, & Butler, 1974) which had the lower AIC value was fitted to determine the relationship between the senescence rate and temperature. The mathematical expression of the model is illustrated as: S(T) is the senescence rate at temperature T(°C). T 0 is the optimum temperature (°C). C 1 and C 2 are the maximum and minimum temperatures (°C) when T ≤T o and T > T o , respectively. K 1 and K 2 are constants representing the slope and the intercept, respectively.
The fecundity was modeled by considering a total number of nymph produced per adult during the entire lifespan. The polynomial 2 function shown below was fitted to represent the temperature effect on this parameter.

| Simulation of life table parameters at constant temperatures
Life table parameters of Brevicoryne brassicae including gross reproductive rate (GRR), net reproductive rate (R o ), intrinsic rate of natural increase (r m ), finite rate of increase (ƛ), mean generation time (T), and doubling time (D t ) were estimated using the module "stochastic simulation tool" in ILCYM, which is based on rate summation and cohort up-dating approach (Curry et al., 1978 where L p (T) represents the respective life table parameters (GRR, R 0 , T, r m , l, D t ) at temperature T (°C), and a, b, and c are the model parameters.  The number in parentheses represents standard errors.

S(T)
No development occurred at 35°C for nymph I (  (Table 3 and Figure 2).

| Mortality of nymphal stages
The mortality of Brevicoryne brassicae nymphal stages varied significantly among the rearing temperatures (  (Table 5 and Figure 3).

| Longevity and fecundity capacity of adult
Temperature had a significant effect on the longevity (F 4-277 = 10.8; p < 0.0001) and fecundity (F 3-274 = 23.19; p < 0.0001) of Brevicoryne brassicae ( Table 6). The longest longevity period was recorded at 10°C and the shortest at 30°C (Table 6). The relationship between temperature and mean senescence rate of B. brassicae was represented by Stinner 4 function (Table 7 and Figure 4a). Our results showed that optimal fecundity was obtained from temperatures ranging between 10 and 20°C. The effect of temperature on the fecundity of B. brassicae was well described by the polynomial 2 function (Table 7 and Figure 4b).

| Demographic parameters of Brevicoryne brassicae at constant temperatures
Results presented in Table 8 show that in Brevicoryne brassicae, the intrinsic rate of increase (r m ), the net reproduction rate (R 0 ), the mean generation time (T), the finite rate of increase ( Figure 5).

| D ISCUSS I ON
The results of this research provided reaction norms that depict the effect of temperature on the biological parameters of Brevicoryne brassicae. This was performed using a friendly-user software called Insect Life Cycle Modelling (ICLYM), in which the aim is to assist researchers in developing insect temperature-based models .  (Fand et al., 2014) and Liriomyza huidobrensis (Mujica, Sporleder, Carhuapoma, & Kroschel, 2017), two insect species with a wide range of thermal tolerance and cosmopolitan distribution as The linear equation used in this study predicted 1.64 C, 1.59 C, 1.56 C, and 1.62°C were the lower lethal temperatures for nymph I, nymph II, nymph III, and nymph IV, respectively. This could explain the presence of B. brassicae in the temperate zones where temperatures decrease dramatically in winter (Hines & Hutchison, 2013). Our prediction corroborates the result of Markkula (1953)  Wang functions, also predicted higher mortality at the temperatures below 10°C and above 30°C.
The longevity and fecundity of adults of B. brassicae were also affected by temperature. They were maximal respectively at 10 and 25°C. The Stinner function fitted well with our longevity data. This model illustrates that adults of B. brassicae have an optimal lifespan TA B L E 5 Estimated parameters (mean ± SE) of the nonlinear models fitted to mortality rate for immature life stages of Brevicoryne brassicae: Polynomial 2 (nymphs I and II), Wang 1(nymph III), and Wang 7 (nymph IV)  Fletcher, Axtell, and Stinner (1990) used the same function to model the effect of temperature on the longevity of the house fly (Musca domestica).
The polynomial function we used to model the effect of temperature on B. brassicae fecundity predicted that temperatures between 10 and 30°C are more favor B. brassicae fecundity. We obtained the highest fecundity value at 20°C (46.36 nymphs). However, this value was low compared to the value obtained by Akinlosotu (1977) at the same temperature (74.5 nymphs). Also, Satar et al. (2005) reported the highest fecundity per day at 25°C (4.2 nymphs). The difference observed in our respective results could be attributed to the different type of cabbage cultivars used in our respective experimentations. Akinlosotu (1977) used the Gemmifera cultivar, while Satar et al. (2005) used the Capitata cultivar. However, in our study, we used the Marcanta cultivar. Indeed, the literature has demonstrated the effect of cabbage cultivar in B. brassicae fecundity (Ellis & Farrell, 1995;Gia & Andrew, 2015;Maremela, Tiroesele, Obopile, & Tshegofatso, 2013).

ACK N OWLED G M ENTS
This study was supported financially and logistically by the International Institute of Tropical Agriculture. We would like to thank all the colleagues including Abdelmutalab Ahmed, Caroline Kungu, Ritter Guimapi, and Olabimpe Olaide who generously provided advice, information, and suggestions to improve the quality of this manuscript.

CO N FLI C T O F I NTE R E S T
None declared.

AUTH O R CO NTR I B UTI O N S
SBBS designed the study, collected and analyzed the data, and wrote the manuscript. NNS and DM assisted in data analysis and interpretation. KS and DM proofread the manuscript.

DATA ACCE SS I B I LIT Y
The authors confirm that all the data supporting the results of this manuscript will be immediately archived in the Dryad system upon acceptance.