Journal of Plant Physiology & Pathology ISSN: 2329-955X

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Research Article, J Plant Physiol Pathol Vol: 5 Issue: 4

Impact of eCO2 and Temperature on Aphis craccivora koch. on Groundnut and Future Pest Status During Climate Change Scenarios

Srinivasa Rao Mathukumalli*1, Shaila Ongolu1, Vennila Sengottaiyan2 and Rama Rao Anantha Chitiprolu1

1ICAR-Central Research Institute for Dryland Agriculture (CRIDA), Hyderabad-500 059, India

2ICAR-National Centre for Integrated Pest Management (NCIPM), Pusa Campus, New Delhi-110012, India

*Corresponding Author : Srinivasa Rao Mathukumalli
ICAR-Central Research Institute for Dryland Agriculture (CRIDA), Hyderabad, 500 059 India
Tel: +90-40-24530161
Fax: +91-40-24531802
E-mail: [email protected]; [email protected]

Received: June 15, 2017 Accepted: August 04, 2017 Published: August 10, 2017

Citation: Mathukumalli SR, Ongolu S, Sengottaiyan S, Chitiprolu RRA (2017) Impact of eCO2 and Temperature on Aphis craccivora koch. on Groundnut and Future Pest Status During Climate Change Scenarios. J Plant Physiol Pathol 5:4. doi: 10.4172/2329-955X.1000171

Abstract

Impact of eCO2 and Temperature on Aphis craccivora koch. on Groundnut and Future Pest Status During Climate Change Scenarios

Studies were conducted to quantify the direct effects of temperature and indirect effect of elevated CO2 (eCO2), on Aphis craccivora Koch. on groundnut (Arachis hypogaea L.). The mean development time (DT) of nymph was significantly reduced by 1-2 days from 20 to 35°C temperature at eCO2 over ambient CO2 (aCO2) conditions. Increased production of offspring was noticed at eCO2. The thermal requirement of nymph varied from 74-102 DD on eCO2 with temperature in the range of 20-30°C as against 90-130 DD on aCO2. Non-linear mostly quadriatic relationship of lifetable parameters rm, Ro, T and λ varied with temperature and CO2 and found to have nonlinear relationship. Prediction of pest scenarios based on PRECIS A1B emission scenario data at eleven groundnut cultivating locations of India during near (NF) and distant future (DF) periods showed that increase of ‘rm’ and ‘λ’ with varied ‘Ro’ and reduced ‘T’. Similar trends were reflected in three decadal periods of NF also. The present results indicate that incidence of A. craccivora is likely to be higher in the future climate change periods.

Keywords: Aphids; Development time; Thermal constant; Life table parameters; Climate change; Pest status

Introduction

Global Mean Surface Temperature (GMST) and Global atmospheric CO2 concentrations have been increasing at a significant rate since last 19th century. It is well known that 0.78°C increase in temperature was noted between average of the 1850–1990 period and the 2003-2012 period. The increase in the amount of CO2 in the atmosphere will be by about 40% when compared with pre-industrial levels [1]. Increase in temperature and elevated CO2 (eCO2) influence crop growth significantly and in turn affect the insect herbivores both directly and indirectly. Though it is known that the increase in temperature will have a greater effect on insects than the rising CO2 concentration, the interactive and combinational effect of both parameters is more evident.

Among various insect pests, Aphis craccivora Koch. is one of the threats to groundnut (Arachis hypogaea L.) growers in all over the country. The area, production and productivity of crop is stagnant since several decades due to the various biotic and abiotic stresses and the productivity of groundnut crop is found to be low. The growth and development of phloem-feeding insect species vary with increase in temperature [2] and elevated CO2 [3]. Under eCO2 conditions the variation of biochemical constituents viz., reduction of nitrogen, increased carbon and C:N ratio was reported [4] which can be the major causative factor in influencing the aphids. In addition to the abiotic factors the role of host plant [5] and quality of the diet are vital in influencing the survival, reproduction and life table parameters of insect herbivore. Understanding of population dynamics of insect pests is possible with the construction of life tables. These life table parameters are dynamic and function of various factors and differ with temperature [6], larval host and diet and was reported with lepidopteran insects [7]. Significant variation of life table parameters of aphids with respect to temperature in case of Aphis glycines in soybean [8] and with eCO2 on other species of aphids [9] was reported.

No studies are available on construction of life table of A. craccivora on groundnut considering the temperature and CO2 concurrently. Hence, the studies were conducted i. to measure the effects of constant temperatures and eCO2 on life table parameters of Aphis craccivora on groundnut ii. to estimate the threshold temperatures and thermal constants and, iii. to predict the aphid pest scenarios during near and distant future climate change periods at different locations of India.

Materials and Methods

Plant growing conditions-CO2 enrichment

Elevated atmospheric CO2 concentration of 550 ± 25 ppm CO2 and ambient CO2, aCO2 (380 ± 25 ppm CO2) were maintained in open top chambers (OTC) of 4 × 4 × 4 m dimensions, constructed at Central Research Institute for Dryland Agriculture (CRIDA), (17.38°N; 78.47°E) India. Elevated CO2 concentration was maintained in two OTC chambers and experiments were conducted and compared over ambient CO2 of two OTC chambers [10]. Groundnut (JL-24) seeds were sown in the month of June 2015 in OTCs and crop plants were raised during the entire crop season. The adults of A. craccivora were collected from infested plants of groundnut from field and maintained in the entomology laboratory of CRIDA at optimum conditions of temperature (25 ± 2°C), humidity (80 ± 5%) and with 14 L/10D cycle.

Growth and development

Feeding trials were carried out at constant temperatures (20, 25, 27, 30, 33 & 35 ± 0.5°C) and CO2 levels (550 ± 25 ppm and 380 ± 25 ppm) to study the growth and development of A. craccivora using ‘cut leaf’ method. The stock cultures were maintained in the CO2 growth chambers and reared on leaves of potted plants of groundnut. The aphids were reared individually in the petridish of 110 mm diameter 10 mm height. A group of adults of A. craccivora were placed in a closed petridishes and were maintained at six constant temperatures at 75 ± 5% relative humidity (RH) and 14L/10D hour photoperiod in CO2 growth chambers. Different sets containing thirty replications were kept for each CO2 level (380 ppm and 550 ppm). The freshly moulted adults of A. craccivora were kept individually in the petridish each consisting of a groundnut leaves and allowed for laying. The total number of aphids at each temperature was observed and various parameters viz., development time (DT) of nymph including early and late nymphs, Reproductive time (RT) of adult, total life cycle (TLC) and fecundity were recorded as per the standard procedure [11].

Degree days requirement

The data obtained from above feeding trials were analyzed to estimate the degree days/thermal constant of each stage of the aphid. Degree days requirement was calculated after considering the average development time for six temperatures tried in the experiment. Linear regression co-efficient (b) and constant (a) were estimated after plotting the reciprocal of development time (development rate) over temperature. The standard formula of Y=a + bx was used to estimate the threshold development (T0) and further degree day calculation based on developmental rate [12] will enable to estimate the physiological time and same was adopted here.

The life table parameters and future pest status

The life table parameters of Aphis craccivora was estimated by adopting the TWOSEX–MS Chart software [13] by using primary parameters data of aphids on groundnut foliage from eCO2 and aCO2 independently. Non-linear equations were arrived after plotting this data against tested temperatures to estimate the thermal requirements.

The future climate data (maximum and minimum temperature- Tmax and Tmin) projections of AIB PRECIS emission scenario was considered for the period of 1961-2098 to estimate the level of pest incidence. The future period was designated as near and distant future periods (NF and DF) with 2021-2050 and 2071-2098 years respectively. The level of pest incidence during these periods were compared over base line (BL) period of 1961-1990. The future daily temperature (maximum and minimum) for 11 groundnut cultivating regions of the country was obtained using PRECIS model. Future pest status in terms of predicted life table parameters of A. craccivora at these 11 locations was estimated for the crop duration of 133 days coinciding with the rainy season of 26-44 Standard Weeks.

Statistical analysis

The data on development rate of each stage of insect pests at six constant temperatures at two CO2 conditions were analyzed by adopting two factorial design considering the temperatures and CO2 levels as main and sub-factors. The mean values of life table parameters of A. craccivora across 11 groundnut cultivating regions for the three periods viz., baseline, NF and DF were compared using two-sample t-test. SPSS version 16.0 was used for statistical analyses.

Results

Variation in growth and development

The results on variation in primary parameters of A. craccivora on groundnut at two CO2 conditions and at six constant temperatures are presented in the Table 1. Development Time (DT) was significantly influenced by first factor, CO2 (F1,29=236.50; P<0.01 ) and second factor, temperature (F5,29=342.57; P<0.01)

Temperature (  ±  0.5) Primary parameters of A.craccivora CO2 Concentrations
Elevated Ambient
20 Development Time (days) 7.40  ±  0.855Ba 9.00  ±  0.182Aa
Reproductive Time (days) 20.00  ±  0.946Aa 19.03  ±  0.182Ba
Total Life Cycle (days) 27.40  ±  0.932Ba 28.06  ±  0.253Aa
Fecundity (female-1) 57.60  ±  5.541Ac 46.70  ±  4.771Bc
25 Development Time (days) 6.43  ±  0.727Bb 7.86  ±  0.571Ab
Reproductive Time (days) 15.40  ±  0.674Ab 14.03  ±  0.182Bb
Total Life Cycle (days) 21.83  ±  1.053Bb 21.90  ±  0.607Ab
Fecundity (female-1) 67.83  ±  8.200Ab 52.83  ±  4.676Bb
27 Development Time (days) 5.20  ±  0.714Bc 7.66  ±  0.479Ab
Reproductive Time (days) 12.03  ±  0.718Ac 10.33  ±  0.546Bc
Total Life Cycle (days) 17.23  ±  1.135Bc 18.00  ±  0.870Ac
Fecundity (female-1) 84.23  ±  7.314Aa 61.56  ±  9.088Ba
30 Development Time (days) 5.10  ±  0.844Bc 6.10  ±  0.784Ac
Reproductive Time (days) 5.10  ±  0.711Ad 4.96  ±  0.587Ad
Total Life Cycle (days) 10.20  ±  1.063Bd 11.06  ±  0.944Ad
Fecundity (female-1) 22.03  ±  4.563Ad 18.23  ±  2.534Bd
33 Development Time (days) 4.06  ±  0.639Bd 5.00  ±  0.668Ad
Reproductive Time (days) 3.60  ±  0.498Ae 2.96  ±  0.454Be
Total Life Cycle (days) 7.66  ±  0.844Be 7.96  ±  0.718Ae
Fecundity (female-1) 14.86  ±  2.991Ae 6.30  ±  1.028Be
35 Development Time (days) 3.73  ±  0.784Bd 4.50  ±  0.568Ae
Reproductive Time (days) 2.96  ±  0.182Af 2.60  ±  0.571Bef
Total Life Cycle (days) 6.70  ±  0.836Bf 7.10  ±  0.844Af
Fecundity (female-1) 7.16  ±  1.577Af 5.23  ±  1.095Be
LSDp ≤ 0.01 CO2 Temperature CO2 × Temp
Development Time (days) 0.246** 0.311** 0.44**
Reproductive Time (days) 0.145** 0.272** 0.384**
Total Life Cycle (days) 0.252** 0.409** 0.578**
Fecundity (female-1) 1.312** 2.473** 3.498**

Table 1: Influence of CO2 and temperature on growth and development of A. craccivora on groundnut.

The findings of the present study indicated that DT of aphid decreased by 1–2 days as temperature increased from 20 to 35°C and more evident at eCO2. A similar trend of shortened DT of A. gossypii in cotton [14] and Rhopalosiphum maidis in barley [15] at eCO2 than ambient was reported. Sun and Ge [16] mentioned that species specific responses to eCO2 with Phloem-sucking insects (aphids) and are able to alleviate the disadvantages of eCO2 by reducing DT. The developmental rate of insect pests is highly responsive to fluctuations in temperature because of their physiological sensitivity [17]. After nymphal development, aphids exhibited increased reproductive time and were able to produce offspring for a longer period and were more evident with elevated CO2.

Increase in Reproductive Time (RT) was noticed with CO2 (F1,29=269.53; P<0.01) and a gradual reduction with temperature (F5,29=8573.25; P<0.01) whereas it was observed that reduction of Total Life Cycle (TLC) with CO2 (F1,29=31.24; P<0.01) and temperature (F5,29=5677.91; P<0.01). The interaction of both the factors was also significant on RT (F5,290=16.45; P<0.01) and TLC (F5, 290=1.90; P<0.01) of A. craccivora. The offspring production per female was also impacted by CO2 (F1,29=485.46; P<0.01) and temperature (F5, 29=1765.60; P< 0.01) considerably. A substantial increase in the production of offspring was noticed at eCO2 (84.23) over aCO2 (61.56). The higher offspring production was noticed between 20-27°C and started declining with increase in temperature (30-35°C). Significant interaction (F5,290=32.10; P<0.01) of CO2 and temperature on fecundity was evident.

In our studies the offspring production of A. craccivora (fecundity per female) was also impacted by CO2 and temperature significantly and substantial increase in the production of offspring was noticed with eCO2 (84) over aCO2 (62). Aphids are able to overcome the indirect effects of eCO2 by increasing fecundity at eCO2 [16]. Several workers reported the increased fecundity of various species of aphids viz., Myzus persicae on Triticum aestivum, Brassica napus [9] and A. craccivora on cow pea at eCO2 [11]. Increase in temperature from 20–27°C resulted in increase in production of progeny but further increased in temperature led to a reduction of fecundity and similar trend was reported by Xie et al. [15].

In the present study we tried to quantify the impact of host mediated effect of eCO2 and direct effect of temperature on A. craccivora and the corroborative evidences for it’s change in the growth and development were identified. We previously reported decreased N (3%) and increased C:N ratio (13%) and polyphenols (2%) in foliage of groundnut eCO2 and significant influence on growth and development of chewing insect herbivore (Spodoptera litura) [10]. The variation of primary parameters of aphids is attributed to change in the biochemical composition of the peanut foliage at eCO2 conditions. The documented information reveals significant impact of elevated CO2 levels on photosynthesis, growth, yield and change in biochemical constituents in crop plants including groundnut [18]. The changes in biochemical constituents in plants grown under eCO2 affect the nutritional quality of the plants, which in turn influences the consumption pattern of lepidopteran and homopteran insect herbivores [19].

Estimation of thermal constants

In the present experiment, linear regression was used to calculate the temperature threshold (X intercept), and thermal requirement (inverse of the slope) of nymph and adult stage of aphid seperately. The development rate of nymph and adult was regressed on temperature and linear regression equations were depicted in Figure 1. The thermal requirement of nymph varied from 74-102 DD on eCO2 with temperature in the range of 20-30°C as against 90-130 DD on aCO2 indicating the lower degree days requirement for completion of nymphal stage at eCO2. In contrast Adult required higher degree days of 74-231 at eCO2 with the corresponding temperatures of 20- 27°C as against 64-210 on aCO2. The mean degree day requirement of nymph (91.294 ± 9.574) and adult (149.089 ± 70.149) at eCO2 varied over aCO2 and similar trend is reflected after the summation of degree days requirement of both nymph and adult stages also at eCO2 (240.3 ± 66.6) and aCO2 (249.5 ± 64.2).

Figure 1: Relation between developement rate (DR), Reproduction rate (RR) with temperature for nymphs and adults of A. craccivora at eCO2 and aCO2.

Development rate and temperature were plotted to determine the lower development thresholds of A. craccivora at two CO2 conditions separately. The best fit linear regression equation for nymph (Y=0.009x– 0.0557, R2=0.9415) and adult (Y=0.0207x–0.4171, R2=0.8826) and thus the mean lower development thresholds for both the stages were 6.1 and 20.1°C on eCO2 foliage. In contrast on aCO2 foliage, similar and significant trends with nymph (Y=0.0077x–0.0596, R2= 0.91) and adult (Y=0.0242x–0.4962, R2=0.88) stages were noted. The mean lower development thresholds for nymph were slightly higher (7.7°C) at aCO2.

Our findings showed the lower thermal requirement for nymph and higher with adult stage at eCO2 foliage at set temperatures over aCO2 indicating the significant variation due to CO2 and temperatures of 20–35°C though the mean thermal constants of both the stages were closer to values of (150-250 DD). Present findings recorded the lower degree days requirement for completion of nymphal stage at eCO2 and might be due to shortening of DT. The lower thermal constants of A. craccivora at eCO2 conditions might be due to reduction of DT as reported earlier [20]. Kuo et al. [21] reported lower thermal constants for R. maidis from 33.15 DD for first instars to 25.96 DD for fourth instars. Similar kind of variation of 513-290 DD for soybean aphid was reported by McCornack et al. [22] in the 20-35°C temperature range.

Construction of life tables

The results on variation of lifetable parameters at two CO2 conditions are given int he Table 2 which indicated that ‘rm’ increased with increase in temperature from 20°C and later started declining from 30°C. The ‘Ro’ of A. craccivora was higher at 27°C temperature by recording 84.23 offspring at eCO2. The ‘rm’ and ‘Ro’ increased gradually with temperature and reached maximum values at 27°C. The reduction of ‘T’ was evident from 13.41 days at 20°C to minimum of 5.91 days at 35°C and followed the non-linear trend at eCO2. The ‘λ’ which is the indicator of reproductive value of aphid was found to be highest 1.61 at 27°C and followed the decreasing trend with an increase in temperature.

Temp ( ±  oC) rm Ro T λ
eCO2 aCO2 eCO2 aCO2 eCO2 aCO2 eCO2 aCO2
20 0.281 ± 0.010
(0.000104)
0.249 ± 0.007
(0.000062)
43.730 ± 4.486 (20.12461) 41.870 ± 2.807 (7.88291) 13.410 ± 0.214 (0.046) 14.950 ± 0.354  (0.125) 1.3254 ± 0.013 (0.000182 ) 1.283 ± 0.010 (0.000103)
25 0.361 ± 0.006 (0.000047) 0.285 ± 0.006 (0.000042) 63.830 ± 3.516 (12.36653) 48.700 ± 3.126
( 9.7729)
11.500 ± 0.145 (0.021) 13.600 ± 0.178  (0.032) 1.435 ± 0.009 (0.000097) 1.330 ± 0.008 (0.000073)
27 0.478 ± 0.008
(0.000073)
0.351 ± 0.005
(0.00003)
84.230 ± 1.324 (1.75387) 61.570 ± 2.339 (5.47298) 9.260 ± 0.169 (0.029) 11.710 ± 0.174  (0.03) 1.613 ± 0.013 (0.000191) 1.432 ± 0.007 (0.000061)
30 0.396 ± 0.0126 (0.000161) 0.359 ± 0.012 (0.000153) 31.270 ± 1.709 (2.92128) 18.830 ± 1.318 (1.73888) 7.710 ± 0.181  (0.033) 8.160 ± 0.2  (0.04) 1.486 ± 0.018 (0.000354) 1.400 ± 0.017 (0.000314)
33 0.219 ± 0.026 (0.000683) 0.239 ± 0.020
( 0.000421)
13.000 ± 1.832 (3.35625) 5.070 ± 0.662 (0.43843) 6.120 ±  0.186 
( 0.035)
6.790 ±  0.17 (0.029) 1.32 ± 0.039 (0.001561) 1.270 ± 0.025 (0.000671)
35 0.138 ± 0.041 (0.001706) 0.157 ± 0.038 (0.001511) 2.270 ± 0.512 (0.26307) 2.800 ± 0.232
(0.45168)
5.910 ± 0.236 (0.056) 6.540 ±  0.232 (0.054 ) 1.148 ±  0.046 (0.002181) 1.170 ± 0.044 (0.002003)

Table 2: Mean ± standard error of life table parameters of A. craccivora on groundnut at six constant temperatures and two CO2 conditions.

The results on non-linear models developed at eCO2 condition for four life table parameters viz., ‘rm’, ‘Ro’, ‘T’ and ‘λ’ were depicted in Figure 2. The best fit quadratic form of equation wirh higher R2 (0.89) at eCO2 was noticed between‘rm’ and temperature. Other parameters viz., ‘Ro’, ‘T’ and ‘λ’ followed the similar trend. When the first order derivative of the equation is taken as ‘Zero’, the temperature at which higher ‘Ro’ was estimated to be 25.15°C on eCO2 foliage as against 23.62 (aCO2) and later started declining. The rm and λ showed declining trend at about 26 at eCO2 and similar non-linear trends were observed at aCO2 which are as follows(rm=–0.002x2 + 0.132x–1.418, R2=0.82), (Ro=–0.428x2 + 20.221x–188.57, R2=0.80), (T=0.007x2–0.238x + 23.04, R2=0.94) and (λ=–0.003x2 + 0.166x–0.813, R2=0.85). When the first order derivative is equated to ‘Zero’ and to solve the ‘x’ (variable) the rm and λ started declining at 33.05°C and 27.66°C on aCO2 foliage and found to be higher than eCO2.

Figure 2: Relationship between temperature and life table parameters of A. craccivora on groundnut at eCO2 and aCO2.

The findings of the present study indicated the increased ‘rm’ and ‘Ro’ with reduced and were proportional to temperature from 20°C-30°C and later started declining and was more evident with eCO2. Similar non-linear trend was noticed by Kuo et al. [21] at eCO2 over aCO2. Similar observations of Increased ‘Ro’ and reduction of ‘T’ were reported in case of Myzus persicae [9] and Rhopalosiphum maidis [15]. In our study eCO2 influenced the ‘rm’ of A. craccivora which was contradictory to Flynn et al. [23] who reported that ‘rm’ of R. padi and M. persicae did not increase significantly due to eCO2.

Future pest status

Across 11 groundnut cultivating regions of the country, it is predicted that substantial increase of Tmax and Tmin by 1.8-4.4°C would occur during NF and DF climate change scenarios which inturn would result in rising of mean temperatures by about 2-4°C higher than BL. The quantified associations of life table parameters with temperature at two CO2 conditions were additionally adopted for predicting the future pest status during NF and DF scenarios. The ‘rm’ values increased during NF (1.289) and DF (1.307) climate change periods when compared to baseline period (0.746) at Vridhachalam location and similar increase was predicted at at majority of locations compared to the baseline. Results on per cent change in predicted ‘rm’ and ‘T’ of A. craccivora at eleven groundnut cultivating locations during climate change scenarios were depicted in Figure 3. The per cent change in ‘rm’ was predicted to be significantly higher at all locations during both NF (up to 79.75 %) and DF (up to 98.75 %) periods.

Figure 3: Percent change in pest scenarios (R0 and T) during NF & DF climate change periods over baseline.

It was predicted that generation time (T) of aphids would decrease at Vridhachalam (6.77 days), Kadri (8.37 days) and Bhubaneswar (8.46 days) during NF while an increased generation time was predicted at rest of locations over BL. The reduction of ‘T’ by 5.76- 9.74 days was observed at all eleven locations studied during DF period over BL. The highest percent reduction of generation time ‘T’ is expected to be in DF (up to 37.86 %) than NF period (up to 26.95 %) and shift was also noticed. At majority of locations, λ and Ro was expected to increase in both NF (23.29 %) and DF (27.12 %) periods.

The other life table parameter (Ro) would be higher during both NF (66.21) and DF (64.58) periods over baseline (49.96) and the ‘λ’ recorded increasing trend in NF (1.74-1.81) and DF (1.64-1.81) periods over baseline (1.41-1.48) at eleven locations studied implying more number of females per female of A. craccivora per day. The ‘λ’ recorded increasing trend in NF and DF periods over baseline at all eleven locations studied and ‘Ro’ would be varied during future climate change periods and similar kinf of prediction was done for leaf miner [24]. The ‘T’ of insect pests is expected to decrease significantly during NF and DF periods leading to occurrence of more number of generations of Cydia pomonella [25], S. litura and H. armigera [7,26] during climate change periods.

Conclusions

The growth and development of A. craccivora was significantly influenced by temperature and the CO2 condition under which host plants were grown. Both lower and upper threshold temperatures were identified and the higher level for the growth of the pest is at 27°C temperature. It was noted that variation of thermal requirement of A. craccivora on groundnut during future climate change period. Our findings on future pest status based on PRECIS A1B showed increased ‘rm’ and ‘λ’ with varied ‘Ro’ and reduced ‘T’ of A. craccivora at 11 groundnut cultivating regions of India. These findings suggest that pest incidence would be higher during future climate periods. Mostly the impacts of climate change on insect pests are complex and confounding in nature and elaborative studies are required to comprehend further.

Acknowledgments

This work was financially supported by grants from the Indian Council of Agricultural Research (ICAR), New Delhi in the form of National Initiative on Climate Resilient Agriculture (NICRA) Project. Authors are thankful to Prof. Dr. Hsin Chi Laboratory of Theoretical and Applied Ecology, Department of Entomology, National Chung Hsing University, Taichung, Taiwan, Republic of China, for providing a computer programme on ‘Age-Stage, Two–Sex life table analysis’.

References

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