곤충의 온도발육모형은 해충의 발생예찰모형을 비롯한 개체군모형에서 기본이 되는 요소이다. 본고에서는 곤충의 온도의존적 비선형 발육 모형에 대하여 고찰하였다. 모형의 종류를 크게 경험모형과 생물리적 모형으로 구분하였으며, 수식의 유사성 내지 기원에 대한 유연관계에 따라 세분하였다. 발육률 곡선의 형태적 묘사에 적합한 수식을 적용하는 경험모형은 Stinner-계열, Logan-계열, 수행모형, 그리고 베타 분포모형으로 세분화하여 고찰하였다. 촉매반응을 바탕으로 하고 있는 생물리적 모형은 Eyring-모형, SM-모형, SS-모형, SSI-모형으로 이어지는 단계통으로 분류하였다. 본 연구에 포함된 각 모형의 개발과정과 형태적합 특성에 대하여 기술하였다.

기장테두리진딧물의 온도의존적 발육과 산자(산란) 특성을 구명하기 위하여 6개의 항온조건(10, 15, 20, 25, 30, 35±1.0℃, RH 50~70%, 16L:8D)에서 실험을 실시하였다. 약충의 발육기간은 10℃에서 42.9일과 30℃에서 4.7일로 온도가 증가할수록 발육기간이 감소하였 다. 약충은 35℃에서 2영기 이후 성충까지 발육하지 못하였다. 선형모형 결과 약충의 발육영점온도는 8.3℃, 발육 유효적산온도는 101.6DD 이 었다. 약충 발육율과 온도와의 관계는 비선형 Lactin 2으로 잘 설명되었다. 약충 발육기간의 분포는 Weibull 함수를 이용하여 분석하였다. 성충 수명은 온도가 증가함에 따라 감소하였는데, 15℃에서 24.0일, 30℃에서 4.3일의 범위에 있었고, 10℃에서 비정상적으로 수명이 짧았다 (11.1 일). 총산자수는 20℃에서 38.2마리로 최대값을 보였고, 10℃에서 3.4마리로 최소값을 나타냈다. 본 실험의 결과를 통하여 무시 성충의 산자모 형을 작성할 수 있는 온도별 총산자수 모형, 연령별 누적생존율 모형, 연령별 누적 산자율 모형 및 생리적 연령 계산을 위한 성충 노화율 모형을 제 시하였다.

The growth, differentiation, development and fecundity of insects are influenced by temperature. The relationship between the development rate of insect and temperature has been studied since 1978 in Korea. The relationship between temperature and insect development was published in the Korean Journal of Applied Entomology (71 papers). The contents about Hemiptera, Lepidoptera, Coleoptera, Diptera, Hymenoptera, Acarina and Neuroptera were published in 27, 16, 7, 6, 4, 5, and 2 papers of the journal. Approximately 33 functions from many international journals were published to figure out the relationship between temperature and development rate of insects. The functions have been developed based on two principal ways – simplified analytic method and biophysiological approach. The empirical models are based on the law of total effective temperature and heat summation. The biophysiological models are based on the equations of Arrhenius and Eying. The thermal constant and lower temperature threshold are estimated using linear functions. The minimal and maximal development rate are presented by nonlinear equations. The Sharpe-Schoolfield-Ikemoto (SSI) model showed the intrinsic optimal temperature. Cumulative proportion of development completion for each life stage of insects was analyzed using Weibull and sigmoid functions. We discussed the application and implication of linear and non-linear temperature dependent development models.

갈색날개매미충(Ricania sp.)은 블루베리에서 흡즙에 의한 양분손실과 감로로 인한 그을음을 유발하고, 암컷 성충은 1년생 가지의 목질부 속에 산란하여 가지를 고사시키는 해충이다. 본 연구는 갈색날개매미충 월동 알들의 실내 온도발육 실험과 노지에서 약충의 부화 시기 조사를 위하여 실시하였다. 충남 예산의 노지재배 블루베리에서 갈색날개매미충 난괴를 채집하여 10, 14, 18, 22, 26, 30, 34℃ (14L:10D) 조건하에서 매일 부화하는 약충수를 조사하였다. 전혀 부화하지 않은 10℃ 처리구를 제외한 월동 난괴의 온도별 부화소요기간은 평균 107.1, 54.5, 33.9, 25.3, 25.1, 16.7일로 온도가 높을수록 짧아졌고 부화율은 23.1, 30.8, 13.8, 21.7, 11.9, 0.6%로 조사되었다. 노지에서 정확한 부화시기 조사를 위하여약충으로 부화하자마자 끈끈이트랩에 포획되도록 클립케이지를 설치하여 3~4일 간격으로 포획된 약충수를 조사하였다. 약충은 5월 19일과 22일 사이에 처음 발견되었으며 평균 19.6%의 부화율을 보였다. 조사한 40개의 피해 가지 중 15개의 가지에서는 약충이 전혀 부화하지 않았다.

갈색거저리의 온도에 따른 유충 발육시험을 15, 17, 20, 22, 25, 28 및 30℃의 7개 항온조건, 광주기 14L:10D, 상대습도 60~70% 조건에서 수행하였다. 유충은 13령까지 경과하였고 항온 조건에서 사망률은 17, 20℃에서 극소수 개체만이 발견되었고, 22℃ 이상의 항온조건에서는 발견되지 않았다. 유충의 발육기간은 17℃에서 244.3일로 가장 길었고, 30℃에서 110.8일로 가장 짧았다. 15℃는 부화되지 않아 유충 발육 조사가 불가능하였다. 온도와 발육율과의 관계를 알아보기 위하여 선형모형과 비선형모형(Logan 6)을 이용하였으며, 선형모형을 이용하여 추정한 전체유충의 발육영점온도는 6.0℃, 발육 유효적산온도는 2564.1DD 였으며 선형, 비선형 모두 결정계수값(r2) 이 0.95로 높은 값을 보였다. 전체유충의 발육완료분포는 2-parameter Weibull 함수를 사용하였으며 전체 유충의 결정계수 값은 0.8502~0.9390의 양호한 모형 적합성을 보였다.

썩덩나무노린재(Hemiptera: Pentatomidae)의 발육을 15, 20, 23, 25, 30℃에서 조사하였다. 종령기까지 발육을 완성한 온도는 20℃와 23℃이었다. 20℃와 23℃에서 약충기간은 각각 46.9일과 35.5일이었으며, 1령 기간이 가장 짧고 5령기간이 가장 길었다. 실험에 사용한 최저 온도인 15℃에서는 2령까지, 30℃에서는 4령까지 발육하는 동안에 모든 개체가 사망하였다. 암수 성충의 수명은 20℃에서는 각각 53.6일과 45.3일이었고, 23℃에서는 각각 50.1일과 68.1일이었다. 암컷 당 총 산란수는 20℃에서는 135.8개, 23℃에서 242.9개이었다. 알에서부터 성충우화까지 필요한 평균 적산온도(발육영점온도 13.94℃ 적용)는 20℃와 23℃에서 각각 314.5 일도와 367.8 일도이었다. 그 외에 약충의 각 령기별 발육기간과 사망율, 산란전기간과 산란후기간, 산란횟수별 산란수, 알에서 산란전기간까지의 적산온도 등이 조사되었다.

흰등멸구, Sogatella furcifera (Horvath), 의 온도에 따른 알 및 약충 발육 기간을 12.5~5±1℃범위에서 2.5℃ 간격으로 10개 항온, 14:10(L:D) h 광, 상대습도 20~30% 조건에서 조사하였다. 알은 12.5℃를 제외한 모든 온도 조건에서 1령으로 성공적으로 발육하였으며, 1.5℃에서 22.5일로 가장 길었고, 32.5℃에서 5.5일로 가장 짧았다. 약충은 15~32.5℃ 온도범위에서 성충까지 발육 가능하였으며, 약충 전체 발육기간은 15℃에서 51.9일로 가장 길었으며 온도가 증가함에 따라 짧아져 32.5℃에서 9.0일로 가장 짧았다. 온도와 발육률과의 관계를 설명하기 위해 선형 및 7개의 비선형(Analytis, Briere 1, 2, Lactin 2, Logan 6, Performance, Modified Sharpe and DeMichele) 모델을 사용하여 분석하였다. 선형 모델을 이용하여 추정한 알과 약충 전기간 발육을 위한 발육영점온도는 각각 10.2℃와 12.3℃였으며 발육에 필요한 유효적산온도는 각각 122.0, 156.3 DD였다. 7가지 비선형 모델 중 Briere 1 모델이 모든 발육단계에서 온도와 발육률과의 관계를 가장 잘 설명하였다(r2= 0.88~0.99). 알 및 유충의 발육단계별 발육완료 분포는 사용된 3가지 비선형(2-parameter, 3-parameter Weibull, Logistic) 모델 모두 2령과 5령을 제외한 발육단계에서는 비교적 높은 r2(0.91~0.96) 값을 보여 양호한 모형 적합성을 보였다.

The developmental time of immature stages of Paromius exiguus (Distant) was studied at eight different constant temperatures (17.5, 20, 22.5, 25, 27.5, 30, 32.5 and 35°C) with a photoperiod of 14:10 (L:D) h on two host plants, Imperata cylinderica and Calamagrostis epigeios. On both host plants, the developmental time decreased with increasing temperatures. A significant difference in the developmental times was observed between two host plants for each nymphal stage and for the total nymphal stage as well. For completion of the total nymphal stage, the development time at 17.5 and 35°C were 69.6 and 16.6 days on I. cylinderica and 38.6 and 13.8 days on C. epigeios, respectively. The relationship between developmental rate and temperature was fitted to a linear regression model and the six nonlinear models (Lactin 1, Lactin 2, Briere 1, Briere 2, Logan 6 and Taylor). Except for the Taylor model, all of the five nonlinear models fitted the data for the total nymphal stage of the current study well, according to the high r2 value, on both host plants. The distribution of completion of each development stage was well described by the two-parameter Weibull function.

비트의 주요 해충인 흰띠명나방을 9개의 다른 온도조건(15.0, 17.5, 20.0, 22.5, 25.0, 27.5, 30.0, 32.5 및 35.0℃), 상대습도 65±5%, 광조건 16L:8D에서 발육특성을 조사한 결과, 알에서 성충 우화 전까지의 발육기간은 17.5℃에서 51.0일로 가장 길었고, 35℃에서 14.6일로 가장짧게 조사되었다. 온도와 발육율의 관계를 직선회귀에 의해 분석한 결과, 결정계수(R2) 값이 0.87 이상으로 나타났으며, 온도에 따른 발육은 직선회귀에 부합되었다. 알부터 성충 우화 전까지의 발육영점온도와 유효적산온도는 10.4℃와 384.7일도를 나타내었다. 각 태별 발육모형은 R2값이0.97～0.99로 비선형회귀식에 잘 부합되었다. 각 태별 발육누적분포와 발육기간에 대한 평균 발육기간으로 나눈 값을 Weibull 함수에 적용한 결과 r2값이 0.63～0.87이었다.

복숭아혹진딧물(Myzus persicae)의 온도에 따른 발육시험을 실내 15, 18, 21, 24, 27, 30℃의 6개 항온, 광주기 14L:10D, 상대습도 50~60% 조건과 고추 비닐하우스에서 3월 23일부터 8월 20일까지 6회 접종하여 수행하였다. 실내사망률은 저온에서는 1~2령충의 사망률이 높았고 온도가 증가할수록 3~4령충의 사망률이 높았으며 고온에서는 66.7%까지 높아졌다. 실내와 포장조건 모두 온도가 증가할수록 발육기간이 짧아지는 경향을 보였으며 포장조건 8월 접종에서 6.03일로 가장 짧았다. 온도와 발육률과의 관계를 보기 위해 선형 및 3개의 비선형 모형(Briere1, Lactin 2, Logan 6)을 이용하여 분석한 결과, 선형모형을 이용하여 전체약충의 발육영점온도는 3.0℃였으며 발육유효적산온도는 111.1DD였다. 3가지 비선형 모형중 Logan-6 모형이 전약충, 후약충 전체약충 단계에서 AIC와 BIC 값이 가장 적어 온도와 발육율과의 관계를 잘 설명하였으며, 발육단계별 발육완료분포는 3-parameter Weibull 함수를 사용하였으며 전약충, 후약충, 전체약충에서 r2 값이 0.95~0.97로 높은 값을 보여 양호한 모형 적합성을 보였으며 정식시기별 성충 발생 예측치와 포장 조사치가 일치하여 방제적기 추정에 유용하게 사용할 수 있을 것이다.

목화진딧물 (Aphis gossypii)의 온도에 따른 발육시험을 실내 15, 18, 21, 24, 27, 30℃의 6개 항온, 광주기 14L:10D, 상대습도 50∼60% 조건과 오이 비닐하우스에서 3월 23일부터 8월 20일까지 6회 접종하여 수행하였다. 실내사망률은 저온에서는 2~3령충의 사망률이 높았고 온도가 증가할수록 3~4령충의 사망률이 높았으며 고온에서 전체 사망률이 높았다. 전체 약충의 발육기간은 실내에서 15℃에서 12.2일로 가장 짧았으며 변온의 28.5℃에서 4.09일로 가장 짧았다. 온도와 발육율과의 관계를 보기위해 선형 및 3개의 비선형 모형(Briere 1, Lactin 2, Logan 6)을 이용하여 분석한 결과, 선형모형을 이용하여 전체약충의 발육영점온도는 6.8℃였으며 발육유효적산온도는 각각 111.1DD였다. 3가지 비선형 모형중 Logan-6 모형이 전약충, 후약충 전체약충 단계에서 AIC와 BIC 값이 가장 적어 온도와 발육율과의 관계를 잘 설명하였으며, 발육단계별 발육완료분포는 3-parameter Weibull 함수를 사용하였으며 전약충, 후약충, 전체약충에서 r2 값이 0.88~0.91로 높은 값을 보여 양호한 모형 적합성을 보였으며 정식시기별 성충 발생 예측치와 포장 조사치가 일치하여 방제적기 추정에 유용하게 사용할 수 있을 것이다.

The developmental time of larvae of mealworm beetle, Tenebrio molitor was studied at six temperatures ranging from 17 to 30℃ with 60~70% RH, and a photoperiod of 14L:10D. Mortality of 1st~13th larva was very low at 17 and 20℃ but did not die over 22℃. Developmental time of larva decreased with increasing temperature. The total developmental time was longest at 17℃ (244.3 days) and shortest at 30℃ (110.8 days), suggesting that the higher temperature, the faster development period. The lower developmental threshold temperature and effective accumulative temperatures for the total larval stages were 6.0℃ and 2564.1 day-degrees. The relationship between developmental rate and temperature fitted a linear model and nonlinear model by Logan-6 (r2=0.95). The distribution of completion of each development stage was well described by the 3-parameter Weibull function (r2=0.89).

 ,  , The striped fruit fly, Bactrocera scutellata, damages pumpkin and other cucurbitaceous plants. The developmental period of each stage was measured at seven constant temperatures (15, 18, 21, 24, 27, 30, and 33±1.0℃). The developmental time of eggs ranged from 4.2 days at 15℃ to 0.9 days at 33℃. The developmental period of larvae was 4.2 days at 15℃, and slowed in temperatures above 27℃. The developmental period of pupa was 21.5 days at 15℃ and 7.6 days at 33℃. The mortality of eggs was 17.1% at 15℃ and 22.9% at 33℃, Larval mortalities (1st, 2nd, 3rd) were 24.1, 27.3 and 18.2%, respectively, at 15℃, Pupal mortalities were 18.2% at 15℃ and 23.1% at 33℃. The relationship between developmental rate and temperature fit both a linear model and a nonlinear model. The lower threshold temperatures of eggs, larvae, and pupae were 12.5, 10.7, and 6.3℃, respectively, and threshold temperature of the total immature period was 8.5℃. The thermal constants required to complete the egg, larval, and pupal stages were 33.2, 118.3, and 181.2DD, respectively. The distribution of each development stages was described by a 3-parameter Weibull function.

 ,  , The developmental period of Laodelphax striatellus Fallen, a vector of rice stripe virus (RSV), was investigated at ten constant temperatures from 12.5 to 35±1℃ at 30 to 40% RH, and a photoperiod of 14:10 (L:D) h. Eggs developed successfully at each temperature tested and their developmental time decreased as temperature increased. Egg development was fasted at 35℃(5.8 days), and slowest at 12.5℃ (44.5 days). Nymphs could not develop to the adult stage at 32.5 or 35℃. The mean total developmental time of nymphal stages at 12.5, 15, 17.5, 20, 22.5, 25, 27.5 and 30℃ were 132.7, 55.9, 37.7, 26.9, 20.2, 15.8, 14.9 and 17.4 days, respectively. One linear model and four nonlinear models (Briere 1, Lactin 2, Logan 6 and Poikilotherm rate) were used to determine the response of developmental rate to temperature. The lower threshold temperatures of egg and total nymphal stage of L. striatellus were 10.2℃ and 10.7℃, respectively. The thermal constants (degree-days) for eggs and nymphs were 122.0 and 238.1DD, respectively. Among the four nonlinear models, the Poikilotherm rate model had the best fit for all developmental stages (r<, SUP>, 2<, /SUP>, =0.98∼0.99). The distribution of completion of each development stage was well described by the two-parameter Weibull function (r<, SUP>, 2<, /SUP>, =0.84∼0.94). The emergence rate of L. striatellus adults using DYMEX<, SUP>, ®<, /SUP>, was predicted under the assumption that the physiological age of over-wintered nymphs was 0.2 and that the Poikilotherm rate model was applied to describe temperature-dependent development. The result presented higher predictability than other conditions.

 ,  , Temperature-related parameters of Panonychus citri (McGregor) (Acarina: Tetranychidae) development were estimated and a stage-structured matrix model was developed. The lower threshold temperatures were estimated as 8.4℃ for eggs, 9.9℃ for larvae, 9.2℃ for protonymphs, and 10.9℃ for deutonymphs. Thermal constants were 113.6, 29.1, 29.8, and 33.4 degree days for eggs, larvae, protonymphs, and deutonymphs, respectively. Non-linear development models were established for each stage of P. citri. In addition, temperature-dependent total fecundity, age-specific oviposition rate, and age-specific survival rate models were developed for the construction of an oviposition model. P. citri age was categorized into five stages to construct a matrix model: eggs, larvae, protonymphs, deutonymphs and adults. For the elements in the projection matrix, transition probabilities from an age class to the next age class or the probabilities of remaining in an age class were obtained from development rate function of each stage (age classes). Also, the fecundity coefficients of adult population were expressed as the products of adult longevity completion rate (liiongevity) by temperature-dependent total fecundity. To evaluate the predictability of the matrix model, model outputs were compared with actual field data in a cool early season and hot mid to late season in 2004. The model outputs closely matched the actual field patterns within 30 d after the model was run in both the early and mid to late seasons. Therefore, the developed matrix model can be used to estimate the population density of P. citri for a period of 30 d in citrus orchards.

The developmental time of immature stages of Paromius exiguus (Distant) was investigated at nine constant temperatures (15, 17.5, 20, 22.5, 25, 27.5, 30, 32.5, 35±1℃), 20-30% RH, and a photoperiod of 14:10h (L:D). Eggs did not develop at 15℃, and their developmental time decreased with increasing temperatures. Its developmental time was longest at 17.5℃ (28.2 days) and shortest at 35℃ (5.9 days). The first nymphs failed to reach the next nymphal stage at 17.5 and 35℃. Nymphal developmental time decreased with increasing temperatures between 20℃ and 32.5℃, and developmental rate was decreased at temperatures above 30℃ in all stages except for the fourth nymphal stage. The relationship between developmental rate and temperature fit a linear model and three nonlinear models (Briere 1, Lactin 2, and Logan 6). The lower threshold temperature of egg and total nymphal stage was 13.8℃ and 15.3℃, respectively. The thermal constant required to reach complete egg and the total nymphal stage was 109.9 and 312.5DD, respectively. The Logan-6 model was best fitted (r²=0.94-0.99), among three nonlinear models. The distribution of completion of each development stage was well described by the 3-parameter Weibull function (r²=0.91-0.99).

Ostrinia zaguliaevi (Lepidoptera: Crambidae) causes serious damage to pods and stems of the red bean, Vigna angularis, during the second half of the reproductive developmental stage. The temperature-dependent development studies of O. zaguliaevi were performed at several constant temperatures ranging from 7℃ to 36℃ in the laboratory, in the purpose of making temperature-dependent development models in the future. Eggs and larvae of O. zaguliaevi could not develop at lower temperatures of 7~13℃. As the temperature increased, the developmental period of the immature stage decreased. The number of larval instar was variable from 5 to 8, depending on temperature. The minimum number of larval instar was observed at only 25℃. Some larvae of colonies maintained at 16~22℃ showed highly longer developmental period. At relatively higher temperatures, 34℃ and 36℃, the larval developmental rates were not slowed down, and the larval survival rates was relatively high, above 60%. The egg mortality was relatively high at 36℃. Using these temperature-dependent development data of O. zaguliaevi, preliminary linear regression equations were estimated to look for a relationship between temperature and developmental rate in egg and larval stages.

The legume pod borer, Maruca vitrata (Fabricius) (Lepidoptera: Crambidae) causes serious damage to some legume crops of genus Vigna and Sesbania in Korea. In the current study, laboratory studies on the temperature-dependent development of the insect were performed at 8 constant temperatures ranging from 13℃ to 34℃ at 3℃ intervals. Lower developmental threshold (LDT) for eggs, larvae, and pupae were calculated as 10.0, 12.5 and 13.3℃, respectively, using the linear-regression equations of the developmental rates. Degree-days required to complete a stage were estimated as 48, 187, and 94, for egg, larval, and pupal stages, respectively. The larvae couldn't survive at 13 and 16℃, and the larval survival rate was the highest at 28℃. The egg hatching rate was the lowest at 13℃. In the adult stage, the pre-oviposition period was the shortest at 22℃, and the total egg number was the most with ca. 500 at 25℃. Degree-days for the stages of 1st-4th larval instars, egg, and adult emergence-50% oviposition were calculated during the reproductive development season of red bean using single sine method and Suwon weather station data based on LDTs, respectively. Finally, the adult occurrence time was estimated after the degree-days were cumulated reversely from the distribution data of larval stages observed in a red bean field

We studied to develop a forecasting model to predict the hatching time of overwintered eggs of Lycorma delicatula. We collected overwintering egg masses on 1st February, 17th February and 4th March. After chilling them at 5℃ for 15 days, development of eggs was investigated at six constant temperature (35, 31, 27, 23, 19, 15℃). The hatching rate of egg was highest at 23℃ (87.88±19.32%) followed by 19℃ (87.71±21.47%), 27℃ (75.96±24.82%), and 31℃ (30.92±24.81%). Eggs did not survive at 35℃. The developmental duration of eggs was 39.47±2.24, 22.96±3.25, 17.56±1.58 and 12.15±6.29, at 19, 23, 27 and 31℃, respectively. The egg developmental rate was described with a linear model (eq. Y=0.0034X-0.0364 (r=0.9649)) between 19℃ and 31℃. The lower developmental threshold temperature was 10.71℃ and effective accumulated temperature for egg development was 286.40 Degree days.

The developmental time and survival of immature stages of N. californicus were studied under laboratory conditions at nine constant temperatures (12, 16, 20, 24, 28, 32, 36, 38, 40℃), 60-70% RH, and a photoperiod of 16:8 (L:D) h. The total developmental period decreased with increasing temperature between 12 and 32℃, and increased beyond 32℃. Total developmental period of immature stages was longest at 12℃ (18.38 days) and shortest at 32℃ (2.98 days). The cumulative mortality of N. californicus was lowest at 24℃ (4.5%) and highest at 38℃ (15.2%). The normalized cumulative frequency distribution of developmental times for each life stage was fitted to the three-parameter Weibull function (r2=0.91~0.93). The relationship between temperature and developmental rate was fitted by five nonlinear development rate models (Logan 6, Lactin 1, 2, and Briere 1,2). The nonlinear shape of temperature development was best described by the Lactin 1 model (r2=0.98). The determined lower developmental temperature thresholds could be used to predict the occurrence, number of generation and population dynamics of N.californicus on fruit orchards and greenhouse