Study on Models of Plant Growth and Fruit Development of Papaya

DAIHongfen, WUXiaming, ZHOUChenping, YANGJunxian, YANGMin, YANGMeizhen, KUANGRuibin, WEIYuerong

Chin Agric Sci Bull ›› 2026, Vol. 42 ›› Issue (21) : 132-140.

PDF(1686 KB)
Home Journals Chinese Agricultural Science Bulletin
Chinese Agricultural Science Bulletin

Abbreviation (ISO4): Chin Agric Sci Bull      Editor in chief: Yulong YIN

About  /  Aim & scope  /  Editorial board  /  Indexed  /  Contact  / 
PDF(1686 KB)
Chin Agric Sci Bull ›› 2026, Vol. 42 ›› Issue (21) : 132-140. DOI: 10.11924/j.issn.1000-6850.casb2025-0822

Study on Models of Plant Growth and Fruit Development of Papaya

Author information +
History +

Abstract

This study was carried out to investigate the patterns of plant growth and fruit development of papaya and to establish mathematical model for high-quality and efficient cultivation and promotion of new varieties. Tissue-cultured seedlings of new papaya cultivars ‘Zihui’ and ‘Huanghuayou’ were planted in March. Growth parameters such as plant height, stem perimeter, longitudinal diameter and transverse diameter of fruit were measured periodically as dependent variables. Logistic growth models were established and the independent variable was growth time. Derived functions of models were growth rate equations. Partial correlation analysis was conducted between dependent variables and independent variables such as growth time, effective accumulated temperature, cumulative sunshine duration, and cumulative relative humidity in order to choose more independent variables for multi-factor growth models. The results showed that the patterns of plants growth and fruits of papaya were “S”-shaped curves and were divided into early, fast-growth and late stage. The Logistic models demonstrated high fitting accuracy (coefficient of determination R2≥0.959). The inflection points of plant and fruit occurred in late June and early July. ‘Huanghuayou’ exhibited higher growth rate than ‘Zihui’ at first, with earlier inflection point and higher maximum growth rate (vm). vm of plant height, stem perimeter, fruit longitudinal diameter, and transverse diameter of ‘Huanghuayou’ were 1.77, 0.33, 0.26, and 0.14 cm/d, which were 1.20, 1.03, 1.04, and 1.27 times of ‘Zihui’. However, the growth rates of all parameters of ‘Zihui’ surpassed ‘Huanghuayou’ at different time after inflection points. The duration of the fast-growth stage of plant height, stem perimeter, fruit longitudinal diameter and transverse diameter of ‘Zihui’ were 113.05, 90.51, 54.09, and 65.52 days, which were 1.17, 0.97, 1.12, and 1.21 times of ‘Huanghuayou’. ‘Huanghuayou’ exhibited greater growth amount of plant height, stem perimeter, and fruit transverse diameter. ‘Zihui’ exhibited greater growth amount of fruit longitudinal diameter due to longer fast-growth stage and the earliest speed-surpassing ‘Huanghuayou’. Cumulative sunshine duration showed more highly significant influence on growth parameters (maximum partial correlation coefficient of 0.948), followed by effective accumulated temperature. Cumulative relative humidity showed little significant effect. Multi-factor models with added meteorological factors demonstrated superior fitting performance (R2≥0.992). In summary, the Logistic growth curve equations and its derivative functions could be used to simulate the growth process of plant and fruit of papaya. Growth parameters are slightly different between ‘Zihui’ and ‘Huanghuayou’. Cumulative sunshine duration and effective accumulated temperature are identified as key meteorological factors. Multi-factor growth models exhibit much better fitting performance.

Key words

papaya / Logistic equation / inflection point / fast-growth stage / growth rate / effective accumulated temperature

Cite this article

Download Citations
DAI Hongfen , WU Xiaming , ZHOU Chenping , et al . Study on Models of Plant Growth and Fruit Development of Papaya[J]. Chinese Agricultural Science Bulletin. 2026, 42(21): 132-140 https://doi.org/10.11924/j.issn.1000-6850.casb2025-0822

References

[1]
吴红丽, 刘惠民. 施肥对新平县引进番木瓜生长的影响[J]. 西南林学院学报, 2006(2):59-61.
[2]
魏岳荣, 杨护, 周陈平, 等. 优质丰产番木瓜新品种紫晖的选育[J]. 果树学报, 2022, 39(6):1129-1132.
[3]
吴夏明, 林伟, 杨敏, 等. 非转基因番木瓜新品种比较试验[J]. 中国农学通报, 2024, 40(16):63-71.
本研究旨在筛选到综合农艺性状优良,适宜在广东及相近气候产区大面积推广的非转基因番木瓜新品种。以非转基因番木瓜新品种‘紫晖’、‘黄花佑’、‘贮丰’和‘泰国红’为对象,调查其两性株组培苗种植后的物候期、植株生长势、结果特性、果实商品性、果实品质、丰产性及抗性表现,并进行比较分析。参试品种生长势旺盛,综合农艺性状在各试点表现稳定,其中‘紫晖’与‘黄花佑’番木瓜具有结果部位低、花序主轴长度中等、节位坐果率高、丰产稳产、果实一致性好、果面光滑、色泽度好等优点;‘贮丰’具有可溶性固形物含量高、丰产稳产、耐贮藏等优点;‘紫晖’、‘黄花佑’和‘贮丰’3个品种品质均表现优良。‘黄花佑’与‘贮丰’番木瓜适宜鲜食,‘紫晖’既可以作鲜食也可以作加工型非转基因优质高产型新品种,以上3个品种均适宜在广东及相近气候产区推广种植。
[4]
吴夏明, 周陈平, 杨敏, 等. 小果型非转基因番木瓜新品种黄花佑的选育[J]. 果树学报, 2024, 41(1):193-196.
[5]
尤海磊, 胡希远, 高金锋, 等. 不同荞麦品种生长模型和生长特性的比较研究[J]. 干旱地区农业研究, 2010, 28(2):53-58.
[6]
朱雨晴, 薛晓萍. 基于不同驱动因子的番茄生长模型比较[J]. 应用气象学报, 2024, 35(6):747-758.
[7]
TSOULARIS A, WALLACE J. Analysis of logistic growth models[J]. Mathematical biosciences, 2002, 179(1):21-55.
A variety of growth curves have been developed to model both unpredated, intraspecific population dynamics and more general biological growth. Most predictive models are shown to be based on variations of the classical Verhulst logistic growth equation. We review and compare several such models and analyse properties of interest for these. We also identify and detail several associated limitations and restrictions.A generalized form of the logistic growth curve is introduced which incorporates these models as special cases. Several properties of the generalized growth are also presented. We furthermore prove that the new growth form incorporates additional growth models which are markedly different from the logistic growth and its variants, at least in their mathematical representation. Finally, we give a brief outline of how the new curve could be used for curve-fitting.
[8]
WEST G B, BROWN J H, ENQUIST B J. A general model for ontogenetic growth[J]. Nature, 2001, 413:628-631.
[9]
SHI P J, MEN X Y, SANDHU H S, et al. The “general” ontogenetic growth model is inapplicable to crop growth[J]. Ecological modelling, 2013, 266:1-9.
[10]
YU Q, LIU J D, ZHANG Y Q, et al. Simulation of rice biomass accumulation by an extended logistic model including influence of meteorological factors[J]. International journal of biometeorology, 2002, 46(4):185-191.
The biomass (X) of a biological population, described by growth models, depends only on time (t), i.e., X = f(t). Some parameters in these models are frequently taken as constants, but they may vary with growth processes under different ecological conditions. An extended logistic model including changes in the influence of meteorological factors is developed to simulate biomass accumulation processes of rice sown on different dates. The model may be generally described as X = f (p, t), in which p stands for meteorological factors. The model can be used to generalize population growth processes in experiments carried out under different environments. It is shown that the model may account for 96.6% of the variance of rice biomass on the basis of sowing dates, developmental stage, solar radiation and temperature in the Yangtze River valley in China.
[11]
王莹, 王良桂, 黄成名, 等. 露地栽培条件下百合的生长规律及种球繁殖技术[J]. 中国农业科学, 2014, 47(8):1558-1566.
【目的】研究露地条件下2个类群百合的生长发育规律及其相应的种球繁殖栽培技术措施,为百合种球的高效、低成本、规模化种球生产以及景观栽培应用提供参考。【方法】本试验以卷丹(Lilium lancifolium)和Lilium ‘Yelloween’为材料,在对其进行物候期及形态发育的观测基础上,运用logistic方程和指数方程对株高和花蕾所实测数据进行曲线拟合,构建其生长发育模型,并研究摘蕾、行栽植方向及栽植密度等技术措施试验对种球重量和周径增加值的影响。【结果】卷丹所需活动积温达4 256℃,而‘Yelloween’所需积温仅为4 981.5℃。卷丹的植株高生长方程为:y=97.5949/(1+e^-(x-62.6822)/22.8819);花蕾直径的生长方程为:y=0.1578e^(0.0358x);花蕾长度生长方程为:y=90.2066/(1+e^-(x-117.1807)/8.7295),均符合logistic曲线规律;‘Yelloween’的植株高生长方程为:y=70.3771/(1+e^-(x-19.1133)/9.5840);花蕾直径的生长方程为:y=41.2215/(1+e^-(x-65.9236)/17.1028);花蕾长度生长方程为:y=158.9531/(1+e^-(x-62.9011)/9.7562),符合或近似于指数函数的增长模型。卷丹以不摘蕾效果最好,鳞茎鲜重均值为87.59g;‘Yelloween’开花当天摘蕾对种球生长效果最佳,鳞茎鲜重均值达89.71g;南北向栽植对株高和茎粗略有提高,但是差异并不显著;‘Yelloween’最佳种植密度为株行距10 cm×20 cm,产量可达26 936 kg/667m2,如果结合摘蕾结果,种球周径可较栽种前增加3个种球等级,均值达到18.93cm。【结论】2个百合品种的高生长以及卷丹花蕾直径的生长规律符合logistic曲线规律,‘Yelloween’花蕾直径符合或近似于指数函数的增长模型。卷丹以不摘蕾、‘Yelloween’以开花当天摘蕾种球的生长效果最佳;结合适宜的种植密度、行种植方向采用南北向,种球周径可增殖2—3个等级。
[12]
张彩琴, 杨持. 内蒙古典型草原生长季内不同植物生长动态的模拟[J]. 生态学报, 2007, 27(9):3618-3629.
[13]
金海湘, 龚雪, 朱报著. 大腹异木棉Ceiba insignis实生苗年生长节律研究[J]. 广东园林, 2020, 42(3):49-54.
[14]
韩树全, 罗立娜, 卢加举, 等. 贵州澳洲坚果果实发育动态及模型建立[J]. 种子, 2023, 42(4):79-85.
[15]
朱海军, 生静雅, 刘广勤, 等. 基于Logistic模型的薄壳山核桃果实生长发育研究[J]. 西南农业学报, 2015, 28(3):1231-1235.
[16]
徐回林, 陈金印, 辜青青, 等. 基于Logistic模型研究南丰蜜橘(Citrus reticulata Blanco)果实的生长动态[J]. 江西农业大学学报, 2010, 32(6):1131-1135.
[17]
黄丽云, 刘立云, 齐兰, 等. 基于Logistic模型的槟榔果实生长发育研究[J]. 热带农业科学, 2018, 38(8):105-108.
[18]
乔嘉, 朱金城, 赵姣, 等. 基于Logistic模型的玉米干物质积累过程对产量影响研究[J]. 中国农业大学学报, 2011, 16(5):32-38.
[19]
程艳, 魏尊苗, 刘佳遥, 等. 基于Logistic方程的油莎豆生长指标拟合与分析[J]. 东北农业科学, 2024, 49(4):47-51.
[20]
胡波, 李国元, 谢志兵, 等. 冬枣果实生长规律Logistic模型研究[J]. 湖北农业科学, 2015, 54(5):1114-1116.
[21]
邱宏业, 朱建华, 徐炯志, 等. 大乌圆龙眼果实发育动态及其模型的建立[J]. 西南农业学报, 2018, 31(1):149-153.
[22]
彭杰椿, 潘介春, 吴玉, 等. 桂丰早龙眼开花习性和果实生长模型研究[J]. 果树学报, 2021, 38(6):947-956.
[23]
王璐瑶, 闫锦涛, 刘涛, 等. 桃果实品质动态变化及其对气象因子的响应[J]. 农学学报, 2023, 13(11):49-54.
为提高桃品质并确定最佳采收期,以‘久保’为供试材料,分析果实的单果重、果径、硬度、可溶性固形物含量和可滴定酸含量的变化规律,并利用多元回归法建立果实品质与关键气象因子的综合模型。结果表明:桃果实单果重和果径生长发育动态呈现“慢—快—慢”阶段性特征,且均符合Logister曲线,单果重增长极大值出现在花后91 d,纵径增长极大值出现在花后66 d,横径增长极大值出现时间比纵径推迟5 d;随着果实的成熟,硬度逐渐下降,可溶性固形物含量呈上升趋势,上升幅度逐渐加快,可滴定酸含量先小范围波动后迅速下降。结合回归分析结果可判定,果实品质主要受≥18℃积温、≥24℃积温、日均气温和累计日照时数的共同影响。在≥18℃积温≥1170.21℃、≥24℃积温≥769.23℃、日均气温≥27.00℃、累计日照时数≥318.89 h条件下,果实品质达到最佳成熟度。
[24]
杨丽丽, 王一鸣, 康孟珍, 等. 基于修正Logistic模型的番茄单个果实生长规律模拟[J]. 农业机械学报, 2008, 39(11):81-84.
[25]
李建明, 邹志荣, 刘迎春, 等. 温度与水分驱动的甜瓜幼苗生长形态模拟模型研究[J]. 农业工程学报, 2006, 22(11):203-208.
[26]
华南农业大学, 广州市果树科学研究所, 农业部科技发展中心. NY/T2519-2013,植物新品种特异性、一致性和稳定性测试指南番木瓜[S]. 北京: 中国农业出版社,2013:2.
[27]
戴宏芬, 李俊成, 孙艺洪, 等. 大红火龙果正造果与反季节果生长发育的比较研究[J]. 广东农业科学, 2022, 49(8):46-53.
[28]
李春喜. 生物统计学(第四版)[M]. 北京: 科学出版社,2008:151,225.
[29]
马鹏里, 蒲金涌, 赵春雨, 等. 光温因子对大田冬小麦累积生物量的影响[J]. 应用生态学报, 2010, 21(5):1270-1276.
[30]
王健, 郑维, 喻树龙. 红花光温指数对其生育期及产量的影响研究[J]. 中国生态农业学报, 2003, 11(4):12-14.
[31]
陈青君, 林成, 秦勇, 等. 温光条件对冬茬黄瓜生长发育及产量形成的影响[J]. 中国蔬菜, 1996(5):6-9.
[32]
曹广才, 吴东兵, 张成琦, 等. 我国地理条件下日长与温度之间的相关性及其对小麦生育的影响[J]. 西南农业学报, 1990, 3(4):47-55.
[33]
杜军. 气候因子对青稞千粒重影响的研究[J]. 生态农业研究, 1998, 6(4):47-49.
[34]
郭荣荣, 成果, 陆正义, 等. 有效积温和光照时数对桂南一年两收栽培模式下巨峰和夏黑葡萄物候期的影响[J]. 南方园艺, 2016, 27(6): 18-20.
[35]
LIN D Y, WEI R H, XU L H. An integrated yield prediction model for greenhouse tomato[J]. Agronomy, 2019, 9(12):873.
[36]
ASSADULLAH U, ISLAM M M. Fitting a logistic model for yield estimation of aus rice[J]. Journal of the Bangladesh agricultural University, 2017, 15(1):141-146.
[37]
NGUYEN T T H, NGUYEN T V. Using Logistic regression models for predicting rice yield in the Mekong Delta, Vietnam[J]. Journal of the science of food and agriculture, 2019, 99(14): 6469-6474.
[38]
张京伟, 孙纪霞, 郭文姣, 等. 蝴蝶兰叶片生长曲线与环境积温的关系研究[J]. 中国农学通报, 2016, 32(1):113-117.
为研究蝴蝶兰生长发育与环境积温之间的关系,运用纸片法、校正系数计算和线性回归分析法对蝴蝶兰叶面积计算公式进行优化,进而建立蝴蝶兰叶片生长速率曲线,并对曲线进行拟合和分析。研究结果表明,蝴蝶兰营养生长期间叶片总面积S 与积温T 呈二次函数关系,数学模型为S=0.043T2+21.36T+215.60。生长模型能较好地反映蝴蝶兰叶片营养生长期内的生长动态变化。运用生长模型对蝴蝶兰叶片生长量进行生长曲线的拟合和分析是可行的。
[39]
SINNATHAMBY S, DOUGLAS-MANKIN K R, CRAIGE C. Field-scale calibration of crop-yield parameters in the Soil and Water Assessment Tool(SWAT)[J]. Agricultural water management, 2017, 180:61-69.
[40]
PAREDES P, TORRES M O. Parameterization of Aquacrop model for vining pea biomass and yield predictions and assessing impacts of irrigation strategies considering various sowing dates[J]. Irrigation science, 2017, 35(1):27-41.
PDF(1686 KB)

Accesses

Citation

Detail

Sections
Recommended

/

〈 〉