### Model Matematika Pengisian Gabah dari Malai Primer dan Sekunder

Rizky Tirta Adhiguna, Sutrisno Sutrisno, Sugiyono Sugiyono, Ridwan Thahir

#### Abstract

Abstract
The present work aimed to develop mathematical model of grain filling of rice from primary and secondary branches within a panicle with increment to their weight (dry basis)-time after anthesis relationships. Three growth models for grain filling of rice were developed follow the exponential, the logistic and Gompertz functions. The grain filling models are expressed with parameters of mass at time zero, mass at time infinity and a measure for relative grain filling rate. Application of all models using data of thousand grain mass (dry basis) of rice from different branches within a panicle for Sintanur and IPB-4S variety were collected every 4 days during 14-30 days after anthesis. Model selection was conducted using Coefficient determination (R2), Root mean square error (RMSE) and Aikake’s Information Criterion (AIC). R2, RMSE and AIC values for the Gompertz models were 0.999, 0.224, -9.949 (rice from primary branch for Sintanur); 0.997, 0.353, -4.512 (rice from secondary branch for Sintanur); 1.000, 0.131, -16.376 (rice from primary branch for IPB-4S) and 0.999, 0.266, -7.877 (rice from secondary branch for IPB-4S) respectively which revealed that the
Gompertz model was considered best to described the increment thousand grain mass (dry basis) of rice from different branches within a panicle for all two varieties.

Abstrak
Penelitian yang dilakukan bertujuan mengembangkan model pengisian gabah dari tingkat malai yang berbeda, terkait dengan terjadinya peningkatan bobot gabah dalam bentuk basis kering dan bertambahnya
waktu pengisian gabah setelah anthesis (pembungaan). Penelitian ini mengembangkan model berdasarkan tiga fungsi pertumbuhan yaitu fungsi eksponensial, logistik dan fungsi Gompertz dalam pengisian gabah.
Persamaan yang diperoleh memiliki parameter bobot gabah awal, bobot gabah akhir dan laju pengisian gabah relatif. Penelitian ini menggunakan data primer berat 1000 butir gabah dalam bentuk basis kering (bk) dari malai primer dan sekunder di kedua varietas Sintanur dan IPB-4S, dari hari ke-14 sampai hari ke-30 setelah pembungaan dengan interval waktu 4 hari. Pemilihan model dilakukan dengan uji kesesuaian menggunakan koefisien determinasi (R2), Root mean square error (RMSE) dan Aikake’s Information Criterion (AIC). Nilai R2, RMSE, AIC pada model Gompertz untuk masing-masing berat kering gabah dari malai primer dan sekunder secara berturut-turut adalah 0.999, 0.224, -9.949 dan 0.997, 0.353, -4.512 (varietas Sintanur), 1.000, 0.131, -16.376 dan 0.999, 0.266, -7.877 (varietas IPB-4S), sehingga dari nilai yang dihasilkan menunjukkan bahwa model Gompertz merupakan model yang terbaik untuk pengisian
bobot 1000 butir gabah (bk) dari malai primer dan sekunder di kedua varietas Sintanur dan IPB-4S.

#### Keywords

Matematical, models, grain filling, rice, branches

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