Using mathematical models to evaluate germination rate and seedlings length of chickpea seed (Cicer arietinum L.) to osmotic stress at cardinal temperatures

Cicer arietinum is the 3(rd) most important cool season legume crop growing in vast arid and semi-arid regions of the world. A lab experiment was designed using hydrothermal time model (HTT) to investigate the chickpea seed germination (SG) behavior, cardinal temperatures and germination responses across fluctuating temperatures (T(s)) and water potentials (Ψ(s)). Seeds of chickpea var. NIFA 1995 were germinated at six constant T(s) (7, 14, 21, 28, 35 and 42°C) each having the following five water potentials: 0, -0.2, -0.4–0.6 and -0.8 MPa. Germination percentage (G%) decreased significantly at (*P ≤ 0.05) from 86.7% at 28°C in -0.2 MPa to 10% in -0.2 MPa at 7°C. The germination rate (GR = 1/t(50)) against different T percentiles exhibited that linear increase was observed in the GR pattern above and below the T(o.) Based on the confidence intervals of the model coefficients and (R(2): 0.96), the average cardinal temperatures were 4.7, 23 and 44.2°C for the base (T(b)), optimal (T(o)) and ceiling (T(c)) temperatures respectively. θT1 value was observed maximum at 28°C in -0.2 MPa and decreases with decreasing Ψ (-0.8 MPa). In comparison with control, the θT2 value was also highest in -0.2 MPa at 28°C. The thermal time (TT) concept is well fitted to germination fraction data in distilled water with an R(2) value increasing 0.972. The hydro time constant (θH) increased with an increase in T to T(o) and then decreased when T>T(o). The ѱ(b(50)) irregularly varied with increasing T, σΨ(b) was also recorded lowest (0.166 MPa) at 28°C and highest (0.457 MPa) at 7°C. Based on the statistical analysis, cardinal temperatures, hydrothermal time constant (θHTT) and germination findings the HTT gives an insight into the interactive effect of T and Ψ on seed germination time courses under varying environmental conditions.