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ABOUT LOGISTIC GROWTH OF A SUNFLOWER PLANT

Individual organisms often show an S-shaped growth pattern, with rapid growth initially and little or no growth later on. S-shaped or sigmoidal growth of an individual can be caused by a number of factors. A common interpretation involves an external limit to growth based on environmental factors, such as a finite amount of food, space, or water. Growth can also be limited because of physiological factors, such as the maximum weight that bones can support.

Data on the height of a single sunflower plant as a function of time show a reasonable sigmoidal growth pattern (albeit with very fast growth early on). The sunflower grows rapidly in the first 50 days, then the growth rate slows until the sunflower reaches its maximum height of approximately 250 cm (about 8 feet tall).

Sigmoidal growth curves are often parameterized using a modified exponential model, the logistic model, where the growth rate decreases as the individual increases in size. The sunflower data fit a logistic model very well. When modelling these data, students must choose reasonable values for the initial height and initial time (very tricky!), the maximum height (pretty obvious), and the initial growth rate in the logistic model.

Analysis of sunflower growth using the logistic model could have some practical applications. For example, if you were trying to develop a fast growing sunflower hybrid that could flourish in a short growing season, the best-fit logistic model would provide quantitative results on r, the initial growth rate, for your various hybrids.

Reference: Reed, H. S. and Holland, R. H. (1919), Growth of sunflower seeds; Proceedings of the National Academy of Sciences, volume 5, p. 140.

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 Reed and Holland (1919) sunflower height versus growing days day height (cm) 0 0.00 7 17.93 14 36.36 21 67.76 28 98.10 35 131.00 42 169.50 49 205.50 56 228.30 63 247.10 70 250.50 77 253.80 84 254.50

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