The great variety in plant form that we see is due to differential growth. It determines the "global" structure of the plants around us. The growth of different parts of an organism is coordinated in such a way that a particular shape or form is produced. Within a given organ, its dimensions grow differentially but in a coordinated pattern. As development proceeds, the relationships between the parts and dimensions of that organ may change progressively and thereby produce differences in form.

      A very common pattern of differential growth is seen in the short-long-short pattern of internodal growth. Some plants have group of leaves clustered together, without elongation, followed by a stretch of elongation. Although these clusters may appear to be a whorl of leaves, closer inspection reveals spiral phyllotaxy with no internodal elongation as in Galium.

      Another common pattern is the absence of internodal elongation which causes clumps of leaves to form rosettes. A good example of a rosette is the common dandelion.

      Bananas and leeks both produce pseudostems in which the apical meristem is located very near the bottom of the plant. The apical meristem produces leaves in succession without any internodal elongation. The collection of leaf bases forms the structure that appears to be the stem.

      An interesting pattern of differential growth occurs in Psilotum when a shoot becomes reproductive. The stem becomes thicker in the fertile portion of the stem and once the shoot returns to a vegetative state, the shoot returns to its thinner dimension.

Allometry

      Allometry is the quantitative study of changes in various parts of an organism as a result of differential growth. It allows one to describe how growth of different parts or dimensions is coordinated. If growth occurs in all dimensions at the same rate, the initial form is replicated.

      If growth is greater in one dimension than another, the final form is different from the initial form.

      Since growth is usually exponential, the relationship between the sizes of two structures or the dimensions of one structure growing in different planes at different rates can be plotted as logarithms of their values against each other. If the absolute values are different but the relationship between them is constant, these values will fall along a straight line, the slope of which measures the growth of one structure relative to another. In most case where two parts of the same growing system or two dimensions of a growing organ are compared, their relative rates are found to be constant, no matter how different their absolute rates may be. Where such a ratio is maintained between different parts of an organism, its growth is said to be allometric. This relationship can be expressed mathematically by the following allometry formula.

      If x and y represent the sizes of two parts growing allometrically, and k equals the ratio of their growth rates, then the formula which expresses this relationship is y = bx^k where b is a constant (b = the value of y when x is taken as unity) this equation may also be written taking logarithms, as follows: log y = log b + k log x If both parts or dimensions are growing at equal rates, the slope of the line is a 45 degree angle and k =1. This would be an example of simple proportional growth. On the other hand, if y grew at a more rapid rate than x, then the slope of the line would be greater than one, whereas if the dimension y grew at a rate less than x, then the slope would be less than one.

Examples:

      When comparing two structures using allometry, it is important to use measurements of homologous structures, otherwise the results will be meaningless.