4 WATER STRESS ON PLANT DEVELOPMENT
4.5 Root/Shoot Interaction
4.5.5 The Allometric Relationship
--> < root CK production
<-- < CK to shoot <---
It was noted previously that the SIR ratio is not ideal for studying root-shoot interactions because it changes with age (size of the plant) (Gales, 1 979; Richards, 1986). Thus size variation is confounded and the ratio tells one nothing about the rate of change of organ growth (Troughton, 1956). A more stable and indeed fundamental way of expressing growth and development patterns of organs from any organism is to use allometry (Gales, 1 979). Allometric relationships have been known in biology since last century but it was not until 1932 that Huxley demonstrated wide biological significance (Causton and Venus, 1981; Reiss, 1989). They have now been found at the biochemical level as well (Causton and Venus, 1 98 1). According to Szaniawski (1987) the allometric relationship "simply reflects the basic biological fact that any multicellular organism whether plant or animal can survive only if it maintains a balance between its various organs".
The most simple form of the allometric relationship is a linear trend where the following formula applies (Troughton, 1955):
Y = b x xk 4.5
Where: X = weight of organ; Y = weight of rest of organism; b, k = constants.
Neither the organ nor the organism needs to be growing logarithmically for this relationship to exist (Troughton, 1955). The allometric formula was first used by Snell in 1892 but not until Pearsall in 1927 was it applied to plant root and shoot dry weights
(froughton, 1956). This development was reiterated by Wareing (1950) and then the work developed further by Troughton (1955, 1956, 1960, 1977). Causton and Venus (1981) give a thorough mathematical treatment of both linear and curvilinear allometry based around three basic theorems. The following point should be noted from these theorems with regard to the shoot-root relationship. If there is a linear allometric relationship between any two plant parts (e.g. shoot and root) then the relationship between any part and the whole will not be linear (Causton and Venus, 1981).
The critical parameter in the allometric relationship is 'k', the exponential growth exponent which Huxley in 1932 termed the "constant differential growth-ratio" (froughton, 1956) and Hunt and Nicholls (1986) termed the "partitioning ratio
(Kp)".
Troughton (1955) concluded that "A study of the values of 'k' enabled the effect of treatments on the relative growth of the root and shoot to be far more clearly defined than did a study of the proportions of the plant" (i.e. the SIR ratio). The constants 'k' and 'b' may be found by re-expressing the allometric formula as:log(Y) = log(b) + k x log(X) 4.6
Hence a plot of log(Y) verses log(X) gives a linear relationship with slope of 'k' and y intercept of log(b). Since 'k' is proportional to (log(Y) I log(X)) i.e. log(shoot) I log(root) it is an expression of the ratio of relative growth rates of the shoot and root i.e. 'k' is proportional to RGR(shoot) I RGR(root). Under natural conditions it is root growth which is restricted (due to mechanical resistance, water deficits etc.). Hence from the allometric relationship it may be stated that the RGR of the root limits the potential for vegetative growth of above ground parts (Chalmers, 1987). If k = 1 the SIR ratio is constant, if k > 1 the SIR ratio declines with age and if k < 1 the SIR ratio increases with age (Richards, 1986).
Causton and Venus (1981) describe the hypothesis put forward by Nelders in 1963, that if 'k' is not equal to one, growth is demand limited, while if 'k' equals one, growth is supply limited. They note that as 'k' commonly does not equal one, supply limitation may be infrequent. The general range from for 'k' is between 0.3 and 3 (Hunt and Nicholls, 1986). It should be noted here ·that the value of b is difficult to interpret, being the value for the organ when the rest of the organism is u nity (froughton, 1956). The allometric constant changes with environmental conditions for a given plant (Chalmers, 1 987). However it is interesting to note that although flowering and fruiting changes k, as first documented by Pearsall in 1927 (Troughton, 1 955), the initial value of 'k' continues throughout fruiting if the weight of
reproductive parts is subtracted (Chalmers and Van den Ende, 1975; Richards, 1 981). The allometric relationship can be related to the C/N ratio (as shoots are providing carbon and roots nitrogen) such that as 'k' decreases the C/N ratio increases (Troughton, 1960).
Linear allometric relationships will exist in the vegetative phase as long as environmental conditions are constant (Scott Russell, 1 982). There are very few documented cases of curvilinear allometric relationships, the best example being from Currah and Barnes (1979). They found that individual carrot plants followed a curved path. However for any one harvest (i.e. for plants of the same age) linear relationships were found. This means that there is discontinuity between harvests for the whole population. Other examples of discontinuity as well as segmented linear allometry are given by Causton and Venus (1981).
Hunt and Nicholls (1986) conclude that "any growth limiting condition or resource will also induce a change in the resource,partitioning of the plant. This will result in proportionally increased allocation of linear size, number or mass in favour of that part of the plant which draws most upon the growth limiting p art of the environment" . Hence there are well known examples such as nutrient deficiency leading to increased 'rootiness' and shade leading to increased 'shootiness ' (Hunt and Nicholls, 1986). Water stress however is more complicated because of direct effects on both plant subsystems and a host of interactive responses.
The slope of the allometric relationship (k) has been observed to decrease in response to increasing water stress (Troughton, 1 960), nutrient stress (Hunt and Nicholls, 1 986) and light intensity (Hunt and Burnett, 1973; Hunt and Nicholls, 1 986; Troughton, 1 960).