Deposition gradients of urediniospores of Puccinia recondita near a source.

Aylor, D. E. 1987. Deposition gradients of urediniospores of Puccinia recondita near a source. Phytopathology 77:1442-1448. Deposition gradients of urediniospores of Puccinia recondita were gradient of the number of pustules (dN/dx)/N, or d(ln N)/dx, decreased measured using potted trap plants exposed at several distances between 0. 1 with distance x from the source. In other words, the length scale of the and 3.7 m downwind of a line source of spores in the middle of a 0.4-ha, deposition gradient increased with distance. These results are explained in 1-m-tall crop. Trap plants were exposed for 2-3 hr on 8 days encompassing terms of a derived equation that simultaneously accounts for the combined a range of average wind speeds of 2-5 m s-' measured 1.5 m above the top of effects of spore deposition and dilution by atmospheric turbulence and has the crop. After exposure in the field, the trap plants were incubated and the both an exponential and a power law component. resulting number, N, of wheat rust pustules was counted. The relative Additional key words: spore deposition, turbulent diffusion, wheat leaf rust. For aerially dispersed plant pathogens, the rate of spread of which the rate of deposition is reduced by a characteristic amount. disease from foci of infection depends, in large part, on the rate of Furthermore, B implies a constant-length scale for the deposition decrease of the numbers of spores deposited on susceptible plants gradient that is considered useful for visualizing gradients (8). with increasing distance from the source, i.e., it depends on the The relative gradients (dDp/dx)/Dp and (dDE/dx)/DE spore deposition gradient. Knowledge of spore deposition determined from equations 1 and 2, respectively, are: gradients very near to a source is important for evaluating the effect of mixtures, or of interplanting, of susceptible and resistant (dDp/dx)/ Dp = -b x 1 (3) cultivars of plants on the rate of buildup and ultimate severity of a disease epidemic (4,15,19). For these purposes, spore deposition gradients have often been described by empirical formulas fitted to (dDE! dx)/ DE = -B. (4) either primary disease gradients or spore deposition gradients (12,17,19,20). These formulas are often based on measurements Comparison of equations 3 and 4 points up a fundamental made at distances from one to several meters from the source and difference between equations 1 and 2, i.e., the exponential law require extrapolation backwards to the source to describe implies a constant-length scale (i.e., 1 / B), whereas the power law inoculation of nearest neighbors and self-inoculation of the source implies a length scale that increases with distance x. plant. In many instances, the length scale derived by fitting an Two equations most often used to model spore deposition exponential law to deposition or disease gradients depends on the gradients near ground-level sources are the power law: range of distance over which the model is fitted, and in general, the length scale gets larger as the range of x of the data increases (6,7). Dp= a x-b (1) This suggests a process whose length scale increases with x and is in accordance with a process dominated by turbulent diffusion. The and the exponential law: length scale of turbulent diffusion increases with distance from a source, as larger and larger eddies come into play. Near a source of DE = A exp(-B x). (2) spores, both deposition and diffusion processes are simultaneously important and there simply is not one length scale that describes Dp and DE are rates of spore deposition (spores per square dispersal, as is implied by equation 2. centimeter per hour) at a given distance, x, from a source, where Near a source, the combined effects of deposition and diffusion the subscripts P and E refer to the power and the exponential law, of spores must be evaluated simultaneously. One way to do this respectively, and exp is the base of natural logarithms. Throughout involves solving a partial differential equation for the conservation this article, distance x is expressed in meters so that a is the value of of numbers of airborne spores per unit volume of air in and above a Dp at x = 1 m. The exponent b is dimensionless, B has units of m'-, crop canopy (2,3,16). Unfortunately, such an equation can usually and A is the value of DE at x = 0. only be solved numerically, so the effects of the crop and wind The ability of equations 1 and 2 to describe spore deposition parameters on spore dispersal are not readily seen. gradients has recently been reexamined (7,8,18). Three main In this paper, I present measurements of deposition gradients of reasons have been advanced for preferring the use of the urediniospores of Puccinia recondita near a line source of spores exponential law (Eq. 2) over the power law (Eq. 1) to describe and compare these measurements with equations 1 and 2. I also deposition gradients. First, equation 2 predicts finite deposition at derive a theoretical equation to help clarify the relative importance x = 0 and therefore can be extrapolated to zero, whereas equation 1 of deposition and turbulent diffusion in determining deposition predicts infinite values at x = 0. Second, equation 2 accounts gradients near a source and use this new equation to discuss under conceptually for spore deposition, whereas equation 1 does not. what conditions an exponential law, a power law, or neither law Third, B, unlike b, automatically carries with it explicit can be expected to describe spore deposition gradients. information about the length scale of x, i.e., the distance over MATERIALS AND METHODS Crop and inoculum. Deposition gradients of urediniospores of © 1987 The American Phytopathological Society P. recondita were measured at Mt. Carmel, CT, during June 1985