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Insect herbivores can affect plants directly, through removal of biomass, and indirectly, through altering competition with other plants. I examined both direct and indirect effects of herbivory in field and greenhouse studies, and I experimentally separated such factors as competition, levels of herbivory, and plant compensation in response to damage. In a field experiment, I tested whether insect herbivores facilitate the invasion of an introduced species, Hypericum perforatum, through damaging neighboring native plants and giving H. perforatum a competitive edge. In the site studied, herbivores did not significantly affect Hypericum or its neighbors; hence they did not benefit juvenile or adult H. perforatum indirectly. In a second field experiment, I found that competition reduced the emergence and survival of the seedlings of three old-field species. Insect herbivores had differential effects, reducing H. perforatum survival in the absence of competitors, reducing Monarda fistulosa survival in the presence of competitors, and having no effect on Achillea millefolium. Thus, Hypericum is more vulnerable to insect herbivores as a seedling than as an adult. Productivity is hypothesized to cause increased herbivory but also to increase the ability of plants to compensate for damage. These two opposing effects are confounded in most field experiments. I isolated plant compensation by controlling the amount of herbivory across productivity levels with artificial defoliation. In greenhouse experiments, I found that compensation for leaf damage by morning glory, Ipomoea tricolor, did not change with fertilization. However, compensation was greater in the fall in the greenhouse, when plants grew faster, than in the winter. These results indicate that productivity gradients are complex and different factors may cause different responses to herbivory. Different responses to herbivory along gradients was also found in a field experiment with Solidago juncea. Fertilizer increased plant compensation for damage whereas a natural gradient in site productivity had no effect. None of these studies showed any effects of herbivory on plant competitive ability. Together these studies demonstrate that plant responses to herbivores and competition are conditional but not interacting. Different types of productivity gradients influence plant compensation in individual ways.

An injection technique, in which undisturbed soil cores are labelled with ³²P to study dissolution of phosphate fertilisers in the soil, was evaluated in field and glasshouse trials. When ³²P was injected between 0-150 mm depths of the undisturbed soil columns and fertilisers applied at the surface, the amounts of fertiliser P dissolved, as measured by the increases in the exchangeable P pools, were overestimated. Three possible reasons were suggested: (i) the interaction between surface-applied fertiliser, ³²P injected through the whole soil column, and the vertical decline in root density, (ii) the decline of specific activity in the exchangeable P pool due to losses of ³²P to nonexchangeable P pools and continuous addition of P from fertiliser dissolution, and (iii) non-uniform distribution of ³²P vis-a-vis ³¹P phosphate. The injection technique may be employed to assess the effectiveness of phosphate fertilisers by introducing a concept, the fertiliser equivalent (FE). The FE is a measure of the amounts of soil exchangeable P that the fertilisers are equivalent to in supplying P to plants, when applied at the specific location. Soluble single superphosphate (SSP) applied at the surface of undisturbed grassland soil cores (Tekapo fine sandy loam), was much more effective than surface-applied unground North Carolina phosphate rock (NCPR) and 30% acidulated NCPR with phosphoric acid (NCPAPR) within the 56 day period of plant growth. An isotopic dilution method, based on tracer kinetic theory, was developed to study the rates of dissolution (F in) and retention (F out) of phosphate fertilisers in the soil in growth chamber experiments. The estimation of F in and F out required labelling of the soils with carrier-free ³²P and determination of the corresponding values of the specific activities of the exchangeable P pools, SA₁ and SA₂, and the sizes of the exchangeable P pools, Q₁ and Q₂, at times t₁ and t₂. Most of the phosphate in the monocalcium phosphate (MCP) solution entered the exchangeable P pool immediately after addition to the soils (Tekapo fine sandy loam and Craigieburn silt loam), and there was little further phosphate input. With increasing periods of incubation, the phosphate was quickly transformed to less rapidly exchangeable forms. In the soils treated with ground North Carolina phosphate rock (

This paper presents a mathematical study of the control of a second order plant having real distinct roots by use of pulse -width-modulation. An integrator connected between the pulse-width-modulator and the plant is a fixed element of the control loop. The integral-square error is used as the Index of performance. The ISE is minimized with the constraint that the pulse modulator is limited to a maximum of one output reversal for a step change in input. Derivation of the equation which will predict the exact switching time of the modulator output to minimize the performance index for any step amplitude is presented. An example problem is worked to illustrate the use of the switching equation in determining switching time. The example is concluded with graphs showing the optimal plant response for various step input amplitudes, variation of switching time as a function of step amplitude, and variation of integral-square error as a function of switching time.