MODEL FOR DISPERSAL AND EPIPHYTIC SURVIVAL OF BACTERIA APPLIED TO CROP FOLIAGE

Guy R. Knudsen and Louise-Marie C. Dandurand

Department of Plant, Soil and Entomological Sciences University of Idaho, Moscow, ID

SUMMARY

Various strains of naturally-occurring or recombinant bacteria offer promise for foliar application to crops for control of insect pests, plant pathogens, weeds, or to protect plants from frost injury. Research on microbial pest control agents for foliar application has progressed to where field tests are needed to evaluate their performance. Concerns about possible environmental effects of genetically engineered microorganisms applied to crop plants include uncertainty about their dispersal, survival, and interactions with indigenous organisms. Predictive models for bacterial dispersal and survival would significantly reduce costs and improve the efficacy of sampling efforts. A predictive model could prescribe optimum placement of sampling devices, probable detection thresholds for sampling, and predict the effects of weather fluctuations, and provide survival estimates to predict density-dependent environmental effects. In this report, we describe initial experiments to integrate a computer simulation model for dispersal of microbial aerosols with a model to predict bacterial survival and activity in phyllosphere habitats. The individual-based modeling approach is intended to accomodate environmental factors that are heterogeneous both in space and time.

INTRODUCTION

Bacteria in several genera, whether naturally-occurring or modified by recombinant DNA techniques, offer promise for foliar application to crops for control of insect pests, plant pathogens, weeds, or to protect plants from frost injury (Armstrong et al., 1987; Blakeman and Brodie, 1976; Falcon, 1971; Freeman and Charudattan, 1980; Knudsen and Spurr, 1987; Lindemann, 1985; Lindow, 1986). Research on microbial pest control agents for foliar application has progressed to where field tests are needed to evaluate their performance. Concerns about possible environmental effects of genetically engineered microorganisms applied to crop plants include uncertainty about their dispersal, survival, and interactions with indigenous organisms.

The first genetically engineered microorganisms to be released legally in the United States were strains of Pseudomonas syringae and P. fluorescens from which the ice nucleation gene was deleted (Lindow, 1986; Supkoff et al., 1988); these were intended to competitively exclude indigenous ice nucleation-active bacteria involved in frost damage. Small-scale field releases of aerosolized ice- bacteria were undertaken by AGS, Inc., and the University of California, Berkeley. There was a large investment in time, money and effort in attempts to determine dispersal patterns and survival of the applied bacteria (Knudsen, 1989; Lindow et al., 1988; Supkoff et al., 1988). Spatial location of sampling devices, and intensity of sampling (e.g., number of sampling devices, dilution series) were arbitrary. Prior knowledge of expected deposition patterns, and epiphytic survival of the applied bacteria, would have facilitated more efficient sampling protocols (optimum placement of sampling devices, probable detection thresholds for sampling) and a stronger data base for risk assessment. Researchers and regulatory agencies need tools to assess the dispersal and survival of bacteria in the atmosphere, subsequent deposition, and fate on plant surfaces. The purpose of this project is to integrate a computer simulation model for dispersal of microbial aerosols (Knudsen, 1989) with a model to predict bacterial survival and activity in phyllosphere habitats. The individual-based modeling approach, described below, will be effective for accomodating environmental factors that are heterogeneous both in space and time. A novel aspect of this research is the use of spatial statistics (geostatistics) to evaluate the accuracy of the simulation model in predicting spatial as well as temporal population dynamics of the introduced bacteria.

Aerial Dispersal Models for Microbes. Various models have been developed to describe dispersion of atmospheric particles from sources. Gaussian plume models predict concentrations of particles in a downwind plume and are probably the most commonly used dispersion models. They assume that turbulence causes airborne particles to randomly disperse, so that an aerosol plume shows increasing scatter around its origin with increasing distance from the source, characterized by a bivariate Gaussian distribution. Variations of these models specify dispersion parameters as functions of downwind distance and atmospheric stability. Such models are relatively easy to manipulate mathematically, but one disadvantage lies in the assumption of a continuous source and uniform wind speed. During experimental releases of recombinant bacteria, the time span of interest may be very short (e.g., minutes), and a high level of precision in estimating movement of airborne particles is required. Because the particle source is small and discontinuous in time, minor variations in wind speed and direction over short time periods can significantly affect predicted dispersal patterns. Puff diffusion models calculate the position of a particle cloud at successive time steps and offer an improvement over simple Gaussian plume models, but their main disadvantage lies in the increasing computational difficulty as the time step length is decreased or wind vectors change. Also, they are not flexible enough to easily adapt to different plot sizes, particle size distributions, evaporation (which effectively alters aerosol droplet size), and deposition of aerosol particles. Thus, the above models are not highly suitable for small-scale field releases of microbes. Random walk models are more suitable: they follow a discrete number of particles released from a source, producing a representative picture of the entire plume in space and time. Time is treated as a discrete variable.

Our laboratory described a microcomputer simulation model (GEMDRIFT, copyright 1989, Idaho Research Foundation, Inc.) that predicted dispersal and deposition patterns for aerosolized bacteria in field trials (Knudsen, 1989). The model was individual-based, in that the fate of individual particles (bacteria-containing droplets) was followed over time and space. The model could accomodate variability in wind speed, direction, and turbulence, and was further designed to accomodate variability in particle size distribution, evaporation, and mortality. Predicted deposition patterns were compared with, and agreed well with, reported field observations (Lindow et al., 1988; Supkoff et al., 1988).

The general form of the GEMDRIFT simulation model (Knudsen, 1989), as modified for this project, is a random walk model. The model describes the motion and dispersal of a large sample of particles (e.g., > 106) released from a point or area source. The trajectory of each particle is divided into discrete time steps (0.5 s), during which the horizontal and vertical velocity components of each particle are held constant. The program tracks the x, y, and z coordinates of each particle over time. Deterministic elements in the model include particle sedimentation due to gravity, advection by prevailing wind, evaporation, mortality, and collection of particles by sampling devices. In the model, advection is either based on average wind speed and direction or calculated by using a data file of wind speed and direction measured at discrete time intervals. The model calculates horizontal movement, i.e., change in the x coordinate (x) and y coordinate (y) of each particle. Terminal velocity (i.e., sedimentation rate) was predicted using Stoke's Law, which describes the terminal velocity of a smooth spherical object falling in a fluid medium. For microbial aerosols suspended in air, assuming that the density of the medium is negligible compared to the density of the falling object, Stoke's Law simplifies to: VT = 0.0121 r2 , where VT is the terminal velocity (ms-1) and r is the radius (µm) of a spherical aerosol droplet (for our simulations of the Tulelake and Brentwood releases, it was assumed that particles were released at terminal velocity, the height of the plant canopy was 0.2 m, and that there was negligible wind within the canopy). Stochastic elements in the aerosol model include individual particle (droplet) sizes and turbulence dispersion vectors. Particle sizes are assumed to be lognormally distributed; mean and variance of the distribution are specified in advance of the simulation run. Dispersion due to turbulence was assumed to be random normally distributed (mean = 0 m) in the parallel, perpendicular horizontal, and perpendicular vertical directions to prevailing winds. The model assumes no covariance relationships between successive time intervals. Standard deviations were selected by running simulations with different values and determining those that generated Gaussian dispersion patterns (at 100 m, 1 msec-1 wind speed), similar to those predicted by standard Gausian plume dispersion models for Pasquill's atmospheric stability classes (Pasquill, 1961; 1974). For all stochastic elements, a Monte Carlo routine selects random normal deviates by using a random number-generating routine and look-up table.

Sequential steps in the GEMDRIFT simulation and a full description of the model are provided in the paper by Knudsen (1989). Although the published version was written in the language Turbo Pascal, it is implemented in the language C++ for this project, which allows for easier use of larger microcomputer memory resources.

In preliminary field experiments, aerosolized bacterial suspensions (Erwinia herbicola 112Y) were applied at different concentrations and volumes to foliage of 2 mo. old bean plants. Experiments were performed at the University of Idaho Parker farm facilities, near Moscow. Seeds of the bean cultivar 'Bush Blue Lake' were sown (33 cm spacing) in a 11 x 11-plant grid (plant spacing distance was chosen for effective sampling rather than for agronomic reasons). Plants were arranged in rectangular grids, with selective 'gravity' plates and water-sensitive cards suspended at upper canopy level. Wind speed and direction were monitored at 1 s intervals. Deposition of bacteria on upper and lower canopy leaves was quantified by washing and dilution plating, colonies on gravity plates were counted, and deposition on individual cards was quantified with video image analysis. All deposition patterns were mapped by spatial coordinates. Each monitoring method yielded qualitatively and quantitatively different information. At low wind speeds (ca. 1 m/s) and higher bacterial concentrations, cards provided more spatial resolution than gravity plates and more accurately predicted recovery from leaves. At higher wind speeds (ca. 5 m/s, turbulent), gravity plates provided more spatial resolution as the mean particle size landing within the grid increased.

Environmental Effects on Survival and Activity of Phyllosphere Bacteria. Populations of epiphytic bacteria differ within plant canopies depending on exposure to wind, rain, and solar radiation (Campbell, 1989). On a larger scale, climate and cropping patterns affect distribution patterns of epiphytic bacteria (Mew and Kennedy, 1971; Surico et al., 1981). Environmental factors severely restrict the growth of microorganisms on leaf surfaces. Physical factors, of which solar radiation, moisture, and temperature are most important, vary on a large scale with climate, on a smaller scale within the plant canopy, and on a microscopic scale over the leaf surface. Solar radiation in the range of 300-320 nm is destructive to exposed bacteria (Ignoffo, 1985). Unprotected spores of Bacillus exposed to direct sunlight have been reported to have a half-life of less than one day (Ignoffo, 1985). Water is frequently limiting on plant surfaces under temperate and arid condiditions, and growth of epiphytic microbes may only occur following rain, periods of dew, or at least high humidity (Campbell, 1989). Water affects survival, multiplication, and dispersal of plant surface bacteria, and free water is probably necessary for diffusion of antimicrobial compounds from epiphytic bacteria used as biocontrol agents (Knudsen and Hudler, 1987). Leben (1974) observed that plant-associated bacteria in a state of reduced metabolism, or hypobiosis (Linton, 1971), are more likely to survive than are active cells. Hypobiotic cells may survive for long periods without added nutrients, and are more able to withstand physical and chemical stresses that would be fatal to cells with high metabolic activity (Leben, 1974). Physical factors including temperature and solar radiation have direct effects (e.g., mortality) and indirect effects (metabolic rates, mutations, etc.) on numbers and types of bacteria on above-ground plant parts. There are also interactions among physical factors. For example, cells with higher metabolic activity due to higher temperatures are likely to be more susceptible to UV radiation. On the other hand, high relative humidity may reduce adverse effects of UV radiation. Drying kills metabolically active cells of most bacteria, but as previously mentioned, metabolically inactive cells usually are much more able to survive dessication. Thus, bacterial survival and metabolic activity are inextricably linked. Epiphytic populations of bacterial species may be highly prone to periodic extinction in parts of their ranges, through competitive exclusion and perturbations in the physical environment (e.g., Hirano and Upper, 1993).

Quantitative Evaluation of Phyllosphere Bacterial Populations. Analytical approaches to predictive microbial ecology involve estimation of constants or parameters in equations chosen to represent processes such as substrate depletion, growth, or surface colonization. Several analytical models are available to describe bacterial growth and kinetics in simple systems such as laboratory culture. The simplest model states that change in growth of the microbial population (dN/dt) is directly proportional to the size of the population; this is exponential growth, and is based upon first-order kinetics and assumes that no increasing growth retardation is operative (Lambrecht et al., 1988). If the value of r is negative, the size of the population declines exponentially. Such a model (exponential decay) may reasonably fit a variety of microbial death processes. Brand and Pinnock (1981) and Pinnock et al. (1978) used exponential decay models to predict the persistence of Bacillus thuringiensis spores on foliage, and to relate these population levels to the mortality of insects feeding on the foliage.

The logistic model is sometimes used to describe growth in a non-replenished medium, and assumes that growth increase is retarded linearly with increasing population size (Lambrecht et al., 1988). The logistic model has drawbacks as a general model of population growth, since its predicted asymptotic stable density is probably almost never achieved by natural populations (Krebs, 1985). Knudsen and Hudler (1987) incorporated logistic growth into a simulation model for Pseudomonas fluorescens on pine foliage, but remarked on the unrealistic limitations imposed by the invariant carrying capacity (asymptote) of the logistic model.

Population models based on exponential, Monod, logistic, or similar descriptive (i.e., statistically derived) models, may not be appropriate for a spatially and temporally heterogeneous environment. Individual bacterial cells in nature may be in a condition ranging from physiological dormancy to active metabolism and cell division. Environmental effects on survival, growth, and potential for ecological effects vary with the physiological state of the cells (Caldwell et al., 1989; Olsen and Bakken, 1987; Reeve et al., 1984; Tempest et al., 1983; Walmsley, 1976). Ideally, a useful and flexible model would account for variability in bacterial populations as described above, and the interaction between environment and physiological status of bacterial cells.

Knudsen and Spurr (1988) combined simple analytical models to predict survival of Pseudomonas cepacia and Bacillus thuringiensis on peanut foliage, where bacteria were applied as aqueous suspensions of freeze-dried vegetative cells (P. cepacia) or spores (B. thuringiensis). The model for P. cepacia assumed that mortality was very high (95%) on the day that cells were applied, but that thereafter cells died at a slower exponential rate during periods of relative humidity less than 95%, and increased slowly (logistic growth) under conditions of high humidity. The model for B. thuringiensis assumed a simple exponential decline over time, and did not distinguish between endospores and vegetative cells. Model predictions, especially for P. cepacia, were a reasonably good fit to field observations, potentially providing a basis to improve field performance of these biocontrol agents by modifying application rates or frequencies. These models made the simplifying assumption that bacterial populations were homogeneous; like most simplifying assumptions, this is incorrect. For example, we observed transitions between life stages (spores, vegetative cells, cells with endospores) for populations of B. thuringiensis applied as spore suspensions to peanut leaf disks (Knudsen and Spurr, 1988). Within a few days under constant environmental conditions, all life stages were present in the population.

Natural populations and habitats are spatially heterogeneous; i.e., organisms and their resources are usually not uniformly distributed over space or time, but are found in different degrees of aggregation. Several theoretical studies have demonstrated the importance of spatial heterogeneity for population and metapopulation persistence (Lomnicki, 1980; Roff, 1974a; 1974b) and abundance (Hanski, 1982; 1985; Taylor and Taylor, 1977). Hirano and Upper (1993) demonstrated changes in frequency distributions of epiphytic bacterial populations on populations of habitats (individual leaflets) within a plant canopy. However, despite continuing demonstration of the theoretical and practical importance of spatial processes to ecology (Jumars et al., 1977; Taylor, 1984; Watt, 1947), relatively few mechanistic studies of the factors that create heterogeneous spatial distributions and the processes by which they occur in nature are available (Czaran and Bartha, 1989). As pointed out by Hirano and Upper (1993), an understanding of factors that regulate epiphytic bacterial population dynamics must address mechanisms that underlie variability.

Spatio-Temporal Model for Epiphytic Bacterial Populations. Because bacterial cells have a genetic constitution that is not immutable, most "pure" cultures are in reality genetically heterogeneous. When the environment changes, it may select for variants within that population. A model should ideally allow for that possibility rather than treating the population as a homogenous group of cells. Heterogeneous constitutive and environmental influences ensure that transitions between life stages generally do not remain synchronous within a bacterial population. There would be obvious advantages to a model that allowed variation among cells in a population and among micro-sites in an environment. One approach is therefore to model environmental effects on metabolism of many individual cells, and then to extrapolate to the larger microbial population. Another advantage of such an approach is to allow for an environment that is spatially heterogeneous with respect to chemical, physical, and biotic conditions.

In our laboratory, a simulation model is under development to fit the above description. The model is described below; an expanded rationale may be found in Knudsen (1991). The model tracks individual representative bacterial cells within a population, treating change in physiological status as a Brownian motion process with drift. Drift refers to the movement of a cell along a physiological "path" under the influence of environmental factors. Such an approach, not previously used in this context, is biologically appealing and readily amenable to computer implementation. Direction and rate of drift, i.e., movement towards either dormancy or increased metabolic activity, are influenced by environmental factors (temperature, moisture, etc.). Also, environmental factors in the model affect mortality according to the status of the cell. Each of these processes is stochastic, and the model tracks a cohort of bacterial cells through time. The structure of the model is also designed to accomodate different environmental influences on spatially dispersed segments of the population.

Knudsen (1991) presented a simplified implementation of this model for a hypothetical bacterial population, considering effects of exogenous nutrients and solar radiation. Nutrients were modeled as a finite pool capable of supporting active growth of a particular size population of cells for a certain number of hours, without replenishment. Solar radiation has the effect of killing cells; in the simulations this is a random process with a relatively high probability for log-phase cells, lower probability for lag-phase cells, and lowest probability for hypobiotic cells. Cells reaching the highest level of physiological activity in the simulations divide by binary fission. The resultant parent cell remains in log phase, and the daughter cell starts in lag phase (Dow and Whittenbury, 1980). There are three attributes of this model that make it useful for modeling bacterial populations. They are: i. environmental factors can influence the metabolic activity of a bacterial cell, and the model has flexibility for different factors to work additively, synergistically, or in opposition; ii. environmental factors can affect different cells in a population differently; iii. not only does the environment influence metabolic activity of cells, but environmental effects can be made dependent on the metabolic status of the cell. For example, metabolically active cells may be more receptive to an influx of nutrients, but are also more susceptible to killing by UV radiation.

The model described above is being adapted for specific strains of applied bacteria, appropriate parameters determined, and tested under controlled environmental conditions. Then, the model will be coupled to our dispersal model described above, and validated in field trials.

As the simulation model is tested and refined to improve its ability to predict i. absolute numbers of bacteria initially deposited on plant surfaces, ii. spatial structures of initial deposition patterns, and, iii. epiphytic population changes following deposition, it should become an effective tool to evaluate the efficacy of different sampling strategies for the released bacteria. For example, the degree of aggregation of bacterial populations, range of spatial dependence, and presence (likely) or absence of directionality all impact the efficiency of sampling. As spatial structure and aggregation increase, the efficiency of random sampling is diminished. Using the validated model, we will generate deposition and subsequent survival patterns for a wide range of weather patterns (e.g., varying wind speed, direction, and turbulence during the spray event, varying canopy microclimatic conditions subsequently). Optimum allocation of sampling resources (time, labor, equipment) under different conditions will be explored, as well as determination of the limits of detection that can be expected under different conditions. The model will be packaged in a user-friendly microcomputer format for use by other researchers and regulatory personnel. We anticipate that prediction ability for microbial population and spatial dynamics will greatly enhance effective risk assessment, and the improved reliability of predicted fate and impacts of introduced microorganisms will help to facilitate environmentally safe implementation of agricultural biotechnology.

REFERENCES

Armstrong, J. L., G. R. Knudsen, and R. J. Seidler. 1987. Survival of recombinant bacteria associated with plants and herbivorous insects in a microcosm. Curr. Microbiol. 15:229-232.

Blakeman, J. P., and Brodie, I. J. S. 1976. Inhibition of pathogens by epiphytic bacteria on aerial plant surfaces. p. 529-557 In: C. H. Dickinson and T. F. Preece (eds.). Microbiology of Aerial Plant Surfaces. Academic Press, London.

Brand, R. J., and D. E. Pinnock. 1981. Application of biostatistical modelling to forcasting the results of microbial control trials. p. 667 In: H. D. Burges (ed.), Microbial Control of Pests and Plant Diseases 1970-1980. Academic Press, London.

Caldwell, B. A., C. Ye, R. P. Griffiths, C. L. Moyer, and R. Y. Morita. 1989. Plasmid expression and maintenance during long-term starvation-survival of bacteria in well water. Appl. and Environ. Microbiol. 55:1860-1864.

Campbell, R. 1989. Biological Control of Microbial Plant Pathogens. Cambridge Univ. Press, Cambridge.

Czaran, T., and S. Bartha. 1989. The effect of spatial pattern on community dynamics; a comparison of simulated and field data. Vegetatio 83:229-239.

Dow, C. S., and R. Whittenbury. 1980. Prokaryotic form and function. p. 391-417 In: D. C. Ellwood, J. N. Hedger, M. J. Latham, J. M. Lynch, and J. H. Slater (eds.). Contemporary Microbial Ecology. Academic Press, London.

Falcon, L. A. 1971. Use of bacteria for microbial control. p. 67-95 In: H. D. Burges and N. W. Hussey (eds.). Microbial Control of Insects and Mites. Academic Press, London.

Freeman, T. E., and R. Charudattan. 1980. Biological control of weeds with plant pathogens. Prospectus pp.293-299 In: E. S. Del Fosse (ed.), Proc. V Int. Symp. Biol. Contr. Weeds, CSIRO, Melbourne.

Hirano, S. S., and C. D. Upper. 1993. Dynamics, spread, and persistence of a single genotype of Pseudomonas syringae relative to those of its conspecifics on populations of smap bean leaflets. Appl. Environ. Microbiol. 59:1082-1091.

Ignoffo, C. M. 1985. Manipulating enzootic-epizootic diseases of arthropods. p. 243-262 In: M. A. Hoy and D. C. Herzog (eds.). Biological Control in Agricultural IPM Systems. Academic Press, Orlando.

Jumars, P. A., D. Thistle, and M. L. Jones. 1977. Detecting two-dimensional spatial structure in biological data. Oecol. 8:109-123.

Knudsen, G. R. 1989. Model to predict aerial dispersal of bacteria during environmental release. Appl. Env. Micro. 55:2641-2647.

Knudsen, G. R. 1991. Models for the survival of bacteria applied to the foliage of crop plants. pp.191-216 In: C. J. Hurst, ed., Modeling the Environmental Fate of Microorganisms. ASM.

Knudsen, G. R., and G. W. Hudler. 1987. Use of a computer simulation model to evaluate a plant disease biocontrol agent. Ecol. Modell. 35:45-62.

Knudsen, G. R., and H. W. Spurr, Jr. 1987. Field persistence and efficacy of five bacterial preparations for control of peanut leaf spot. Plant Disease 71:442-445.

Knudsen, G. R., and H. W. Spurr, Jr. 1988. Management of bacterial populations for foliar disease biocontrol. pp. 83-92 In: K. G. Mukerji (ed.). Biocontrol of Plant Diseases. CRC Press.

Krebs, C. J. 1985. Ecology: The Experimental Analysis of Distribution and Abundance, 3rd ed. Harper and Row, Inc., NY.

Lambrecht, R. S., J. F. Carriere, and M. T. Collins. 1988. A model for analyzing growth kinetics of a slowly growing Mycobacterium sp. Appl. and Environ. Microbiol. 54:910-916.

Leben, C. 1974. Survival of Plant Pathogenic Bacteria. Ohio Agr. Res. and Dev. Center Special Circular 100, Wooster, Ohio.

Lindemann, J. 1985. Genetic manipulation of microorganisms for biological control. p. 116-170 In: C.E. Windels and S.L. Lindow (eds.). Biological Control on the Phylloplane. Am. Phytopathol. Soc., St. Paul, MN.

Lindow, S. E. 1986. Strategies and practice of biological control of ice nucleation active bacteria on plants. p. 293-311 In: N. Fokkema (ed.), Microbiology of the Phyllosphere. Cambridge University Press, Cambridge.

Lindow, S. E., G. R. Knudsen, R. J. Seidler, M. V. Walter, V. W. Lambou, P. S. Amy, D. Schmedding, V. Prince, and S. Hern. 1988. Aerial dispersal and epiphytic survival of Pseudomonas syringae during a pretest for the release of genetically engineered strains into the environment. Appl. Environ. Microbiol. 54:1557-1563.

Linton, A. H. 1971. Influence of external factors on viability of micro-organisms, p. 193-217 In: L. E. Hawker and A. H. Linton (eds.), Micro-organisms, function, form and environment. American Elsevier Pub. Co., Inc., New York.

Lomnicki, A. 1980. Regulation of population density due to individual differences and patchy environment. Oikos 35:185-193.

Mew, T. W., and B. W. Kennedy. 1971. Growth of Pseudomonas glycinea on the surface of soybean leaves. Phytopath. 61:715-716.

Olsen, R. A., and L. R. Bakken. 1987. Viability of soil bacteria: optimization of plate-counting technique and comparison between total counts and plate counts within different size groups. Micro. Eco.13:59-74.

Pasquill, F. 1961. The estimation of the dispersion of windborne material. Meteorol. Mag. 90:33-49.

Pasquill, F. 1974. Atmospheric diffusion, 2nd ed. Ellis Horwood Ltd., Publisher, Chichester, United Kingdom.

Pinnock, D. E., R. J. Brand, J. E. Milstead, M. E. Kirby, and N. F. Coe. 1978. Development of a model for prediction of target insect mortality following field application of a Bacillus thuringiensis formulation. J. Invertebr. Pathol. 31:31.

Reeve, C. A., A. T. Bockman, and A. Martin. 1984. Role of protein degradation in the survival of carbon-starved Escherichia coli and Salmonella typhimurium. J. Bacteriol. 157:758-763.

Roff, D. A. 1974a. Spatial heterogeneity and the persistence of populations. Oecologia 15:245-258.

Roff, D. A. 1974b. The analysis of a population model demonstrating the importance of dispersal in a heterogeneous environment. Oecologia 15:259-275.

Supkoff, D. M., L. G. Bezark, and D. Opgenorth. 1988. Monitoring of the winter 1987 field release of genetically engineered bacteria in Contra Costa County, report BC 88-1. CA Dept. of Food and Agriculture, Sacramento, CA.

Surico, G., B. W. Kennedy, and G. L. Ercolani. 1981. Multiplication of Pseudomonas syringae pv. glycinea on soybean primary leaves exposed to aerosolized inoculum. Phytopathology 71:532-536.

Taylor, L. R. 1984. Assessing and interpreting the spatial distributions of insect populations. Ann. Rev. Ento. 29:321-3357.

Taylor, L. R., and R. A. Taylor. 1977. Aggregation, migration and population mechanics. Nature 265:415-421.

Tempest, D. W., O. M. Neijssel, and W. Zevenboom. 1983. Properties and performance of microorganisms in laboratory culture: their relevance to growth in natural ecosystems. p.119-152 In: J. H. Slater, R. Whittenbury, and J. W. T. Wimpenny (eds.). Microbes in their Natural Environments. 34th Symp. Soc. Gen. Microbiol. Cambridge University Press.

Walmsley, R. H. 1976. Temperature dependence of mating-pair formation in Escherichia coli. J. Bacteriol. 126:222-224.

Watt, A. S. 1947. Pattern and process in the plant community. J. Ecol. 35:1-22.