Dispersion Gradient Research Articles

On Using Random Walks to Solve the Space-Fractional Advection-Dispersion Equations

The solution of space-fractional advection-dispersion equations (fADE) by random walks depends on the analogy between the fADE and the forward equation for the associated Markov process. The forward equation, which provides a Lagrangian description of particles moving under specific Markov processes, is derived here by the adjoint method. The fADE, however, provides an Eulerian description of solute fluxes. There are two forms of the fADE, based on fractional-flux (FF-ADE) and fractional divergence (FD-ADE). The FF-ADE is derived by taking the integer-order mass conservation of non-local diffusive flux, while the FD-ADE is derived by taking the fractional-order mass conservation of local diffusive flux. The analogy between the fADE and the forward equation depends on which form of the fADE is used and on the spatial variability of the dispersion coefficient D in the fADE. If D does not vary in space, then the fADEs can be solved by tracking particles following a Markov process with a simple drift and an α-stable Lévy noise with index α that corresponds to the fractional order of the fADE. If D varies smoothly in space and the solute concentration at the upstream boundary remains zero, the FD-ADE can be solved by simulating a Markov process with a simple drift, an α-stable Lévy noise and an additional term with the dispersion gradient and an additional Lévy noise of order α−1. However, a non-Markov process might be needed to solve the FF-ADE with a space-dependent D, except for specific D such as a linear function of space.

Sirococcus clavigignenti‐juglandacearum

<i>Sirococcus clavigignenti‐juglandacearum</i>

The Effects of Dispersal Gradient and Pathogen Life Cycle Components on Epidemic Velocity in Computer Simulations

ABSTRACT The velocity of expansion of focal epidemics was studied using an updated version of the simulation model EPIMUL, with model parameters relevant to wheat stripe rust. The modified power law, the exponential model, and Lambert's general model were fit to primary disease gradient data from an artificially initiated field epidemic of stripe rust and employed to describe dispersal in simulations. The exponential model, which fit the field data poorly (R (2) = 0.728 to 0.776), yielded an epidemic that expanded as a traveling wave (i.e., at a constant velocity), after an initial buildup period. Both the modified power law and the Lambert model fit the field data well (R(2) = 0.962 to 0.988) and resulted in dispersive epidemic waves (velocities increased over time for the entire course of the epidemic). The field epidemic also expanded as a dispersive wave. Using parameters based on the field epidemic and modified power law dispersal as a baseline, life cycle components of the pathogen (lesion growth rate, latent period, infectious period, and multiplication rate) and dispersal gradient steepness were varied within biologically reasonable ranges for this disease to test their effect on dispersive wave epidemics. All components but the infectious period had a strong influence on epidemic velocity, but none changed the general pattern of velocity increasing over time.

Effects of Single-Drop Impactions and Natural and Simulated Rains on the Dispersal of Botryosphaeria dothidea Conidia

ABSTRACT Laboratory and field experiments were conducted to study the dispersal of Botryosphaeria dothidea conidia using single-drop impactions and natural and simulated precipitations. For laboratory studies, 200 single drops were released from a height of 1 m on infected pistachio nuts. On pieces of photographic film, 50% of the droplets were collected within 20 mm (average droplet travel distance) of the target area, and the droplets ranged from 0.041 to 3.19 mm in diameter, with an average of 0.3 mm. Each droplet carried an average of 23 B. dothidea conidia. In 3 years of field experiments, rainwater was collected in funnels connected to bottles positioned at different heights inside the tree canopy and at different distances away from the edge of tree canopy in three commercial pistachio orchards in San Joaquin, Yolo, and Glenn counties in California. Numbers of conidia in rainwater varied among and within sampling seasons by sampling dates and orchards. Up to 67,000 conidia/ml were obtained in rainwater samples collected from an orchard in Yolo County. Rainwater from orchards in Yolo and Glenn counties contained a consistently higher number of conidia than rainwater collected from the orchard in San Joaquin County. Variation in numbers of conidia also existed among heights where bottles were located. There were significantly more conidia in rainwater collected inside than outside tree canopies. Inside tree canopies, bottles located at 100 and 150 cm above ground collected more B. dothidea conidia than those placed at 50 and 200 cm. Conidia were collected as far as 1 m from the tree canopy edge. Based on data from the Glenn County orchard, a linear relationship between number of conidia (Y) and rainfall amount (X) in millimeters was determined as Y = 240X - 3,867, with r(2) = 0.91, which meant that a minimum of 16.1 mm of rain was needed to disperse conidia of B. dothidea. The power law model best described the dispersal gradients of B. dothidea propagules in the 1999-2000 and 2001-02 sampling seasons, with r(2) values of >/=0.73, whereas the exponential law model fit best for the 2000-01 data, with r(2) values of >/=0.81. In a rain simulation experiment, the intensity of the rain generated by a nozzle at 138 kPa of pressure inside the tree canopy was approximately five times higher than rain recorded outside the tree canopy. Rain removed up to 65% of conidia from infected fruit. These results confirmed that B. dothidea is a splash-dispersed pathogen with relatively short distances of spore dispersal within pistachio orchards. Only pycnidia are present in pistachio orchards; therefore, the results also indicate that inoculum of B. dothidea should be entirely splashed dispersed.

Cultivar Mixtures for the Simultaneous Management of Multiple Diseases: Tan Spot and Leaf Rust of Wheat

ABSTRACT Because of differences in life histories between Puccinia triticina, a highly specialized, polycyclic, windborne pathogen with a shallow dispersal gradient, and Pyrenophora tritici-repentis, a residue-borne pathogen with a steep dispersal gradient, wheat mixtures are expected to be more effective at controlling leaf rust than tan spot. The objectives of this research were to determine the effect of two-cultivar mixtures with varying proportions and different pathogen resistance profiles on the severity of tan spot and leaf rust, to evaluate yield of the mixtures in the presence or absence of disease, and to directly compare the relative effectiveness of cultivar mixing for tan spot versus leaf rust. In a field experiment at two sites in Kansas over two growing seasons, winter wheat cvs. Jagger and 2145, which have differential resistance reactions to leaf rust and tan spot, each were planted in proportions of 0.25, 0.50, 0.75, and 1.00. Plots were inoculated with each pathogen alone, both pathogens, treated with a fungicide, or exposed to ambient conditions. For both diseases for all siteyears, severity decreased substantially on the susceptible cultivar as the proportion of that cultivar decreased in mixture. Mixtures were significantly more effective at reducing leaf rust than tan spot in three of four site-years. Mixtures generally yielded the same as the weighted mean of components in monoculture although, in two of three site-years, at least one fungicide-treated and one diseased mixture each yielded higher than expected values. Although this particular mixture produced only modest yield benefits, the potential for simultaneous reductions in tan spot and leaf rust was demonstrated.

A two-dimensional stochastic model of downy mildew of radish

A two-dimensional stochastic model that simulates the spread of disease over space and time was recently proposed by Xu and Ridout [Xu, X.M., Ridout, M.S., 1998. Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. Phytopathology 88, 1000–1012]. In a theoretical study, the authors showed the ability of their model to generate a broad range of disease patterns and disease progress rates. The objective of our study was to test if this theoretical approach was able to describe disease progress and the disease pattern of a specific disease, downy mildew ( Peronospora parasitica) of radish ( Raphanus sativus L.). Two field experiments with artificial inoculation were carried out and disease incidence and spatial pattern were assessed twice a week until disease incidence was greater than 0.25. Four model parameters were estimated by an algorithm that uses a least square regression together with an evolutionary optimisation strategy. Moran's I indices of spatial autocorrelation calculated both for measured und simulated data were significantly correlated ( α = 0.05, r = 0.61). Also observed variances in measurements and in simulations were closely and significantly correlated ( α = 0.05, r = 0.95). Thus, disease pattern (as assessed in terms of variance inflation and spatial autocorrelation) was well described by the model. The model accounted for 94% of the variation in the disease incidence data. It has, therefore, the potential to be developed into a forecast model for risk analysis and for decision support in plant protection. However, in the specific case of downy mildew on radish more experimental data are required for model validation and to parameterise the effects of environment on infection, sporulation and spore dispersal.

Spatial and Genetic Analysis of a Flag Shoot Subpopulation ofErysiphe necatorin Italy

ABSTRACT Erysiphe necator overwinters as ascospores in cleistothecia and mycelium in dormant buds of grapevines. Shoots developing from infected buds early in the growing season are covered with dense mycelium and are known as "flag shoots". Combining epidemiological and genetic analyses, the objective of this study was to analyze the spatial and genetic structure of a flag shoot subpopulation of E. necator as a way to assess the contribution of flag shoots as primary inoculum, and to determine if flag shoot subpopulations are clonal with only one mating type. One vineyard in Tuscany, Italy was surveyed intensively for flag shoots for 8 years; isolations of E. necator were made from flag shoots for 5 years. We observed distinct disease foci developing around flag shoots early in epidemics, demonstrating a steep dispersal gradient of conidia and the importance of flag shoots as primary inoculum sources. Flag shoots were spatially aggregated within and between years, most likely as a result of short-distance dispersal of conidia from flags early in the season when dormant buds for the next year's shoots are formed and are susceptible to infection. The two mating types were found in 1:1 ratios in this flag shoot subpopulation. Genotypic diversity, based on inter-simple sequence repeat markers, was high in all years with only two haplotypes occurring twice, and subpopulations were genetically differentiated between years. Similarities between haplotypes were not spatially autocorrelated. One multilocus analysis of population structure is consistent with the hypothesis of random mating but another is not. These results are not consistent with expectations for a strictly clonal or strictly randomly mating flag shoot subpopulation. Instead, the hypothesis that the flag shoot subpopulation of E. necator may reproduce clonally and sexually needs further testing.

Spatially resolved spectroscopy of Coma cluster early-type galaxies

Based on Paper I of this series (Mehlert et al. [CITE]), we derive central values and logarithmic gradients for the , Mg and Fe indices of 35 early-type galaxies in the Coma cluster. We find that pure elliptical galaxies have on average slightly higher velocity dispersions, lower , and higher metallic line-strengths than galaxies with disks (S0). The latter form two families, one comparable to the ellipticals and a second one with significantly higher , and weaker metallic lines. Our measured logarithmic gradients within the effective radius are , , and . The gradients strongly correlate with the gradients of σ, but only weakly with the central index values and galaxy velocity dispersion. Using stellar population models with variable element abundance ratios from Thomas et al. ([CITE]) we derive average ages, metallicities and [ ] ratios in the center and at the effective radius. We find that the ratio correlates with velocity dispersion and drives 30% of the Mg–σ relation, the remaining 70% being caused by metallicity variations. We confirm previous findings that part of the lenticular galaxies in the Coma cluster host very young (∼2 Gyr) stellar populations, hence must have experienced relatively recent star formation episodes. Again in accordance with previous work we derive negative metallicity gradients ( dex per decade) that are significantly flatter than what is expected from gaseous monolithic collapse models, pointing to the importance of mergers in the galaxy formation history. Moreover, the metallicity gradients correlate with the velocity dispersion gradients, confirming empirically earlier suggestions that the metallicity gradient in ellipticals is produced by the local potential well. The gradients in age are negligible, implying that no significant residual star formation has occurred either in the center or in the outer parts of the galaxies, and that the stellar populations at different radii must have formed at a common epoch. For the first time we derive the gradients of the ratio and find them very small on average. Hence, enhancement is not restricted to galaxy centers but it is a global phenomenon. Our results imply that the Mg–σ local relation inside a galaxy, unlike the global Mg–σ relation, must be primarily driven by metallicity variations alone. Finally we note that none of the stellar population parameters or their gradients depend on the density profile of the Coma cluster, even though it spans 3 dex in density.

Dispersal of spores following a persistent random walk.

A model of a persistent random walk is used to describe the transport and deposition of the spore dispersal process. In this model, the spore particle flies along straight line trajectories, with constant speed v, which are interrupted by scattering, originating from interaction of spores with the field and wind variations, which randomly change its direction. To characterize the spore dispersal gradients, we have derived analytical expressions of the deposition probability epsilon (r|v) of airborne spores as a function of the distance r from the spore source in an infinite free space and in a disk of radius R with an absorbing edge that mimics an agricultural field surrounded with fields of nonhost plants and bare land. It is found in the free space that epsilon (r|v) approximately e(-alphar/l), with alpha a function of l(d)/l, where l and l(d) are the scattering and deposition mean free paths, respectively. In the disk, however, epsilon (r|v) is an infinite series of Bessel functions and, exhibits three regimes: absorbing (R<l(d)), intermediate (R=l(d)), and deposition (R>l(d)).

Quantification of Raindrop Kinetic Energy for Improved Prediction of Splash-Dispersed Pathogens

ABSTRACT An electronic sensor, based on a piezoelectric transducer, was tested in the laboratory using simulated raindrops, and in natural rainfall. Data were also collected for splash dispersal using tracer dyes in laboratory experiments and the Long Ashton splashmeter in field experiments. Droplets impacting on sensor produce sound waves that are detected by an omnidirectional microphone sealed within an acoustic chamber. An electrical charge, proportional to the sound wave, is produced by the microphone and is converted to a categorical scale and then stored to provide an accumulation of impacts over a specified period of time. Calibration of the sensor was done using single-droplet impacts of known mass and impacting velocity. A linear relationship was shown between the categorical scale and the kinetic energy of impacting droplets (adjusted r(2) = 0.99). The best relationship fitted between splash dispersal from dye cup, and kinetic energy was a second-order polynomial (adjusted r(2) > 0.99). Splash height, recorded by the Long Ashton splashmeter during 41 natural rainfall events, was correlated closely with sensor output (adjusted r(2) = 0.87). Our studies indicate that the sensor provides quantitative data which could be incorporated into disease management systems to provide estimates of inoculum dispersal gradients within crop canopies.

High-order-harmonic generation: towards laser-induced phase-matching control and relativistic effects

We present a review of some recent results on high-order-harmonic generation, aiming at optimizing the photon flux to allow for future applications in extreme-ultra-violet non-linear optics. We first present new schemes to control phase matching of high harmonics in gases, by using the effect of the spatially varying atomic phase displayed by the high harmonics. An enhancement by a factor of 50 is observed in neon in conditions for which the gradient of the atomic dispersion balances the electronic dispersion. A new scheme to manipulate the laser field was demonstrated, and shown to improve phase matching. We then turn to high-harmonic generation by solid targets, and show that high harmonics generated by an intense 30-fs laser pulse remain collimated even at the threshold of the relativistic regime.

Shape Variations and Control in Self-Assembled Metal Nanoclusters

ABSTRACTThe selective interaction of metal clusters with various polymers constitutes the basis for the self-assembly approach to the synthesis of organic-inorganic hybrid materials, that leads to the control of particle size, geometry and dispersion gradient. Metal particles were synthesized by the thermal decomposition of an organometallic precursor, in this case, iron pentacarbonyl, in the presence of a polymer matrix. Under the conditions utilized for these reactions, the aggregation of the metallic clusters competed with the interactions between the growing metal fragments and the polymer matrix. The dominance of one reaction route as compared to the other, ultimately determined the equilibrium particle shape, size and distribution for each metal-polymer system. In this work, we attempted to analyze the formation of iron oxide nanoclusters in several structurally-distinct polymers, and developed a general mechanistic view to explain the characteristics of the polymer-metal oxide hybrid materials that were obtained.

Abstracts, The Canadian Phytopathological Society annual meeting, London, Ontario, 2001

Abstracts, The Canadian Phytopathological Society annual meeting, London, Ontario, 2001

Unifying the relationships of species richness to productivity and disturbance.

Although species richness has been hypothesized to be highest at 'intermediate' levels of disturbance, empirical studies have demonstrated that the disturbance-diversity relationship can be either negative or positive depending on productivity On the other hand, hypothesized productivity diversity relationships can be positive, negative or unimodal, as confirmed by empirical studies. However, it has remained unclear under what conditions each pattern is realized, and there is little agreement about the mechanisms that generate these diverse patterns. In this study, I present a model that synthesizes these separately developed hypotheses and shows that the interactive effects of disturbance and productivity on the competitive outcome of multispecies dynamics can result in these diverse relationships of species richness to disturbance and productivity The predicted productivity diversity relationship is unimodal but the productivity level that maximizes species richness increases with increasing disturbance. Similarly, the predicted disturbance diversity relationship is unimodal but the peak moves to higher disturbance levels with increasing productivity Further, these patterns are well explained by the opposite effects of productivity and disturbance on competitive outcome that are suggested by the change in community composition along these two environmental gradients: higher productivity favours superior competitors while higher disturbance levels favour inferior competitors.

Conidial movement of nontoxigenic Aspergillus flavus and A. parasiticus in peanut fields following application to soil.

The use of nontoxigenic strains of Aspergillus flavus and A. parasiticus in biological control effectively reduces aflatoxin in peanuts when conidium- producing inoculum is applied to the soil surface. In this study, the movement of conidia in soil was examined following natural rainfall and controlled precipitation from a sprinkler irrigation system. Conidia of nontoxigenic A. flavus and A. parasiticus remained near the soil surface despite repeated rainfall and varying amounts of applied water from irrigation. In addition, rainfall washed the conidia along the peanut furrows for up to 100 meters downstream from the experimental plot boundary. The dispersal gradient was otherwise very steep upstream along the furrows and in directions perpendicular to the peanut rows. The retention of biocontrol conidia in the upper soil layers is likely important in reducing aflatoxin contamination of peanuts and aerial crops such as corn and cottonseed.

Effects of Quadrat Size and Shape, Initial Epidemic Conditions, and Spore Dispersal Gradient on Spatial Statistics of Plant Disease Epidemics

ABSTRACT The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (alpha, beta) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The alpha and beta estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (kappa) was calculated for each quadrat type; kappa decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (alpha (1), beta(1), beta(2)) was used to relate kappa to the disease incidence (p); beta1 was highly correlated to beta: beta1 approximately beta - 1. In general, initial conditions and quadrat size affected alpha, beta, alpha(1), beta(1), and beta(2) greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and mu. Compared with initial conditions and quadrat size, the overall effects of mu and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was determined from the alpha and beta estimates. D was greatest when p was 0.5 and decreased when p approached 0 or 1. It increased with quadrat size and the rate of the increase was maximum when p was 0.5 and decreased when p approached 0 or 1.

Orbital Deformation of Satellites by Dynamical Friction in Spherical Halos with Anisotropic Velocity Dispersion

Deformation of satellite orbits around a spherical galaxy is considered. In general, a satellite sinks into the center of its parent galaxy by dynamical friction. Unless the orbit is exactly circular, the orbital shape changes, owing to a difference in decaying rate between energy and angular momentum. This deformation depends on the density and velocity distributions of the surrounding galactic halo. We have made a perturbative analysis of the orbital deformation in a scale-free halo that has a density profile ρ ∝ rn(-3 ≤ n ≤ 0), with anisotropic velocity dispersion characterized by β = 1 - σ/σ(-1 ≤ β ≤ 1). We classify four major effects on the orbital deformation. The dominant effect originates from the density gradient for n < -2 and the gradient of velocity dispersion for n > -2. Both effects lead to more circular orbits. Larger β makes the rate of orbital circularization smaller. For positive β (radially dominated anisotropy), initially eccentric orbits conserve their shape during orbital decay when the velocity dispersion is radially dominated.

Epidemiology in Mixed Host Populations

ABSTRACT Although plant disease epidemiology has focused on populations in which all host plants have the same genotype, mixtures of host genotypes are more typical of natural populations and offer promising options for deployment of resistance genes in agriculture. In this review, we discuss Leonard's classic model of the effects of host genotype diversity on disease and its predictions of disease level based on the proportion of susceptible host tissue. As a refinement to Leonard's model, the spatial structure of host and pathogen population can be taken into account by considering factors such as autoinfection, interaction between host size and pathogen dispersal gradients, lesion expansion, and host carrying capacity for disease. The genetic composition of the host population also can be taken into account by considering differences in race-specific resistance among host genotypes, compensation, plant competition, and competitive interactions among pathogen genotypes. The magnitude of host-diversity effects for particular host-pathogen systems can be predicted by considering how the inherent characteristics of a system causes it to differ from the assumptions of the classic model. Because of the limited number of studies comparing host-diversity effects in different systems, it is difficult at this point to make more than qualitative predictions. Environmental conditions and management decisions also influence host-diversity effects on disease through their effect on factors such as host density and epidemic length and intensity.

The Double Nucleus and Central Black Hole of M31

New spectroscopy of M31 supports Tremaine's model in which both nuclei are parts of a single eccentric disk of stars orbiting the black hole (BH). The kinematics and Hubble Space Telescope photometry are used to measure the offset of the BH from the center of mass. This confirms that the BH mass is ~ 3 × 107 M☉ by a technique that is nearly independent of stellar-dynamical models. We present spectroscopy of the nucleus of M31 obtained with the Canada-France-Hawaii Telescope and Subarcsecond Imaging Spectrograph. Spectra at the Ca infrared triplet lines (seeing σ* = 027) are used to measure the stellar kinematics, and spectra at the Mg I b lines (σ* = 031) are used to measure metallicities. We also measure nonparametric line-of-sight velocity distributions (LOSVDs). All spectra confirm the steep rotation and velocity dispersion gradients that imply that M31 contains a 3.3 × 107 M☉ central dark object. At σ* = 027, the maximum bulge-subtracted rotation velocity of the nucleus is 233 ± 4 km s-1 on the P2 side, and the maximum velocity dispersion is 287 ± 9 km s-1. The dispersion peak is displaced by 020 ± 003 from the velocity center in the direction opposite to P1, confirming a result by Bacon and coworkers. The higher surface brightness nucleus, P1, is colder than the bulge, with σ 100 km s-1 at r 1''. Cold light from P1 contributes at the velocity center; this explains part of the σ(r) asymmetry. The nucleus is cold at r 1'' on both sides of the center. Our results are used to test Tremaine's model in which the double nucleus is a single eccentric disk of stars orbiting the BH. (1) The model predicts that the velocity center of the nucleus is displaced by 02 from P2 toward P1. Our observations show a displacement of 008 ± 001 before bulge subtraction and 010 ± 001 after bulge subtraction. (2) The model predicts a minimum σ 135 km s-1 at P1. We observe σ = 123 ± 2 km s-1. Observations (1) and (2) may be reconciled with the model if its parameters are tweaked so that the orbital eccentricity is made larger and the orientation of the orbits is made to point more nearly at us. (3) The model rotation curve is asymmetric; at perfect resolution, V is 60 km s-1 higher on the P2 side than on the P1 side. At σ* = 027, we observe an asymmetry of 54 ± 4 km s-1 after bulge subtraction. We regard this as confirmation of the model's essential idea that stellar orbits are eccentric and coherently aligned. (4) The model predicts that P1 and P2 should have the same stellar population. We confirm this: P1 is more similar to P2 than it is to the bulge or to a globular cluster or to M32. This makes it unlikely that P1 consists of accreted stars. (5) Our observation that there is cold light on both sides of the center implies, if the nucleus is an eccentric disk, that some stars have escaped from the P1-P2 alignment and have phase-mixed around the galaxy's center. The dispersion peak coincides with a cluster of ultraviolet-bright stars seen in Hubble Space Telescope images. We propose that the BH is in this cluster. Its center is displaced by 0068 ± 0010 from the bulge center. If we put a 3.3 × 107 M☉ dark object in the UV cluster and adopt the dynamically determined mass-to-light ratio of the stars, then the center of mass (COM) of the bulge, nucleus, and dark object coincides with the bulge center to within 0017 ± 0016. The COM also agrees with the velocity center of the bulge and outer nucleus. Therefore, the asymmetry of the stars in the double nucleus supports our suggestion that the BH is in the UV cluster. If the stars have a normal mass-to-light ratio, then the location of the COM also confirms the mass of the BH, largely independent of dynamical models. Tremaine's model implies that any dark cluster alternative to a BH is less than 013 ± 003 = 0.49 pc in radius. The observed mass-to-light ratio is M/LV 300 in a cylinder of radius r = 013 and M/LV 2200 in a sphere of radius r = 013. This is much larger than previous measurements of M/LV. This result and the COM argument greatly strengthen the detection of a central dark object in M31.

Effects of Initial Epidemic Conditions, Sporulation Rate, and Spore Dispersal Gradient on the Spatio-Temporal Dynamics of Plant Disease Epidemics

ABSTRACT A stochastic model that simulates the spread of disease over space and time was developed to study the effects of initial epidemic conditions (number of initial inocula and their spatial pattern), sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). The rate of temporal increase in disease incidence (beta(I), per day) was influenced jointly by mu and by the sporulation rate lambda (spores per lesion per day). The relationship between beta(I) and mu was nonlinear: the increase in beta(I) with increasing mu was greatest when mu was small (i.e., when the dispersal gradient was steep). The rate of temporal increase in disease severity of diseased plants (beta(S)) was affected mainly by lambda: beta(S) increased directly with increasing lambda. Intraclass correlation (kappa(t)), the correlation of disease status of plants within quadrats, increased initially with disease incidence, reached a peak, and then declined as disease incidence approached 1.0. This relationship was well described by a power-law model that is consistent with the binary form of the variance power law. The amplitude of the model relating kappa(t) to disease incidence was affected mainly by mu: kappa(t) decreased with increasing mu. The shape of the curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. Generally, the relationship of spatial autocorrelation (rho(t,k)), the correlation of disease status of plants at various distances apart, to disease incidence and distance was well described by a four-parameter power-law model. rho(t,k) increased with disease incidence to a maximum and then declined at higher values of disease incidence, in agreement with a power-law relationship. The amplitude of rho(t,k) was determined mainly by initial conditions and by mu: rho(t,k) decreased with increasing mu and was lower for regular patterns of initial inocula. The shape of the rho(t,k) curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. At any level of disease incidence, autocorrelation declined exponentially with spatial lag; the degree of this decline was determined mainly by mu: it was steeper with decreasing mu.