Contagious Distributions Research Articles

Risk management and components’ coordination assessment in the design of a composite riverine flood defence system

ABSTRACT Flood control is one of the most important and difficult tasks in river basin management in terms of present several uncertainties. This study aims to follow the risk management and coordination analysis in designing a riverine flood defence system, actually, a composite multi-section flood control levee system considering the aleatory and epistemic uncertainties using contagious distributions. A stochastic optimization model was developed based on Monte Carlo analysis for uncertainty propagation, and then the system's optimum dimensions were computed in the single-section and multi-section cases for overall comparisons. Using the concept of ‘scenario probability’, the coordination of the system and its individual components was analysed. The results indicated that by increasing the complexity (from a single-section to a multi-section model) and by the separation of uncertainties (into epistemic and aleatory), the coordination of the system decreases 130% and 30%, respectively. Moreover, it was found that when economic uncertainty was considered, unexpected results may be obtained so that by increasing the system dimensions the total cost decreases. Finally, after analysing the sample histograms of the system's components, several distributions have been suggested. When there are vast datasets that might be confusing for decision-makers, the systematic method proposed here makes risk management easier.

Statistical analysis of the phytocoenose homogeneity. I. Distribution of the total species diversity and evenness indices as a homogeneity measure

Homogeneity of the <em>Leucobryo-Pinetum</em> phytocoenose was assessed on the grounds of distributions of the total species diversity (H) and evenness e indices. In spite of the uniform physiognomy of the patch. caused by pure, even-aged, one-layered forest stand and apparent dominance of dwarf-shrubs in the ground layer, phytocoenose under study was heterogeneous. It resulted in the discrepancy between empirical distributions of H and e, and the normal distribution, as well as in the contagious spatial distributions of both indices.

Spatial structure in the zooplankton of a newly formed and heavily disturbed urban lake

Physico-chemical gradients and local biotic interactions combine at different scales to cause spatial heterogeneity among lake zooplankton. However, current understanding is based overwhelmingly on natural systems and there have been few assessments of zooplankton spatial pattern in artificial lakes subjected to intensive management. Here, we investigate spatial structure among crustacean zooplankton at scales ranging from 1 m to 2700 m in the newly-formed Cardiff Bay (UK). We hypothesised that zooplankton spatial structuring in Cardiff Bay would be weakened by artificial aeration that was expected to create intense, continuous disturbance that homogenised physico-chemical conditions. Water quality across Cardiff Bay varied only moderately, and variations in zooplankton community composition were weakly related to temperature, oxygen, chlorophyll-a concentration and salinity at scales of around 2 km. However, spatial pattern explained over 60 % of variance in zooplankton composition at the smallest scales (0-5 m), implying that inter-specific interactions were involved. Additionally, the numerically dominant zooplankton (Daphnia hyalina (Leydig 1860), Eurytemora affinis (Poppe 1880) and Eucyclops agilis (Koch 1838)) had highly contagious distributions in warmer locations with increased chlorophyll-a reflecting aggregated response to abundant food. These data suggest that local biotic interactions among zooplankton and broader-scale links between dominant species and their algal food are sufficiently intense to persist despite the homogenising effects of artificial aeration and lake mixing. Such spatial pattern and scale-dependence has ramifications for zooplankton sampling while illustrating the self-organising capacity of predator-prey interactions even in novel, disturbed environments.

Spatial pattern analysis of dominant species in the Prepuna: Gaining insight into community dynamics in the semi-arid, subtropical Andes

We conducted a point pattern analysis of dominant woody and cactus species in a permanent plot located in the little known semi-arid Andes (Prepuna region) for gaining insight into community dynamics and, specifically, to determine the microhabitat (beneath or away from shrubs) where shrubs and cacti tend to recruit. Several null models were employed. We found that small individuals of the shrub species did not show attraction for larger individuals, which may show that the former are not facilitated by the latter. One of the two columnar cactus species presented a markedly aggregated pattern, and showed attraction for shrubs at small spatial scales. This could be related to vegetative propagation of the cactus and a facilitative interaction with the shrubs. Adult shrubs (whether considering or not the species) were distributed randomly in the plot. However, when the evaluation considered the species and included seedlings/saplings, shrub species showed aggregation at some spatial scale. We found a progression from aggregation at young age to increasingly less contagious distributions at older stages, which might indicate self-thinning. The two dominant shrub species showed neither attraction nor repulsion between each other. Our results could in part be explained by the characteristic climate of subtropical, high altitude semi-deserts.

Between-group contest competition for food in a highly folivorous population of black and white colobus monkeys (Colobus guereza)

In theory, between-group contest (BGC) competition for food can greatly influence female social relationships and reproductive success in primates, but few studies have investigated whether such effects occur and, if so, under what ecological conditions. There is evidence that adult male black and white colobus monkeys (Colobus guereza, “guerezas”) defend the food their mates need against other groups, suggesting that BGC competition is important in this species. Using data on feeding, ranging, vegetation patterns, and intergroup encounters between six neighboring guereza groups, I provide evidence that the highly folivorous guerezas at Kanyawara, Kibale National Park, Uganda, engaged in BGC competition over unevenly dispersed, relatively high-quality feeding areas or “core areas”. Intergroup aggression was common, and groups’ home ranges overlapped. Groups were more likely to initiate high-level aggression if they encountered another group within or near their core area, and groups that initiated and won encounters often fed in the same areas in which losing groups had fed. Guerezas fed selectively on species with contagious (clumped) distributions and concentrated their feeding efforts in areas of the forest that contained the most food (core areas). Groups could be ranked in a linear dominance hierarchy, and group rank number was inversely related to the quantity and quality of food in groups’ core areas. This study not only provides good evidence that BGC competition occurs in primates but it also reinforces the idea that folivore food resources may be worth defending.

Semiconductor yield models using contagious distributions and their limiting forms

In order to set up a semiconductor yield model, one should consider defect density variations not only among chips but also within a chip. In this paper, we propose semiconductor yield models based on the contagious distributions reflecting the variations. These models incorporate the probability that a defect becomes fatal. We also consider various limiting forms of a proposed contagious distribution by taking extreme values of the related parameters. A simplified form of the proposed yield formula based on the limiting distribution is derived and its performance is compared with others using computer simulation. The proposed three yield models are shown in a simulation study to outperform alternative models based on the existing ideas.

A PROBLEM IN ASCERTAINMENT

In studies of disease inheritance, it is more convenient to collect family data by first locating an affected individual and then enquiring about the status of his or her relatives. Although the different categories of children classified by disease, sex, and other covariates may have a particular multinomial distribution among families of a given size, the numbers as ascertained do not have the same distribution because of unequal probabilities of selection of families. The introduction of weighted distributions to correct for ascertainment bias in the estimation of parameters in the classical segregation model can be traced to Fisher in 1934. This theory was presented in a general formulation by C. R. Rao at the First International Symposium on Classical and Contagious Distributions in 1963. Further expansion on the topic was given by C. R. Rao in the ISI Centenary Volume published in 1985. The effects of different two-phase sampling designs on the estimation of parameters in the classical segregation model are examined. An approximation to the classical segregation likelihood model is found to produce results close to those of the exact likelihood function in Monte Carlo simulations for a balanced two-phase design. This has implications for more complex models in which the computation of the exact likelihood is prohibitive, such as for the enhancement of a typical survey sampling plan designed initially for linkage analysis but then used retroactively for a combined segregation and linkage analysis.

Use of contagious distributions in the semiconductor yield models considering cluster effect

As semiconductor chips become larger, more than one cluster can be expected to form on a single chip and consequently defect density variations may be apparent not only among chips but also within a chip. In order to reflect this situation more effectively, we propose semiconductor yield models based on the contagious distributions. These models incorporate the probability that a defect or a cluster becomes fatal. Furthermore, we consider various limiting forms of the proposed contagious distribution by taking extreme values of the related parameters, A simplified form of the proposed yield formula based on the limiting distribution is also derived and its performance is compared with others using computer simulation. The proposed three yield models are shown in a simulation study to outperform alternative models based on the existing ideas.

Selectivity and Efficiency of Two Otter Trawls Used to Assess Estuarine Fish and Macroinvertebrate Populations in North Carolina

Otter trawl surveys are frequently used to assess estuarine fish and macroinvertebrate communities. Although these surveys may have similar objectives and sampling areas and seasons may overlap, the sampling gear is usually unique to the agency conducting the survey. An example of this is the North Carolina Division of Marine Fisheries (NCDMF) and Environmental Monitoring and Assessment Program-Estuaries (EMAP) surveys in North Carolinian estuaries. We estimated experimentally the selectivity and efficiency of the trawls used for these surveys to determine the comparability of data used to estimate community structure and the abundance of dominant species. The catch percent similarity of the trawls was low (12.0%). The NCDMF net (3.2-m flat otter trawl, 6.4-mm mesh body, 3.2-mm cod-end, plus tickle chain) precisely (11.7%) and accurately (4.5%) sampled brown shrimp, Penaeus aztecus, density but overestimated spot, Leiostomus xanthurus, densities (22.8% accuracy), possibly because these fishes had highly contagious distributions. The EMAP net (4.9-m high-rise otter trawl, 38.1-mm mesh body and cod-end) was precise (17.9–37.4%) but inaccurate (76.8–97.2%), probably because of the single large mesh size and the lack of a tickler chain. Our study suggests the EMAP and NCDMF surveys collect different subsamples of the same fish and macroinvertebrate estuarine populations, and therefore could deliver different results and conclusions.

Facilitation among Woody Plants Establishing in an Old Field

Trees and shrubs establishing in grasslands frequently occur in clumps associated with increased soil moisture and N availability. We tested whether the presence of conspecifics or enhanced soil resources increased the growth and survivorship of a shrub (Symphoricarpos occidentalis) and a tree (Picea glauca) in the presence of the perennial grass (Bromus inermis). Rhizomes of Symphoricarpos and seedlings of Picea were transplanted into plots either singly or with four conspecific neighbors, and with grass neighbors present or removed. Half the plots received additional water, N, and shade to simulate a forest environment. Roots and shoots of transplants were harvested after two growing seasons. Soil moisture and available N were lowest at high transplant density, and highest in the simulated-forest environment and in treatments where grass was removed. Transplant survivorship was generally enhanced in plots where grasses were removed and in the simulated-forest environment. Picea survivorship was reduced by grasses in plots without resource manipulations but was unaffected by grasses in the simulated-forest environment, suggesting that the simulated-forest environment enhanced the ability of Picea to compete with grasses. Picea growth, however, was reduced by conspecific neighbors in all cases. For Symphoricarpos conspecific neighbors significantly decreased growth rates with grasses absent but significantly increased growth rates with grasses present. Thus the direct effect of high density in monoculture was to reduce Symphoricarpos growth, but the indirect effect of high density in the presence of grass was to facilitate Symphoricarpos growth. In summary, conspecific neighbors increased the growth rate of Symphoricarpos in competition with grass, and a simulated-forest environment enhanced the ability of Picea to survive in the presence of grasses. The results support the idea that contagious distributions of woody species invading grasslands enhance woody plant establishment.

FACILITATION AMONG WOODY PLANTS ESTABLISHING IN AN OLD FIELD

Trees and shrubs establishing in grasslands frequently occur in clumps associated with increased soil moisture and N availability. We tested whether the presence of conspecifics or enhanced soil resources increased the growth and survivorship of a shrub (Symphoricarpos occidentalis) and a tree (Picea glauca) in the presence of the perennial grass (Bromus inermis). Rhizomes of Symphoricarpos and seedlings of Picea were transplanted into plots either singly or with four conspecific neighbors, and with grass neighbors present or removed. Half the plots received additional water, N, and shade to simulate a forest environment. Roots and shoots of transplants were harvested after two growing seasons. Soil moisture and available N were lowest at high transplant density, and highest in the simulated-forest environment and in treatments where grass was removed. Transplant survivorship was generally enhanced in plots where grasses were removed and in the simulated-forest environment. Picea survivorship was reduced by grasses in plots without resource manipulations but was unaffected by grasses in the simulated-forest environment, suggesting that the simulated-forest environment enhanced the ability of Picea to compete with grasses. Picea growth, however, was reduced by conspecific neighbors in all cases. For Symphoricarpos conspecific neighbors significantly decreased growth rates with grasses absent but significantly increased growth rates with grasses present. Thus the direct effect of high density in monoculture was to reduce Symphoricarpos growth, but the indirect effect of high density in the presence of grass was to facilitate Symphoricarpos growth. In summary, conspecific neighbors increased the growth rate of Symphoricarpos in competition with grass, and a simulated-forest environment enhanced the ability of Picea to survive in the presence of grasses. The results support the idea that contagious distributions of woody species invading grasslands enhance woody plant establishment.

Oviposition pattern of phytophagous insects: on the importance of host population heterogeneity.

Frequency distributions of insect immatures per host are often fitted to contagious distributions, such as the negative binomial, to deduce oviposition pattern. However, different mechanisms can be involved for each theoretical distribution and additional biological information is needed to correctly interpret the fits. We chose the chestnut weevil Curculio elephas, a pest of the European chestnut Castanea sativa, as a model to illustrate the difficulties of inferring oviposition pattern from fits to theoretical distributions and from the variance/mean ratio. From field studies over 13-16 years, we show that 20 out of the 31 yearly distributions available fit a negative binomial and 25 a zero-inflated Poisson (ZIP). No distribution fits a Poisson distribution. The ZIP distribution assumes heterogeneity within the fruit population. There are two categories of host: the first comprises chestnuts unsuitable for weevil oviposition or in excess relative to the number of weevil females, and the second comprises suitable fruits in which oviposition behavior is random. Our results confirm this host heterogeneity. According to the ZIP distribution, the first category of hosts includes on average 74% of the chestnuts. A negative binomial distribution may be generated by either true or false contagion. We show that neither interference between weevil females, nor spatial variation in the infestation rate exist. Consequently, the observed distributions of immatures are not the result of false contagion. Nevertheless, we cannot totally exlude true contagion of immatures. In this paper we discuss the difficulty of testing true contagion in natural conditions. These results show that we cannot systematically conclude in favour of contagion when fitting a distribution such as the negative binomial or when a variance/mean ratio is higher than unity.

A track count for estimating mountain lion Felis concolor californica population trend

Reliable estimates of status and population trend are critical for conservation of large terrestrial carnivores, but are usually lacking due to the high costs of sampling across large geographic areas. For detecting population trends of mountain lion Felis concolor californica, we evaluated counts of track sets on 48 randomly chosen quadrats in California. Each quadrat contained 33.8 km of transect on dusty, dirt roads, which were chosen by local wildlife biologists. A count of track sets by one person on all quadrats was more efficient than recording presence/absence by local survey teams. We estimated an efficient sample size of 44 quadrats in California after applying our data to a general formula for contagious distributions. This sample size can be reduced substantially by choosing new transect locations based on associations of tracks with topography and habitat. Tracks were most likely found on roads along 1st- and 2nd-order streams, on mountain slopes and knolls/peaks and in oak woodland and montane hardwood conifer forest. A changing mountain lion population can be detected with an inexpensive, periodic track survey and self-stratifying, non-parametric tests. Each track survey across California can be finished in 30 days. The many mountain lions and the variety of environmental conditions included at this extraordinarily large spatial scale permit estimates of: (1) trends among population strata in quadrats that are clustered according to typical number and age/sex class of track sets; (2) population size and demography after individuals are identified by their tracks, and after linear density on roads is calibrated from spatial density at intensive study, sites: and (3) spatio-temporal associations with bobcat Felis rufus, black bear Ursus americanus, coyote Canis latrans, and fox Vulpes vulpes and Urocyon cinereoargenteus.

Population structure of Thenus orientalis and T. indicus (Decapoda: Scyllaridae) in northeastern Australia

[Extract] Bay lobsters of the genus Thenus are a valuable component of the incidental catch of the penaeid trawl fisheries of northern Australia. The 2 species present, Thenus indicus Leach, 1815 and Thenus orientalis (Lund, 1793), have mutually exclusive distributions. For each species, relative abundance, size and sex composition were measured monthly and related to physical characteristics including temperature, salinity, depth and sediment type. Both species populations were characterised by contagious distributions. Mean density of T. indicus was 1.78 (±0.15) lobsters ha⁻¹, while that of T. orientalis was 2.02(±0.13). In both populations, depth and sediment type were significantly correlated with abundance. T. indicus was most abundant in depths of 10-30 m and where sediments were characterised by a preponderance of find sands and silt. In contrast, T. orientalis was most abundant in 1.00 mm particle size. In both species, mean size varied significantly thorughout the year as a function of growth and recruitment. Male and female T. indicus were equally abundant, while male T. orientalis were significantly more abundant than females.

Faunal associations on scallop grounds in the western Gulf of Maine

Benthic photographic transects were made during 1986–1987 across productive scallop beds on Jeffreys and Fippennies Ledges, western Gulf of Maine, from a manned submersible at depths of 56–84 m. Three megafaunal invertebrates dominated at each site: the sabellid worm Myxicola infundibulum (Renier) (mean densities ranging from 3.3 ± 4.2 to 7.1 ± 9.6· m −2); the burrowing cerianthid anemone Cerianthus borealis Verrill (1.0 ± 1.2 to 2.0 ± 0.5· m −2); and the sea scallop Placopecten magellanicus (Gmelin) (0.2 ± 0.5 to 1.0 ± 2.2· m −2). All three species exhibited contagious distributions (i.e., occurred in largescale clusters or patches), which could be modeled by negative binomial functions. On Fippennies Ledge, where little scallop dredging occurred in 1986, but, where appreciable fishing was conducted in 1987, sea scallops were positively associated with M. infundibulum and negatively associated with C. borealis in both years. In contrast, the association between M. infundibulum and C. borealis changed from a significant negative association in 1986 to random in 1987. The marked increase in scallop dredging on Fippennies Ledge between 1986 and 1987 was apparently the cause of a significant decline in the mean densities of all three megafaunal species (70% decline in sea scallops; 25–27% decline in cerianthids and myxicolids), although the pattern of faunal association with the sea scallops remained intact. On Jeffreys Ledge, where intensive dredging had occurred prior to our 1986 sampling, the pattern of faunal association described for Fippennies Ledge was absent. Thus, natural faunal associations may be severely impacted by fishing operations. We propose that C. borealis controls the spatial distribution and patch size of both M. infundibulum and P. magellanicus by preying on the larvae of the latter two species.

Estimation and evaluation methods for population growth models with spatial diffusion: Dynamics of mountain pine beetle

This study approaches a problem of estimation and evaluation of population models from the viewpoint that a forest ecosystem manager needs to know how the pest (mountain pine beetle) and related tree (pine) mortality, will spread to surrounding stands over time. A model is proposed, based on a diffusion equation (second order, partial differential equation) to describe in spatial terms the functional relationships between pest and host. Pest density, food availability for the pest, and the diffusivity of the pest in space are the variables used in the model. To estimate parameters, the differential equation model was approximated as a difference equation model, and a first-order autoregressive error structure with contemporaneous correlation between cross sections was assumed. A generalized least squares ( gls) estimation was applied and the estimates were used to predict mountain pine beetle ( mpb) outbreaks. Three types of maps ( mpb density surfaces) were constructed for a certain area: one showing the actual pest condition for 1984 ( am), one showing the output of a predictive model that uses food availability, lagged density, a covariate and diffusivity as the predictors (diffusion-advection, pm1), and one using only the diffusivity and the lagged density as the predictor variables (simple diffusion, px2). The results indicate that 3-year history of mpb population dynamics is adequate to provide an 1-year projection of mpb densities. The evaluation of the models was performed by translating and rotating the predictive maps ( pm1, pm2) over the observed map ( am) and calculating geometric distortions. A variogram analysis and several aggregation indices, as well as contagious distributions, were used to test the agreement between the spatial patterns of the maps. These comparisons suggest that the prediction generated by the simple two-dimensional diffusion model ( pm2) is the best. Including terms for resource availability (food in form of phloem of living lodgepole pine) does not improve the precision of the projection. This does not imply that food is unimportant to mpb ecology, but rather that it is less important than prior population density for short-term projections.

Small-scale patterns of forest plants and environmental heterogeneity

Small-scale pattern analysis of plant populations was done in nine forest communities of the Moscow region (USSR). In most cases the vegetatively immobile and low-mobile species were found to have less contagious distributions than vegetatively mobile species. In different communities one and the same species may display a different kind of pattern, though no relationship between the abundance of species and the kind of its spatial distribution could be identified. Ecological indicator values were used to obtain data on the variability of environmental parameters inside the communities. Environmental heterogeneity appears to be the major factor determining the kind of vascular plant pattern. The kind of distribution of bryophytes (as a rule, high-contagious) is insignificantly related to environmental heterogeneity.

A remark on the poisson-pascal and some other contagious distributions

Some contagious distributions are found to be valid in a larger parameter space. One of these is a distribution which is a long-tailed, unimodal, mixed Poisson extension to the Poisson-Pascal.

Parameter Orthogonality for a Family of Discrete Distributions

Abstract The standard contagious distributions (see Douglas 1980) have been used in such varied fields as biology and automobile insurance, often to model various physical phenomena as well as provide a good fit to count data when other models are inadequate. Unfortunately, the parameterizations often used when working with these distributions normally lead to extremely high correlations of the maximum likelihood estimators (MLE's). This tends to lead to mathematical complexities, and causes difficulty or even errors in their interpretation. Furthermore, numerical difficulties may arise when using numerical procedures to locate the estimates. Some of these difficulties were discussed by Douglas (1980, pp. 171, 204-205), who suggested that a reparameterization to reduce or even eliminate such correlation is desirable. If the MLE's are asymptotically uncorrelated, the parameterization is orthogonal. Philpot (1964) derived an orthogonal parameterization for the Neyman Type A distribution; Stein, Zucchini, an...

Discussion of Dr JØrgensen’s Paper

Discussion of Dr JØrgensen’s Paper