Computer simulation of Gumboro disease outbreak. II. Results obtained with models G-1 and G-2.

The authors conducted a computer simulation with their Models G-1 and G-2 for Gumboro disease ten times in each of the following initial conditions: (1) size of population, 50, 100, and 1,000 chickens; (2) age of housing, 1, 7, 14, and 21 days; (3) nine levels of parentally conferred immunity in one-day-old chicks; (4) four levels of virus contamination; and (5) three steps of coefficient for aggravating morbid status. Every simulation was operated up to the age when all the birds of a flock turned to be insusceptible so as to yield the daily numbers of chickens (1) susceptible, (2) diseased, (3) immunized, and (4) removed, and (5) the accumulation of diseased chickens. The innate resistance, parentally conferred immunity, virus contamination, and morbid status were expressed in such values that they could be compared with one another. As a result, Model G-2 produced a more realistic epizootic pattern than Model G-1, but both models concealed the effect of differences in size of population and in age of housing. Notwithstanding the incompleteness of the models, the computer simulation gave valuable information for a further advancement in this series of studies.     

Computer simulation of Gumboro disease outbreak. IV. Epizootics obtained by mode G-4 with flock size, age and immunity changed

For the computer simulation of Gumboro disease outbreak by Model G-4 a program was written in FORTRAN. Of over twenty parameters involved in the model, the following three were used as input variables: (1) age of chickens at housing a1 (= 1 and 21); (2) size of flock at housing, N(a1) (= 100 and 1,000); and (3) geometric mean of the level of parentally conferred immunity at hatching, G(1) (= 0, 2, 8, and 32). The outputs were the graphic images demonstrating the chronological changes in a flock of innate resistance, parentally conferred immunity, and their sum, and the epizootic patterns composed of numbers of chickens at subclinical stage, clinically diseased, recovered, condemned, etc. at each age. As a result, stronger epizootics were produced at a lower level of parentally conferred immunity, and a higher age and a larger size of flocks. It was suggested that the subclinical stage might not be understood as an inapparent infection, and that a further postulate on the infection might be necessary to be introduced into this model to increase the practical utility, as well as the theoretical soundness, of this series of studies.     

A cost-benefit analysis of feeding in female tsetse

Abstract. Three models for feeding in female tsetse are considered. Model I: there is a prolonged non-feeding phase after each meal followed by feeding at a constant rate, with a constant probability of dying as a consequence of feeding. Model II: the feeding rate increases linearly after each meal. Model III: the feeding rate increases exponentially after each meal. In Models II and III the feeding hazard is a linear function of the probability of feeding. Production of viable female offspring is estimated under each model, making allowance for losses of adults due to starvation and to background and feeding mortality, losses of pupae due to predation and parasitization, and losses of young flies if their mothers take insufficient blood during pregnancy. Under Model I, if females require three meals to produce viable pupae in 9 days, then for a non-decreasing population with a background mortality of 1%/day, and 25% pupal losses due to predation and parasitism, the feeding risk must be ≤5%/feed. At this maximum level the non-feeding phase should be 2–2.5 days for optimal productivity, with a mean feeding interval of 60–72 h. If the background mortality is 2%/day, feeding losses cannot exceed 1%/feed for a non-decreasing population. If four or five meals are required for the production of fully viable pupae, the optimal values of the non-feeding phase and mean feeding interval tend towards 1 and 2 days respectively. Under Models II and HI the mean feeding interval is 50–60 h for optimal productivity (with variances 3 times as large as for Model I), in good agreement with estimates from recent models for feeding and digestion. Field evidence suggests that feeding tsetse take greater risks as their fat levels dwindle. This should result in feeding (and feeding mortality) rates which increase during the feeding phase - as assumed in Models II and III but not in Model I. These models allow greater flexibility than Model I, because flies can feed early in the hunger cycle, at low probability, as long as the feeding risk is also low.     

Inter- and intrapopulation variation in thermal reaction norms for growth rate: evolution of latitudinal compensation in ectotherms with a genetic constraint

In ectotherms, lower temperatures in high-latitude environments would theoretically reduce the annual growth rates of individuals. If slower growth and resultant smaller body size reduce fitness, individuals in higher latitudes may evolve compensatory responses. Two alternative models of such latitudinal compensation are possible: Model I: thermal reaction norms for growth rates of high-latitude individuals may be horizontally shifted to a lower range of temperatures, or Model II: reaction norms may be vertically shifted so that high-latitude individuals can grow faster across all temperatures. Model I is expected when annual growth rates in the wild are only a function of environmental temperatures, whereas Model II is expected when individuals in higher latitudes can only grow during a shorter period of a year. A variety of mixed strategies of these two models are also possible, and the magnitude of horizontal versus vertical variation in reaction norms among latitudinal populations will be indicative of the importance of "temperature" versus "seasonality" in the evolution of latitudinal compensation. However, the form of latitudinal compensation may be affected by possible genetic constraints due to the genetic architecture of reaction norms. In this study, we examine the inter- and intrapopulation variations in thermal reaction norms for growth rate of the medaka fish Oryzias latipes. Common-environment experiments revealed that average reaction norms differed primarily in elevation among latitudinal populations in a manner consistent with Model II (adaptation to "seasonality"), suggesting that natural selection in high latitudes prefers individuals that grow faster even within a shorter growing season to individuals that have longer growing seasons by growing at lower temperatures. However, intrapopulation variation in reaction norms was also vertical: some full-sibling families grew faster than others across all temperatures examined. This tendency in intrapopulation genetic variation for thermal reaction norms may have restricted the evolution of latitudinal compensation, irrespective of the underlying selection pressure.     

Torque and rotation rate of the bacterial flagellar motor.

This paper describes an analysis of microscopic models for the coupling between ion flow and rotation of bacterial flagella. In model I it is assumed that intersecting half-channels exist on the rotor and the stator and that the driving ion is constrained to move together with the intersection site. Model II is based on the assumption that ion flow drives a cycle of conformational transitions in a channel-like stator subunit that are coupled to the motion of the rotor. Analysis of both mechanisms yields closed expressions relating the torque M generated by the flagellar motor to the rotation rate v. Model I (and also, under certain assumptions, model II) accounts for the experimentally observed linear relationship between M and v. The theoretical equations lead to predictions on the relationship between rotation rate and driving force which can be tested experimentally.     

MORBILLIVIRUS INFECTION IN BOTTLENOSE DOLPHINS: EVIDENCE FOR RECURRENT EPIZOOTICS IN THE WESTERN ATLANTIC AND GULF OF MEXICO

Morbillivirus infection is widespread among odontocetes of the western Atlantic and Gulf of Mexico. Serologic evidence of infection in bottlenose dolphins, Tursiops truncatus , was first detected during an epizootic along the mid-Atlantic coast in 1987. Here, we report recurrent epizootics in the coastal dolphin population since at least the early 1980s based on serological surveys and regional stranding frequencies. The first observed epizootic of this series occurred in the Indian and Banana Rivers in 1982 and was followed by others on the mid-Atlantic coast in 1987–1988 and in the Gulf of Mexico between 1992 and 1994. This temporal pattern of infection is likely facilitated by the population size and its fragmentation into relatively discrete coastal communities. Introduction of morbillivirus into a community with a sufficient number of naive hosts may precipitate an epizootic, depending on the potential for transmission within the group. Propagation of an epizootic along the coast is probably determined by frequency of contact between adjacent communities and seasonal migrations.
Morbillivirus antibodies were also detected in serum from offshore bottlenose dolphins. The sero-prevalence in the latter may be higher than in coastal dolphins because of their close association with enzootically infected pilot whales ( Globicephala spp.). Occasional contact between offshore and coastal dolphins may provide an epizootiologic link between pilot whales and coastal dolphin communities.     

The hermeneutics of ecological simulation

Computer simulation has become important in ecological modeling, but there have been few assessments on how complex simulation models differ from more traditional analytic models. In Part I of this paper, I review the challenges faced in complex ecological modeling and how models have been used to gain theoretical purchase for understanding natural systems. I compare the use of traditional analytic simulation models and point how that the two methods require different kinds of practical engagement. I examine a case study of three models from the insect resistance literature in transgenic crops to illustrate and explore differences in analytic and computer simulation models. I argue that analyzing simulation models has been often inappropriately managed with expectations derived from handling analytic models. In Part II, I look at simulation as a hermeneutic practice. I argue that simulation models are a practice or techné. I the explore five aspects of philosophical hermeneutics that may be useful in complex ecological simulation: (1) an openness to multiple perspectives allowing multiple levels of scientific pluralism, (2) the hermeneutic circle, a back and forth in active communication among both modelers and ecologists; (3) the recognition of human factors and the nature of human practices as such, including recognizing the role of judgments and choices in the modeling enterprise; (4) the importance of play in modeling; (5) the non-closed nature of hermeneutic engagement, continued dialogue, and recognizing the situatedness, incompleteness, and tentative nature of simulation models.

QTL linkage analysis of connected populations using ancestral marker and pedigree information

The common assumption in quantitative trait locus (QTL) linkage mapping studies that parents of multiple connected populations are unrelated is unrealistic for many plant breeding programs. We remove this assumption and propose a Bayesian approach that clusters the alleles of the parents of the current mapping populations from locus-specific identity by descent (IBD) matrices that capture ancestral marker and pedigree information. Moreover, we demonstrate how the parental IBD data can be incorporated into a QTL linkage analysis framework by using two approaches: a Threshold IBD model (TIBD) and a Latent Ancestral Allele Model (LAAM). The TIBD and LAAM models are empirically tested via numerical simulation based on the structure of a commercial maize breeding program. The simulations included a pilot dataset with closely linked QTL on a single linkage group and 100 replicated datasets with five linkage groups harboring four unlinked QTL. The simulation results show that including parental IBD data (similarly for TIBD and LAAM) significantly improves the power and particularly accuracy of QTL mapping, e.g., position, effect size and individuals’ genotype probability without significantly increasing computational demand.     

Study of strategies for selecting quantitative trait locus mapping procedures by computer simulation

Along with the development and integration of molecular genetics and quantitative genetics, many quantitative trait locus (QTL) mapping studies have been conducted using different mapping populations in various crop species. Existing QTLs can be used for marker-assisted breeding and map-based cloning, whereas the false-positive QTLs are no use. The purpose of this study is to evaluate the suitability of different mapping procedures for data from different genetic models. In this study, four types of recombinant inbred lines (RILs) with different genetic models, viz. additive QTLs (Model I), additive and epistatic QTLs (Model II), additive QTLs and QTL × environment interaction (Model III), additive, epistatic QTLs and QTL × environment interaction (Model IV), were simulated by computer. Six types of QTL mapping procedures, viz. CIM, MIMF, MIMR, ICIM, MQM and NWIM, on four kinds of QTL mapping software, viz. WinQTL Cartographer Version 2.5, IciMapping Version 2.0, MapQTL Version 5.0 and QTLnetwork Version 2.0, were used for screening QTLs of the simulated RILs. The results showed that different mapping procedures have different suitability for different genetic models. CIM and MQM can only screen Model I data. MIMR, MIMF and ICIM can only screen Model I and Model II data. NWIM can screen all four models’ data. It can be concluded that different genetic models’ data have different most suitable mapping procedures. In practical experiments where the genetic model of the data is unknown, a multiple model mapping strategy should be used, that is a full model scanning with complex model procedure followed by verification with other procedures corresponding to the scanning results.     

Lysine 188 of the catabolite gene activator protein (CAP) plays no role in specificity at base pair 7 of the DNA half site.

Two similar, but not identical, models have been proposed for the amino acid-base pair contacts in the CAP-DNA complex ('model I,' Weber, I. and Steitz, T., Proc. Natl. Acad. Sci. USA, 81, 3973-3977, 1984; 'model II,' Ebright, et al., Proc. Natl. Acad. Sci. USA, 81, 7274-7278, 1984). The most important difference between the two models involves Lys188 of CAP. Model I predicts that Lys188 of CAP makes a specificity determining contact with base pair 7 of the DNA half site. In contrast, model II predicts that Lys188 makes no contact with base pair 7 of the DNA half site. In the present work, we have used site-directed mutagenesis to replace Lys188 of CAP by Asn, an amino acid unable to make the putative contact. We have assessed the specificities of the following proteins, both in vitro and in vivo: wild-type CAP, [Asn188]CAP, [Val181]CAP, and [Val181;Asn188]CAP. The results indicate that Lys188 makes no contribution to specificity at base pair 7 of the DNA half site. We propose, contrary to model I, that Lys188 makes no contact with base pair 7 of the DNA half site.     

Allometric scaling and seasonality in the epidemics of wildlife diseases

We present a susceptibles-exposed-infectives (SEI) model to analyze the effects of seasonality on epidemics, mainly of rabies, in a wide range of wildlife species. Model parameters are cast as simple allometric functions of host body size. Via nonlinear analysis, we investigate the dynamical behavior of the disease for different levels of seasonality in the transmission rate and for different values of the pathogen basic reproduction number (R(0)) over a broad range of body sizes. While the unforced SEI model exhibits long-term epizootic cycles only for large values of R(0), the seasonal model exhibits multiyear periodicity for small values of R(0). The oscillation period predicted by the seasonal model is consistent with those observed in the field for different host species. These conclusions are not affected by alternative assumptions for the shape of seasonality or for the parameters that exhibit seasonal variations. However, the introduction of host immunity (which occurs for rabies in some species and is typical of many other wildlife diseases) significantly modifies the epidemic dynamics; in this case, multiyear cycling requires a large level of seasonal forcing. Our analysis suggests that the explicit inclusion of periodic forcing in models of wildlife disease may be crucial to correctly describe the epidemics of wildlife that live in strongly seasonal environments.     

Parametric analysis of the errors associated with the Michaelis-Menten equation

Based on the well-known mechanism describing Michaelis-Menten kinetics, three rate expressions may be developed: the exact solution (Model 1), a rate equation resulting from the pseudo-steady-state assumption (Model 2), and Model 2 with the additional assumption that the amount of free substrate is approximately equal to the total amount of substrate (Model 3). Although Model 1 is the most precise, it must be integrated numerically and it requires three experimentally determined parameters. Models 2 and 3, however, are simpler and require only two parameters. Using dimensionless forms of the three models, we have evaluated the errors in the two simplified models relative to the exact solution using a wide range of parameter values. The choice of model for reactor design depends on the initial substrate to enzyme ratio (alpha(0)), and on the ratio of the Michaelis-Menten constant to the enzyme concentration (sigma). Based on a 2% model error criteria, when alpha(0) > 15 or sigma >/= 100, Model 3 is adequate; if 5 < alpha(0) < 15, or if sigma >/= 10, then Model 2 may be used; and if alpha(0) < 5 and sigma < 10, then the exact solution (Model 1) is required.     

DNA-sequence recognition by CAP: role of the adenine N6 atom of base pair 6 of the DNA site.

Two similar, but not identical, models have been proposed for the amino acid-base pair contacts in the CAP-DNA complex ('Model I,' Weber, I. and Steitz, T., Proc. Natl. Acad. Sci. USA, 81, 3973-3977, 1984; 'Model II,' Ebright, et al., Proc. Natl. Acad. Sci. USA, 81, 7274-7278, 1984). One difference between the two models involves Glu181 of CAP. Model I predicts that Glu181 of CAP makes two specificity determining contacts: one H-bond with the cytosine N4 atom of G:C at base pair 7 of the DNA half site, and one H-bond with the adenine N6 atom of T:A at base pair 6 of the DNA half site. In contrast, Model II predicts that Glu181 makes only one specificity determining contact: one H-bond with the cytosine N4 atom of G:C at base pair 7 of the DNA half site. In the present work, we show that replacement of T:A at base pair 6 of the DNA half site by T:N6-methyl-adenine has no, or almost no, effect on the binding of CAP. We conclude, contrary to Model I, that Glu181 of CAP makes no contact with the adenine N6 atom of base pair 6 of the DNA half site.     

Modelling Asymmetrical Growth Curves that Rise and then Fall: Applications to Foliage Dynamics of Sugar Beet (Beta vulgaris L.)

This paper discusses the derivation and fitting of three empiricalmodels with turning points for describing the growth of plantcomponents, such as shoot weight, leaf area and root length,that typically rise and then fall during the course of the growingseason. The models (Models I, II and III) have analytical solutionsand may be viewed as extensions of the Gompertz, Richards andChanter growth equations. They differ by having an additionalparameter which, following a sigmoidal rise of the dependentvariable, determines subsequent net rate of decline. The modelswere fitted to sequential measures of foliage cover of sugarbeet crops grown in the UK during 1980–1991. It was importantthat this could be done with relative ease using standard statisticalprocedures. Partial linear transformations of two of the models,with one non-linear parameter remaining, are described; thesewere useful for estimating initial values for the parameters.All three models described the data well, although the fittingof Model II invariably failed to converge. For Models I andIII common and separate parameters, amongst years, were estimatedrelating to date of emergence, initial relative growth rate,maximum cover attained and rate of late season decline of foliagecover. The reduction in the residual mean square on fittingseparate, rather than common, parameters was usually significant.The models accommodate several biological processes that yieldsimilar shapes. This is demonstrated for Model I, in relationto its formulation and to effects of small perturbations inthe values of the parameters on the shape of the curves. ModelI, the simplest of the three models tested, has good fittingproperties, and in practice was best suited to describing foliagecover dynamics of sugar beet. Beta vulgaris L.; sugar beet; foliage cover; senescence; models; parameter estimation; growth functions     

The habitat quality index applied to New Mexico streams

The accuracy of two trout biomass (standing stock) prediction models, developed for Wyoming streams by Binns & Eiserman (1979), was evaluated for New Mexico streams inhabited by brown trout, Salmo trutta L. and rainbow trout, Oncorhynchus mykiss Walbaum. Thirty-two representative sites in 15 different streams were sampled under summer low-flow conditions in 1988 and 1989. The 11 phyiscal, chemical, and biological variables used in original models were used as independent variables for simple and multiple regression analysis designed to predict total trout biomass. Model I of Binns and Eiserman proved to be of limited utility; it explained 53% of the variation in total trout biomass at each of the New Mexico sites (kg ha⁻¹ = 8.916 + 0.830/Model U). Only 9.5% of the biomass variations was explained by Model II. Statistical analysis showed that trout biomass was significantly correlated with nitrate-nitrogen concentration and macroinvertebrate diversity in Model I. Because both variates are time consuming to estimate, Model I may not be any more cost-effective than sampling trout directly. The low predictive power of Model II probably indicates that it is limited to the geographical area of field measurement origin.     

Human head dynamic response to side impact by finite element modeling

The dynamic response of the human head to side impact was studied by 2-dimensional finite element modeling. Three models were formulated in this study. Model I is an axisymmetric model. It simulated closed shell impact of the human head, and consisted of a single-layered spherical shell filled wiht an inviscid fluid. The other two models (Model II and III) are plane strain models of a coronal section of the human head. Model II approximated a 50th percentile male head by an outer layer to simulate cranial bone and an inviscid interior core to simulate the intracranial contents. The configuration of Model III is the same as Model II but more detailed anatomical features of the head interior were added, such as, cerebral spinal fluid (CSF); falx cerebri, dura, and tentorium. Linear elastic material properties were assigned to all three models. All three models were loaded by a triangular pulse with a peak pressure of 40 kPa, effectively producing a peak force of 1954 N (440 lb). The purpose of this study was to determine the effects of the membranes and that of the mechanical properties of the skull, brain, and membrane on the dynamic response of the brain during side impact, and to compare the pressure distributions from the plane strain model with the axisymmetric model. A parametric study was conducted on Model II to characterize fully its response to impact under various conditions.(ABSTRACT TRUNCATED AT 250 WORDS)     

Source of ethane in expirate of rats ventilated with 100% oxygen

Ethane in alveolar expirate may have its source in organs other than the lung and be transported to the lung for elimination. We determined ethane production rates in rats (group I) ventilated with hydrocarbon-free air (HFA) before and after exsanguination. To determine whether the lung is the source of increased ethane production during exposure to 100% O2, we measured ethane in the expirate of nine exsanguinated, Sprague-Dawley rats (group II) mechanically ventilated with HFA and then with 100% O2. In all nine animals, ethane elimination rates on 100% O2 increased compared with HFA values. In five of the nine rats, HFA ventilation was reinstated after O2 (group III). In all five, ethane elimination fell with HFA ventilation compared with the value on 100%. Six rats with circulation intact were ventilated with HFA and then 100% O2 (group IV). Ethane production rate for group IV animals breathing HFA was not significantly different from the exsanguinated animals in group II while ventilated with HFA. The mean increase in ethane production for the group II animals was not significantly different from the group IV animals. Lung slices from four other rats (group V) were incubated in saline at 37 degrees C with FeCl2 (10 mg) added to enhance free radical formation. Paired lung samples from the same rat were incubated with either HFA or 100% O2. Headspace gas was analyzed chromatographically for ethane at 120 min. Mean ethane in the O2 samples was higher than for HFA. Rat lung tissue is the main source of increased ethane production during 100% O2 exposure.     

Incorporating rhizosphere processes into field-scale (agro)ecosystem models

Three different strategies for incorporating rhizosphere processes within field-scale models are compared, taking triple-cropped irrigated rice production as a common system and CH₄ emission as a common focus of interest. The strategies may be characterised as homogeneous (model I; root C deposition is added to the bulk soil compartment), areal (model II; roots contribute via aerenchymatous exchange to an increased soil–atmosphere interfacial surface area), and volumetric (model III; roots create around themselves a specific rhizosphere compartment). Model I is simpler than model II, which is simpler than model III. With identical parameters all models lead to similar seasonally integrated CH₄ emissions, but when the pattern of emission and the simulated CH₄ concentration in the soil is brought into the reckoning, the following order of precedence (greater is better) becomes clear: model IIImodel II>model I. Current field-scale models of soil organic matter (SOM) transformation, especially in rice soils, could be improved by taking explicit account of the rhizosphere and the processes which occur within it.     

Extinction, colonization, and species occupancy in tidepool fishes

Despite the increasing sophistication of ecological models with respect to the size and spatial arrangement of habitat, there is relatively little empirical documentation of how species dynamics change as a function of habitat size and the fraction of habitat occupied. In an assemblage of tidepool fishes, I used maximum-likelihood estimation to test whether models which included habitat size provided a better fit to empirical data on extinction and colonization probabilities than models that assumed constant probabilities over all habitats. I found species differences in how extinction and colonization probabilities scaled with habitat size (and hence local population size). However, there was little evidence for a relationship between extinction and colonization probabilities and the fraction of occupied tidepools, as assumed in simple metapopulation models. Instead, colonization and extinction were independent of the fraction of occupied tidepools, favoring a MacArthur-Wilson island-mainland model. When I incorporated declines in extinction probability with tidepool volume in a simple simulation model, I found that predicted occupancy could change greatly, especially when colonization was low. However, the predicted fraction of occupied patches in the simulation model changed little when I incorporated the range of values reported here for extinction and colonization and the rate at which they scale with habitat size. Quantifying extinction and colonization patterns of natural populations is fundamental to understanding how species are distributed spatially and whether metapopulation models of species occupancy provide explanatory power for field populations. Received: 14 March 1997 / Accepted: 21 September 1997