Populations and infectious diseases: Dynamics and evolution

The host-parasite or host-pathogen system was analyzed from dynamical and evolutionary viewpoints using simple mathematical models incorporating vertical transmission, immunity and its loss. We first analyzed a model without density regulation of host population. In the analysis on dynamics, the condition for the pathogen to work as a density regulating factor was obtained. In the analysis on evolution, criteria for the evolution of host and pathogen were proposed. These criteria implies that the evolution of hosts should result in an increase in infected host density, whereas the evolution of pathogens a decrease in susceptible host density. The direction of evolution at some parameters of host and that of pathogen were examined when the parameters were independently and freely changeable. Among the parameters, only reduction in additional mortality due to infection was the evolutionary trend common to both host and pathogen. In all the other parameters examined, trend of evolution predicted in host is reversed in pathogen. We then analyzed whether the obtained criteria still hold in models with density regulation of hosts. Using randomly generated parameter sets, we obtained the result that the criteria should hold very likely though they do not always hold. We discussed evolution of virulence when there is a constraint between the traits.     

Oviposition behaviour of Tamarixia radiata: effects of host density and exposure time

1. The number of hosts attacked as a function of host density is considered to be an important characteristic of parasitoid behaviour and is used to estimate key parameters such as handling time and ‘instantaneous rate of discovery’. However, little has been done to validate functional response models by direct observation of parasitoid oviposition behaviour. 2. Tamarixia radiata is the most promising parasitoid for biological control attacking Diaphorina citri. Mass rearing and augmentative release seen as a potential strategy for suppression of D. citri has been documented in abandoned citrus, residential areas, and organic groves. Nevertheless, parasitism rates in culture and in the field are only moderate, leading to questions about oviposition behaviour in response to host density. 3. Behaviours of gravid T. radiata females presented with susceptible host instars were categorised and documented by direct observation for 30 min and by camera recordings made over 12 h. Frequency of searching and antennating increased with host density during the 30 min. Probing rejection rates and search duration increased significantly with host density over 12 h. These factors resulted in significantly lower fecundity than expected, possibly due to host mark‐mediated deterrence within the small searching area. Females took approximately 3.6–4.2 min to probe and parasitise a host regardless of host density and exposure duration. These results were markedly different from the 52.2 min estimated from the functional response equation. 4. Further experiments are required to assess the range and persistence of the putative host‐marking pheromone, and to better understand the relationship between functional response parameters and actual behaviour.     

The distribution of eggs per host in a herbivorous insect--intersection of oviposition, dispersal and population dynamics

1. The dynamics of parasitic organisms depend critically upon the frequency distribution of parasite individuals per host. However, the processes giving rise to this frequency distribution have rarely been modelled and tested for organisms with complex host selection behaviour. 2. In this study Microrhopala vittata, a chrysomelid beetle, was used to investigate how oviposition behaviour, movement and density of host plants interact in shaping the frequency distribution of egg clusters per host in the field. 3. Enclosures were stocked with two different host species and different beetle densities and various stochastic process models were fitted to egg cluster count data obtained from these enclosures. The different models were derived considering different scenarios, in particular whether or not plant density limits oviposition rate, whether or not ovipositing females actively seek out the most attractive plant within their perception radius and whether a female's oviposition rate is determined by plant intrinsic factors, the plant's egg cluster load or the surrounding beetle density. 4. The model parameters fitted to cage data were used to describe the frequency distribution of egg cluster counts obtained in a release experiment in the field. A total of 220 beetle pairs were released at five locations in a field where this beetle was not observed previously. Each release point was at a border between the two host species. 5. One model predicted for the preferred host species the egg cluster count frequencies in the field from parameters estimated in the cages. This model assumed that egg clusters present on a plant increased subsequent oviposition on this plant. All other models could not describe the distribution of egg cluster counts for either of the two host species. 6. The results suggest that females seek out attractive hosts actively and the attractiveness of a plant increases with its egg cluster load. This behaviour creates a frequency distribution of egg clusters per host that depends only on beetle density but not on plant density. This conclusion has important implications for modelling insect-plant interactions.     

The importance of environmental spatial heterogeneity and host social structure in disease transmission

[First paragraph]The spatial structure of a host population determines the spatial probability distribution of interaction between individuals, and therefore influences the spatio-temporal dynamics of disease transmission within the host population (Keeling, 1999; Gudelj and White, 2004). Nigel Barlow recognised this and included non-linear transmission in his later models (Barlow, 1991), simulating the result of spatial heterogeneity of risk in susceptible hosts. These models produced behaviour that could not be found in models with homogeneously mixed host populations: more rapid disease dynamics and a greater robustness of disease to control measures. However, in this model there was no causal mechanism driving the initial spatial heterogeneity of risk in host individuals. Environmental heterogeneity is likely to be a key factor in determining the spatial distribution of host individuals (Cronin and Reeve, 2005). We attempted to explore how environmental heterogeneity may affect disease dynamics via its influence on the spatial distribution of host individuals. We developed a spatially explicit stochastic model that incorporated spatially variable host density distributions, primarily driven by environmental heterogeneity.     

Modelling epiphyte metapopulation dynamics in a dynamic forest landscape

We combine simulations with spatial statistics to estimate the parameters of a metapopulation model for the epiphytic lichen Lobaria pulmonaria specializing on aspen ( Populus tremula ) and goat willow ( Salix caprea ) in Fennoscandian boreal old-growth forests. We estimated the parameters of a forest landscape model (FIN-LANDIS) by repeatedly running simulations and selecting the set of parameters for tree ecology and fire regime that reproduced empirical host tree density and spatial patterns. Second, we tested which variables were important in epiphyte colonization and estimated the dispersal kernel. Third, we run a metapopulation model for the lichen across the estimated landscape scenarios and selected values for the remaining parameters that reproduced the empirical patterns of epiphyte occurrence. There was little variation in predicted dynamics, occupancy and spatial patterns between replicate metapopulation simulations. However, more data would be required for accurately estimating the parameters of FIN-LANDIS primarily because of the inherent stochasticity in large scale forest fires. Following the beginning of fire suppression in the study area 150 years ago, the model predicts that lichen occupancy first increases but subsequently declines. The lower occupancy in the past than at present is explained by high rate of tree destruction by fires, which increases local extinction rate in patch-tracking metapopulations. In the absence of fires, the occupancy increases because of lower extinction rate, but without forest fires or alternative means of host tree regeneration, the lichen is predicted to go ultimately extinct because of severely reduced density of aspen and goat willow.     

Ratio-dependent parasitism with Trissolcus basalis (Wollaston) (Hymenoptera: Scelionidae) on egg rafts of Nezara viridula (Linnaeus) (Hemiptera: Pentatomidae): effect of experimental variables and compatibility of 'ratio' and 'Holling' models

Abstract Egg rafts of Nezara viridula were exposed to the parasitoid wasp Trissolcus basalis in experimental arenas to establish the relationship of the rates of attack and parasitism to various combinations of arena size, parasitoid density, host density and parasitoid-to-host ratio. Arena sizes were varied in the ratio 1:9:63, with the largest having a search area of 1.44 m². Parasitoid and host densities were varied over a 27-fold range. The parasitoid-to-host ratios used were 1:1, 3:1 and 6:1. Finding time was related to a constant factor (flight propensity), rather than to the difficulty of finding (density of hosts). Initial attack rates were therefore related only to parasitoid numbers (or density), even at the lower densities and ratios. Parasitism rates (a function of attack rate per host) were thus also strongly related to parasitoid to host ratio, regardless of densities used and arena sizes. Even reducing host density, while keeping time and parasitoid density constant, increased the parasitism rate. A ratio model for parasitism rate was therefore compatible with the data but the more explicit Holling 'disc' equation was also compatible because handling time was sufficiently large to make it sensitive to the ratio of parasitoids to hosts for the densities used. We conclude that the two models would predict different results if the density of host egg rafts was in a range below one per square metre.     

Changes in seasonal climate outpace compensatory density‐dependence in eastern brook trout

Understanding how multiple extrinsic (density‐independent) factors and intrinsic (density‐dependent) mechanisms influence population dynamics has become increasingly urgent in the face of rapidly changing climates. It is particularly unclear how multiple extrinsic factors with contrasting effects among seasons are related to declines in population numbers and changes in mean body size and whether there is a strong role for density‐dependence. The primary goal of this study was to identify the roles of seasonal variation in climate driven environmental direct effects (mean stream flow and temperature) vs. density‐dependence on population size and mean body size in eastern brook trout (Salvelinus fontinalis). We use data from a 10‐year capture‐mark‐recapture study of eastern brook trout in four streams in Western Massachusetts, USA to parameterize a discrete‐time population projection model. The model integrates matrix modeling techniques used to characterize discrete population structures (age, habitat type, and season) with integral projection models (IPMs) that characterize demographic rates as continuous functions of organismal traits (in this case body size). Using both stochastic and deterministic analyses we show that decreases in population size are due to changes in stream flow and temperature and that these changes are larger than what can be compensated for through density‐dependent responses. We also show that the declines are due mostly to increasing mean stream temperatures decreasing the survival of the youngest age class. In contrast, increases in mean body size over the same period are the result of indirect changes in density with a lesser direct role of climate‐driven environmental change.     

A partial likelihood approach to smooth estimation of dynamic covariate effects using penalised splines

Survival data are often modelled by the Cox proportional hazards model, which assumes that covariate effects are constant over time. In recent years however, several new approaches have been suggested which allow covariate effects to vary with time. Non-proportional hazard functions, with covariate effects changing dynamically, can be fitted using penalised spline (P-spline) smoothing. By utilising the link between P-spline smoothing and generalised linear mixed models, the smoothing parameters steering the amount of smoothing can be selected. A hybrid routine, combining the mixed model approach with a classical Akaike criterion, is suggested. This approach is evaluated with simulations and applied to data from the West of Scotland Coronary Prevention Study.     

A Bayesian framework for the analysis of cospeciation

Abstract.— Information on the history of cospeciation and host switching for a group of host and parasite species is contained in the DNA sequences sampled from each. Here, we develop a Bayesian framework for the analysis of cospeciation. We suggest a simple model of host switching by a parasite on a host phylogeny in which host switching events are assumed to occur at a constant rate over the entire evolutionary history of associated hosts and parasites. The posterior probability density of the parameters of the model of host switching are evaluated numerically using Markov chain Monte Carlo. In particular, the method generates the probability density of the number of host switches and of the host switching rate. Moreover, the method provides information on the probability that an event of host switching is associated with a particular pair of branches. A Bayesian approach has several advantages over other methods for the analysis of cospeciation. In particular, it does not assume that the host or parasite phylogenies are known without error; many alternative phylogenies are sampled in proportion to their probability of being correct.     

Interactions between frequency-dependent and vertical transmission in host-parasite systems.

We investigate host-pathogen dynamics and conditions for coexistence in two models incorporating frequency-dependent horizontal transmission in conjunction with vertical transmission. The first model combines frequency-dependent and uniparental vertical transmission, while the second addresses parasites transmitted vertically via both parents. For the first model, we ask how the addition of vertical transmission changes the coexistence criteria for parasites transmitted by a frequency-dependent horizontal route, and show that vertical transmission significantly broadens the conditions for parasite invasion. Host-parasite coexistence is further affected by the form of density-dependent host regulation. Numerical analyses demonstrate that within a host population, a parasite strain with horizontal frequency-dependent transmission can be driven to extinction by a parasite strain that is additionally transmitted vertically for a wide range of parameters. Although models of asexual host populations predict that vertical transmission alone cannot maintain a parasite over time, analysis of our second model shows that vertical transmission via both male and female parents can maintain a parasite at a stable equilibrium. These results correspond with the frequent co-occurrence of vertical with sexual transmission in nature and suggest that these transmission modes can lead to host-pathogen coexistence for a wide range of systems involving hosts with high reproductive rates.     

Populations in variable environments: the effect of variability in a species' primary resource

Mechanistic models for herbivore populations responding to rainfall-driven pasture are used to explore the effect of temporal variability in a primary resource on the abundance and distribution of a species. If the numerical response of the herbivore to pasture is a convex function, then gains made over time intervals with above average rainfall do not compensate for losses incurred when rainfall is below average. Populations therefore fare worse when rainfall is variable compared with when rainfall is reliable. It is demonstrated that this result is independent of the distribution of rainfall. Sensitivity of a species to variability, and hence the limit to its distribution in variable environments, is directly proportional to the difference between population growth rate under ideal conditions and the estimated rate of decline as the species' resource tends to zero. When density dependence is included in the numerical response, the average abundance of a species declines with increasing variability in its primary resource. However, a model for the dynamics of pasture and rabbits (Oryctolagus cuniculus) and red foxes (Vulpes vulpes) in southern Australia, is used to illustrate that trophic interactions can reverse the effect of variability: in the absence of foxes, the mean abundance of rabbits declines with variability as expected, but in the full model the mean abundance of rabbits increases.     

Assessing the spatial variability of density dependence in waterfowl populations

Population models commonly assume that the demographic parameters are spatially invariant, but there is considerable evidence that population growth rate (r) and the strength of density dependence (β) can vary over a species' range. To address this issue we developed a spatially explicit Gompertz population model based on the spatially varying coefficients approach to assess the spatial variation in population drivers. The model was fit to spatially stratified time series population estimates of the mallard Anas platyrhynchos in western North America. We included precipitation during the previous year and spring maximum temperature in the current year as environmental factors in the density dependent population model. Because density dependent models can give biased estimates for time series of abundance data, we fit a naïve model without informative priors and a model where we constrained the mean and variance of r to biologically realistic values that were derived via a comparative demography approach. In the naïve model, r and β were not separately identifiable and their values were overestimated, leading to unrealistic population growth. The naïve model also implied spatial variation in population r and the return time to equilibrium [1?(– β)] across the survey area. In contrast, in the informative model, r and the return time to equilibrium did not vary markedly among populations and were generally equal across populations. The effects of the climatic factors were similar across models. Population growth rates in the Prairie‐pothole region were positively correlated with precipitation, while in Alaska rates were positively correlated with spring temperature. Although it has been argued in the past that adding ecological realism could help avoid the pitfalls associated with density dependent models, our results demonstrate that imposing constraints on the population parameters is still the best course of action.     

Analysis of Foraging Behaviour of the Whitefly Parasitoid Encarsia formosa on a plant: A Simulation Study

The foraging behaviour of Encarsia formosa was analyzed using a stochastic simulation model of the parasitoid's behaviour. Parasitoids were allowed to search during a day on a tomato plant infested with immatures of the greenhouse whitefly, Trialeurodes vaporariorum. The model simulates searching, host selection, host handling and patch leaving behaviour, and the physiological state of the parasitoid. The outputs of the model are the number of visited leaflets and the number of hosts encountered, parasitized or killed by host feeding. The simulation results agreed well with observations of parasitoids foraging on tomato plants. The number of encounters and ovipositions on the plant increased with host density according to a type II functional response. At a clustered host distribution over leaflets and low host densities, the most important parameters affecting the number of ovipositions were the leaf area, the parasitoid's walking speed and walking activity, the probability of oviposition after encountering a host, the initial egg load and the ratio of search times on both leaf sides. At high densities, the maximum egg load and the giving-up time on a leaflet since latest host encounter were the most essential parameters.     

Measuring the functional responses of farmland birds: an example for a declining seed-feeding bunting

1. Many farmland bird species have undergone significant declines. It is important to predict the effect of agricultural change on these birds and their response to conservation measures. This requirement could be met by mechanistic models that predict population size from the optimal foraging behaviour and fates of individuals within populations. A key component of these models is the functional response, the relationship between food and competitor density and feeding rate. 2. This paper describes a method for measuring functional responses of farmland birds, and applies this method to a declining farmland bird, the corn bunting Miliaria calandra L. We derive five alternative models to predict the functional responses of farmland birds and parameterize these for corn bunting. We also assess the minimum sample sizes required to predict accurately the functional response. 3. We show that the functional response of corn bunting can be predicted accurately from a few behavioural parameters (searching rate, handling time, vigilance time) that are straightforward to measure in the field. These parameters can be measured more quickly than the alternative of measuring the functional response directly. 4. While corn bunting violated some of the assumptions of Holling's disk equation (model 1 in our study), it still provided the most accurate fit to the observed feeding rates while remaining the most statistically simple model tested. Our other models may be more applicable to other species, or corn bunting feeding in other locations. 5. Although further tests are required, our study shows how functional responses can be predicted, simplifying the development of mechanistic models of farmland bird populations.     

QTL methodology for response curves on the basis of non-linear mixed models, with an illustration to senescence in potato

The improvement of quantitative traits in plant breeding will in general benefit from a better understanding of the genetic basis underlying their development. In this paper, a QTL mapping strategy is presented for modelling the development of phenotypic traits over time. Traditionally, crop growth models are used to study development. We propose an integration of crop growth models and QTL models within the framework of non-linear mixed models. We illustrate our approach with a QTL model for leaf senescence in a diploid potato cross. Assuming a logistic progression of senescence in time, two curve parameters are modelled, slope and inflection point, as a function of QTLs. The final QTL model for our example data contained four QTLs, of which two affected the position of the inflection point, one the senescence progression-rate, and a final one both inflection point and rate.     

Errors associated with estimating parasitism using a modified version of Southwood's graphical method

A simulation model is used to examine the errors in estimating parasitized and nonparasitized host densities independently with Southwood's graphical technique. This technique is accurate when parasitoid attack occurs prior to the sampling period (e.g. the previous life stage of the host). When this is not the case, the parasitized host density is estimated accurately, but the unparasitized host density is over estimated by those individuals that are sampled as healthy prior to attack. This error is neglible at low levels of parasitism (<20% parasitized), but increases with increasing parasitism. Of the biological parameters tested, only the parasitoid attack pattern (shape of the parasitoid attack curve) has a significant influence on the magnitude of this error. A generalized simulation model is presented for evaluating errors in estimates of seasonal parasitism for specific host-parasitoid interactions. University of Rhode Island, Agricultural Experiment Station Journal, Article Number 2479.     

The Relative Importance of Fungal Infection,Conspecific Density and Environmental Heterogeneity for Seedling Survival in a Dominant Tropical Tree

A gap remains in our understanding of how host‐specific fungal pathogens impact negative density dependence (NDD). Here, we investigated survival of Cinnamomum subavenium Miq. seedlings, the dominant canopy species in a seasonal tropical evergreen forest, Thailand. It is infected by a host‐specific fungus that is easily identifiable in the field. We quantified the effects of conspecific seedling and adult density on fungal infection and seedling survival over a wide range of environmental heterogeneity in elevation, understory vegetation and presence of forest gaps. Generalized linear mixed models (GLMMs) for seedling survival revealed that fungal infection significantly reduced survival and had the strongest effect on seedling survival as compared with conspecific density and environmental heterogeneity. Adult conspecific density was not, however, significantly correlated with the probability of infection, and conspecific seedling density was positively associated with increased infection only at high elevations. In contrast to infection, we found a significant positive correlation between conspecific seedling density and the probability of seedling survival. Consequently, our results demonstrate that fungal infection can have major impacts on seedling survival, but not in a manner consistent with local NDD effects on seedlings, as assumed in the Janzen–Connell hypothesis. Our study provides an example of how quantifying the interaction between environmental heterogeneity and a host‐specific plant‐pathogen can yield unexpected insights into the dynamics of seedling populations. The combined effects of host‐specific pathogens and environmental heterogeneity on survival of dominant seedling species may ultimately provide a chance for rarer species to recruit.