An approach to the teaching of host/parasite population modelling

Computer-aided learning is considered to be useful in the teaching of host/parasite population modelling. The STELLA programme for the Apple Macintosh microcomputer allows dynamic models to be developed by drawing a diagram of the interactions and then defining the relationships between variables in terms of simple mathematics or as graphs. Our experience in using this programme for project-based teaching is described.     

An approach to modelling in immunology

Like most other fields in biology, immunology has been revolutionised by the techniques of molecular biology and the resulting explosion in available experimental data. It is argued that efforts to integrate the data to gain insight into how various subsystems in the immune system interact and function require mathematical modelling and computer simulation in close collaboration with experimentalists. This paper illustrates some of the techniques available for modelling immune systems, and highlights the issues that should be borne in mind by anyone starting down the modelling path.     

A modelling approach to estimate the effect of exotic pollinators on exotic weed population dynamics: bumblebees and broom in Australia

The role of mutualisms in contributing to species invasions is rarely considered, inhibiting effective risk analysis and management options. Potential ecological consequences of invasion of non‐native pollinators include increased pollination and seed set of invasive plants, with subsequent impacts on population growth rates and rates of spread. We outline a quantitative approach for evaluating the impact of a proposed introduction of an invasive pollinator on existing weed population dynamics and demonstrate the use of this approach on a relatively data‐rich case study: the impacts on Cytisus scoparius (Scotch broom) from proposed introduction of Bombus terrestris. Three models have been used to assess population growth (matrix model), spread speed (integrodifference equation), and equilibrium occupancy (lattice model) for C. scoparius. We use available demographic data for an Australian population to parameterize two of these models. Increased seed set due to more efficient pollination resulted in a higher population growth rate in the density‐independent matrix model, whereas simulations of enhanced pollination scenarios had a negligible effect on equilibrium weed occupancy in the lattice model. This is attributed to strong microsite limitation of recruitment in invasive C. scoparius populations observed in Australia and incorporated in the lattice model. A lack of information regarding secondary ant dispersal of C. scoparius prevents us from parameterizing the integrodifference equation model for Australia, but studies of invasive populations in California suggest that spread speed will also increase with higher seed set. For microsite‐limited C. scoparius populations, increased seed set has minimal effects on equilibrium site occupancy. However, for density‐independent rapidly invading populations, increased seed set is likely to lead to higher growth rates and spread speeds. The impacts of introduced pollinators on native flora and fauna and the potential for promoting range expansion in pollinator‐limited ‘sleeper weeds’ also remain substantial risks.     

An estimate of the global error frequency in translation

Summary Electrophoretic heterogeneity in a set of selected proteins is used to estimate the average error frequency during translation. Estimates based upon streptomycin-induced heterogeneity as well as mistranslation of an ochre codon yield an average error frequency of 4x10^-4 for normally growing cells.     

An examination of methods to estimate population size in wintering geese

We estimated the size of the Svalbard population of Pink-footed Geese Anser brachyrhynchus in 1991–98 using three different methods: (a) counts; (b) mark–resight estimates; (c) annual productivity and survival. Count data showed a slight increase of population size, from 33 000 in 1991 to 38 500 in 1998. Mark–resight estimates showed a larger fluctuation, but were almost always greater than counts. By contrast, estimates of survival and productivity suggested stability or at least a less pronounced increase in the population size, the discrepancy in the number estimated when compared to the other methods being especially large in the last two years of the study. A detailed examination of the assumptions underlying each of the methods reveals possible explanations for some, but not all, of the discrepancies. We conclude that goose population estimates derived from total population counts may be less reliable than commonly assumed, and moderate year-to-year trends should not be over-interpreted. Similarly, assessment of annual productivity and survival may be subject to undetected biases, and these uncertainties should be considered when interpreting results and trends in these parameters. Repeated cross-validation of parameter estimation methods in this and other populations is highly desirable.     

Accurate and fast methods to estimate the population mutation rate from error prone sequences

Background  

The population mutation rate (θ) remains one of the most fundamental parameters in genetics, ecology, and evolutionary biology. However, its accurate estimation can be seriously compromised when working with error prone data such as expressed sequence tags, low coverage draft sequences, and other such unfinished products. This study is premised on the simple idea that a random sequence error due to a chance accident during data collection or recording will be distributed within a population dataset as a singleton (i.e., as a polymorphic site where one sampled sequence exhibits a unique base relative to the common nucleotide of the others). Thus, one can avoid these random errors by ignoring the singletons within a dataset.     

An approach to multiscale modelling with graph grammars

Background and Aims

Functional–structural plant models (FSPMs) simulate biological processes at different spatial scales. Methods exist for multiscale data representation and modification, but the advantages of using multiple scales in the dynamic aspects of FSPMs remain unclear. Results from multiscale models in various other areas of science that share fundamental modelling issues with FSPMs suggest that potential advantages do exist, and this study therefore aims to introduce an approach to multiscale modelling in FSPMs.

Methods

A three-part graph data structure and grammar is revisited, and presented with a conceptual framework for multiscale modelling. The framework is used for identifying roles, categorizing and describing scale-to-scale interactions, thus allowing alternative approaches to model development as opposed to correlation-based modelling at a single scale. Reverse information flow (from macro- to micro-scale) is catered for in the framework. The methods are implemented within the programming language XL.

Key Results

Three example models are implemented using the proposed multiscale graph model and framework. The first illustrates the fundamental usage of the graph data structure and grammar, the second uses probabilistic modelling for organs at the fine scale in order to derive crown growth, and the third combines multiscale plant topology with ozone trends and metabolic network simulations in order to model juvenile beech stands under exposure to a toxic trace gas.

Conclusions

The graph data structure supports data representation and grammar operations at multiple scales. The results demonstrate that multiscale modelling is a viable method in FSPM and an alternative to correlation-based modelling. Advantages and disadvantages of multiscale modelling are illustrated by comparisons with single-scale implementations, leading to motivations for further research in sensitivity analysis and run-time efficiency for these models.     

A network modelling approach to assess non-pharmaceutical disease controls in a worker population: An application to SARS-CoV-2

As part of a concerted pandemic response to protect public health, businesses can enact non-pharmaceutical controls to minimise exposure to pathogens in workplaces and premises open to the public. Amendments to working practices can lead to the amount, duration and/or proximity of interactions being changed, ultimately altering the dynamics of disease spread. These modifications could be specific to the type of business being operated. We use a data-driven approach to parameterise an individual-based network model for transmission of SARS-CoV-2 amongst the working population, stratified into work sectors. The network is comprised of layered contacts to consider the risk of spread in multiple encounter settings (workplaces, households, social and other). We analyse several interventions targeted towards working practices: mandating a fraction of the population to work from home; using temporally asynchronous work patterns; and introducing measures to create ‘COVID-secure’ workplaces. We also assess the general role of adherence to (or effectiveness of) isolation and test and trace measures and demonstrate the impact of all these interventions across a variety of relevant metrics. The progress of the epidemic can be significantly hindered by instructing a significant proportion of the workforce to work from home. Furthermore, if required to be present at the workplace, asynchronous work patterns can help to reduce infections when compared with scenarios where all workers work on the same days, particularly for longer working weeks. When assessing COVID-secure workplace measures, we found that smaller work teams and a greater reduction in transmission risk reduced the probability of large, prolonged outbreaks. Finally, following isolation guidance and engaging with contact tracing without other measures is an effective tool to curb transmission, but is highly sensitive to adherence levels. In the absence of sufficient adherence to non-pharmaceutical interventions, our results indicate a high likelihood of SARS-CoV-2 spreading widely throughout a worker population. Given the heterogeneity of demographic attributes across worker roles, in addition to the individual nature of controls such as contact tracing, we demonstrate the utility of a network model approach to investigate workplace-targeted intervention strategies and the role of test, trace and isolation in tackling disease spread.     

A first test of a new modelling approach to estimate food consumption in particle-feeding fish

Models for estimating food consumption in fish by analysing changes in stomach fullness over time are invariably based on a stomach evacuation rate obtained when the fish is fasting, on the assumption that this rate also applies to when the fish is feeding. However, this often is not the case in fish that feed on small particles. A new modelling approach was therefore tested, which is based not only on stomach fullness but also on gut contents. To eliminate errors arising from assimilation in the gut, titanium(IV) oxide (TiO₂) was used as an indigestible marker. When applied to a dataset obtained from tilapia given several equal doses of pelleted feed over a 2.5‐h period, the new approach gave a closer true consumption estimate than a conventional model. The evacuation rate proved to be a more sensitive parameter than the ingestion rate, but the former was no longer required by the new approach for estimating ingestion, thus liberating the food consumption estimate from any errors and dependencies inherent in the evacuation rate. The new approach assumes that the digesta of previous feedings can be distinguished from those of the feeding phase being analysed and therefore needs further refinement for those cases when this does not apply. Suggestions for such refinements are also given. This new approach is expected to be equally suitable for estimating consumption in stomachless fish.     

An ecophysiological approach to modelling resource fluxes in competing plants

A conceptual model of resource acquisition and allocation within a generalized, individual plant growing vegetatively in competition with others is presented. The model considers C and N acquisition, synthesis of assimilates and their transport and partitioning, growth of new tissues, reserve formation and recycling, and losses due to root exudation and respiration. These processes are regulated by the relative size of the C and N substrate pools in shoot and roots, in relation to meristematic sink strength. Translocation and allocation patterns are represented according to the Minchin phloem transport model. The current model is used to consider the impact of competition on resource acquisition and allocation, first by considering a plant growing in isolation and its response to manipulation of light, CO2 and N supplies. Secondly, competitive plants are introduced and the direct effects on plant responses in terms of resource depletion are considered separately from indirect effects such as potential changes in the quality of resources available (e.g. light quality or soil N sources). In the past, many studies of plant competition have not established the importance of these indirect effects because they have not established all the processes involved in competition. This model can be used to interpret responses of whole plants to their neighbours in terms of the relative importance of both the direct and indirect effects of competition.     

An algorithmic approach to modelling the retinal receptor topography

Based on published research results on the structure of the human retina and the initial assumption of tight hexagonal packing of cones, the mean cone-distance function is derived. Disorder in the cone lattice is explained as the superposition of increasing topological distortion in the hexagonal lattice (providing a possible explanation for observed systematic lattice distortions) and local jitter of neighbor-toneighbor distances, for which a simple statistical model is provided. These individual results are incorporated into a proposed algorithm for simulating the cone receptors' topography in 3D-space. Finally, possible software and hardware applications of the algorithmically defined retina model are briefly touched.     

An agent-based modeling approach to represent infestation dynamics of the emerald ash borer beetle

Agent-based modeling (ABM) is a bottom-up approach capable of operationalizing complex systems. The approach can be used to reproduce the spatio-temporal patterns in ecological processes such as insect infestation by representing individual dynamics and interactions between “agents” and their environment from which complex behavior emerges. The emerald ash borer (Agrilus planipennis; EAB) is an invasive species native to south-east Asia which has infested and killed millions of ash trees (Fraxinus sp.) across the eastern United States as well as Ontario and Quebec in Canada. Efforts to model the insect's behavior are ongoing, but current models are limited to approaches that do not address the complexity that emerges from the dynamics between individual beetles and their varying spatial environments. The objective of this study is to develop an ABM to represent the interactions of the EAB and the emerging spatio-temporal pattern of the insect spread. The model is implemented on real datasets from the Town of Oakville, Ontario, Canada from 2008 to 2010. Tree inventory and land use data acquired from the Town of Oakville were used to represent the spatial environment of the EAB agents. The EAB interactions are implemented in the model as subroutines, each representing a stage in the EAB life cycle using a temporal resolution of one day. Model verification was performed based on the literature documenting the life cycle processes of the EAB to represent EAB behavior. The model is calibrated using the rate of spread observed in the Town of Oakville from 2008 to 2009 and is validated using datasets delimiting the spatial extent and severity of EAB infestation in 2009. When comparing simulated and observed data, there is a 72% agreement for the locations of the infestation. This indicates that the developed ABM approach offers a model able to capture the complex behavior of EAB where both the spatial extent and severity of infestation are simulated realistically. The model generates insights about the underlying processes governing EAB behavior, highlights areas of uncertainty in modeling the complex spatio-temporal patterns of EAB infestation, and is a useful tool for forest and pest management.     

Density-dependent population dynamics in clonal organisms: a modelling approach

1. Density dependence may act at several stages in an organisms life-cycle (e.g. on mortality, fecundity, etc.), but not all density-dependent processes necessarily regulate population size. In this paper I use a density manipulation experiment to determine the effects of density on the transition rates between different size classes of the clonal zoanthid Palythoa caesia Dana 1846. I then formulate a density-dependent matrix model of population dynamics of Palythoa , and perform a series of sensitivity analyses on the model to determine at what stage in the life-cycle regulation acts.
2. Seven of the 16 transition probabilities decreased with density, most of them being shrinkage (due to loss of tissue or fission) and stasis (the self–self transition) of medium and large colonies. The only probability to increase was for the stasis of large colonies. Recruitment was quadratically dependent on density, peaking at intermediate densities.
3. Equilibrium cover in the model was 84% and was reached in ≈40 years. To determine which density-dependent transitions were involved in population regulation, the strength of density dependence was varied in each independently. This sensitivity analysis showed that only changes in the probabilities of large colonies remaining large and producing medium colonies, were regulating.
4. These results suggest that regulation is primarily acting on fission of large colonies to produce intermediate-sized colonies, in combination with size specific growth rates. Fission rates decrease greatly with density, resulting in a greater proportion of large colonies at high densities and large colonies grow more slowly than small. Overall, this behaviour is very similar to that of clonal plants which have a phalanx type life history.     

An approach to the conditional error rate principle with nuisance parameters

In the presence of nuisance parameters, the conditional error rate principle is difficult to apply because of the dependency of the conditional error function of the preplanned test on nuisance parameters. To use the conditional error rate principle with nuisance parameters, we propose to search among tests that guarantee overall error control for the test that maximizes a weighted combination of the conditional error rates over possible values of the nuisance parameters. We show that the optimization problem that defines such a test can be solved efficiently by existing algorithms.     

A better way to estimate population trends

Estimation of a population trend from a time series of abundance data is an important task in ecology, yet such estimation remains logistically and conceptually challenging in practice. First, the extent to which unequal intervals in the time series, due to missing observations or irregular sampling, compromise trend estimation is not well‐known. Furthermore, the predominant trend estimation method (loglinear regression of abundance data against time) ignores the possibility of process noise, while an alternative method (the ‘diffusion approximation’) ignores observation error in the abundance data. State‐space models that account for both process noise and observation error exist but have been little used. We study an adaptation of the exponential growth state‐space (EGSS) model for use with missing data in the time series, and we compare its trend estimation to the status quo methods. The EGSS model provides superior estimates of trend across wide ranges of time series length and sources of variation. The performance of the EGSS model even with half of the counts in the time series missing implies that trend estimates may be improved by diverting effort away from annual monitoring and towards increasing time series length or improving precision of the abundance estimates for years that data are collected.     

An approach to the nonlinear dynamics of Russian wheat aphid population growth with the cusp catastrophe model

Many insect field populations, especially aphids, often exhibit irregular and even catastrophic fluctuations. The objective of the present study is to explore whether or not the population intrinsic rates of growth ( r _m) obtained under laboratory conditions can shed some light on the irregular changes of insect field populations. We propose to use the catastrophe theory, one of the earliest nonlinear dynamics theories, to answer the question. To collect the necessary data, we conducted a laboratory experiment to investigate population growth of the Russian wheat aphid (RWA), Diuraphis noxia (Mordvilko), in growth chambers. The experiment was designed as the factorial combinations of five temperatures and five host plant-growth stages (25 treatments in total): 1800 newly born RWA nymphs arranged in the 25 treatments (each treatment with 72 repetitions) were observed for their development, reproduction and survival through their entire lifetimes. After obtaining the population intrinsic rates of growth ( r _m) from the experimental data under various environmental conditions, we built a cusp catastrophe model for RWA population growth by utilizing r _m as the system state variable, and temperature and host plant-growth stage as control variables. The cusp catastrophe model suggests that RWA population growth is intrinsically catastrophic , and dramatic jumps from one state to another might occur even if the temperature and plant-growth stage change smoothly . Other basic behaviors of the cusp catastrophe model, such as catastrophic jumps , hystersis and divergence , are also expected in RWA populations. These results suggest that the answer to the previously proposed question should be "yes".     

Population growth of Rhopalosiphum padi under different thermal regimes: an agent-based model approach

1. Rhopalosiphum padi (Linnaeus, 1758) is abundant and has a broad geographic distribution. It is one of the most important cereal pests. In Brazil, the economic losses associated with this aphid result mainly from the transmission of the barley yellow dwarf viruses.
2. Decision-making for the adoption of management measures must consider the initial population size, the potential for population increase, and the time when this population will reach levels at which the resulting damage is equal to the costs of control measures. Consequently, the establishment of management programmes and decision support systems should be based on models that estimate the potential population growth of this pest species.
3. Temperature is one of the main factors that determine the growth rate of insect populations. Generally, controlled experiments are designed to examine the relationship of temperature at fixed intervals in relation to the development phases of insects. In nature, thermal regimes are not constant, and population growth is the result of a series of combined events.
4. In this work, the effects of different thermal regimes on the population growth of R. padi were compared.
5. An agent-based model was used to estimate population growth, and the parameters defined in controlled regimes were compared with fluctuating temperatures under natural conditions.
6. The temperature-driven model presented here can serve as a tool to predict population growth and decision-making for aphid management.
7. The model structure and the proposed experimental design allow the addition of modules and layers of factors that can progressively affect the populations of aphids to gradually improve the model.