Influence of low and decreasing food levels on Daphnia-algal interactions: Numerical experiments with a new dynamic energy budget model

Based on numerical experiments with a new physiologically structured population model we demonstrate that predator physiology under low food and under starving conditions can have substantial implications for population dynamics in predator-prey interactions. We focused on Daphnia-algae interactions as model system and developed a new dynamic energy budget (DEB) model for individual daphnids. This model integrates the κ-rule approach common to net assimilation models into a net-production model, but uses a fixed allocation of net-productive energy in juveniles. The new DEB-model agrees well with the results of life history experiments with Daphnia. Compared to a pure κ-rule model the new allocation scheme leads to significant earlier maturation at low food levels and thus is in better agreement with the data. Incorporation of the new DEB-model into a physiologically structured population model using a box-car elevator technique revealed that the dynamics of Daphnia-algae interactions are highly sensitive to the assumptions on the energy allocation of juveniles under low food conditions. Additionally we show that also other energy allocation rules of our DEB-model concerning decreasing food levels and starving conditions at the individual level have strong implications for Daphnia-algae interactions at the population level. With increasing carrying capacity of algae a stable equilibrium with coexistence of Daphnia occurs and algae shifts to limit cycles. The amplitudes of the limit cycles increase with increasing percentage of sustainable weight loss. If a κ-rule energy allocation is applied to juveniles, the stable equilibrium occurs for a much narrower range of algal carrying capacities, the algal concentration at equilibrium is about 2 times larger, and the range of algae carrying capacities at which daphnids become extinct extends to higher carrying capacities than in the new DEB-model. Because predator-prey dynamics are very sensitive to predator physiology under low food and starving conditions, empirical constraints of predator physiology under these conditions are essential when comparing model results with observations in laboratory experiments or in the field.     

Modeling individual and population dynamics in a consumer–resource system: Behavior under food limitation and crowding and the effect on population cycling in Daphnia

In population modeling, a considerable level of complexity is often required to provide trustworthy results, comparable with field observations. By assuring sufficient detail at the individual level while preserving the potential to explore the consequences at higher levels, individual-based modeling may thus provide a useful tool to investigate dynamics at different levels of organization. Still, population dynamics resulting from such models are often at odds with observations from the field. This may be partly caused by a lack of focus on the individual dynamics under conditions of food stress and starvation. I developed a physiologically structured, individual-based simulation model to investigate life history of Daphnia and its effect on population dynamics in response to the productivity of the system. In verifying model behavior with available literature data on life history and physiology, I paid special attention to the dynamics of food intake and the verification of individual level results under conditions of food limitation and starvation. I show that the maximum filtering rates under low food levels used in the current model are much closer to measured filtering rates than the ones used in other models. Being consistent with results on physiology and life history from experiments at a wide range of food availability (including starvation), the model generates low amplitude or high amplitude population density cycles depending on the productivity of the system, as observed in field and experimental populations of Daphnia and with the minimum population densities being one to two orders of magnitude lower in the high amplitude than in the low amplitude cycles. To generate results which are not only qualitatively but also quantitatively comparable to experimental and field observations, however, a crowding effect on the filtering response has to be incorporated in the model.     

Zooplankton population model coupled to a biogeochemical model of the North Western Mediterranean Sea ecosystem

A stage structured population (SSP) model based on Fennel's [Fennel, W., 2001. Modelling copepods with links to circulation models. Journal of Plankton Research, 23, 1217–1232] equations is applied to Centropages typicus (Kröyer), a dominant copepod species of the North Western Mediterranean Sea (NWMS) and a prey of small pelagic fish. The model considers five groups of stages and development rates are represented by a mechanistic formulation depending on individual specific growth in each stage. Individual growth is calculated from the individual energy budget depending on food availability and temperature.     

Modeling the population dynamics of cotton bollworm Helicoverpa armigera (Hübner) (Lepidoptera: Noctuidae) over a wide area in northern China

The cotton bollworm Helicoverpa armigera (Lepidoptera: Noctuidae) is one of the most serious crop pests in northern China, calling for accurate prediction of pest outbreaks and strategies for pest control. A computer model is developed to simulate the population dynamics of H. armigera over a wide area in northern China. The area considered covers 12 provinces where serious outbreaks of H. armigera have been observed. In this model, pest development is driven by local ambient temperature, and adults migrate long distances between regions and select preferred hosts for oviposition within a region. Six types of host including cotton, wheat, corn, peanut, soybean and a single category composed of all other minor hosts are considered in this model. Survival rates of eggs and larvae are based on life-table data, and simulated as a function of host type, host phenology and temperature. The incidence of diapause depends on temperature and photoperiod experienced during the larval stage. Survival rate of non-diapause pupae is a nonlinear function of rainfall, and overwinter survival rate is a nonlinear function of temperature. Insecticide is applied when population density exceeds the economic threshold on a host crop within a region. Comparisons of model output with light-trap data indicate that our model reflects the pest population dynamics over a wide area, and could potentially be used for testing novel pest control strategies in northern China.     

Modelling llama population development under environmental and market constraints in the Bolivian highlands

Changes in the size of animal populations over time are mainly determined by demographic and environmental factors. Livestock population dynamics are additionally influenced by harvesting decisions taken by herders. In Bolivia, not much is known about current llama husbandry and the main influencing factors determining population sizes. We collected data on demography, environmental factors and market values affecting the current and future llama population in three different regions in Bolivia. We generated a population model and assessed the future development of the llama population including environmental factors (rangeland carrying capacity, disturbance phenomena), herd structure and dynamics, and economic market demands. We calibrated and validated the llama model on the basis of 20-year data sets of the regions of Oruro, Potosi and La Paz, respectively. Model calibration by means of the Gauss-Marquardt-Levenberg algorithm yielded a model efficiency of 0.94. For model validation, however, the simulation slightly overestimated the observed llama population yielding model efficiencies of 0.91 and 0.87 for Potosi and La Paz, respectively. Model outcomes were most sensitive to death and birth rates of juveniles and death rate of females compared to environmental or other demographic factors. Population trajectories approached an overall carrying capacity for Oruro, Potosi and La Paz of 8.8 × 10⁵, 9.1 × 10⁵, and 9.0 × 10⁵ llama individuals after 100 years of simulation. Hence, detailed monitoring of demographic, environmental, and economic factors can improve predictions of llama population development over time. Further management should focus on improving birth rates and lowering female mortality through providing supplemental food and shelters against the harsh environmental conditions of the Andean highlands.     

A process-based population dynamics model to explore target and non-target impacts of a biological control agent

The risks and benefits associated with efforts to control invasive alien species using classical biological control are being subjected to increasing scrutiny. A process-based population dynamics model was developed to explore the interactions between a folivorous biological control agent, Cleopus japonicus, and its plant host Buddleja davidii. The model revealed that climate could have a significant impact upon the interactions between B. davidii and C. japonicus. At the coolest sites, the impact of C. japonicus on B. davidii was slowed, but it was still eventually capable of controlling populations of B. davidii. At the warmer sites where both B. davidii and C. japonicus grew faster, B. davidii succumbed rapidly to weevil damage. We hypothesise that barring an encounter with a natural enemy, C. japonicus will eventually be able to provide sustained control B. davidii throughout the North Island of New Zealand. The model scenarios illustrate the potential for the C. japonicus population to attain high densities rapidly, and to defoliate patches of B. davidii, creating the potential for spill-over feeding on non-target plants. The potential magnitude of this threat will depend partly on the climate suitability for C. japonicus, the pattern by which it migrates in response to a reduction in the available leaf resource, and the suitability of non-target plants as hosts. In all migration scenarios considered, the pattern of population growth and resource consumption by C. japonicus was exponential, with a strong tendency toward complete utilisation of resource patches more quickly at the warmer compared to colder sites. In addition to providing some useful hypotheses about the effects of climate on the biological control system, and the non-target risks, it also provides some insight into the mechanisms by which climate affects the system.     

A model approach to evaluate the effect of temperature and food concentration on individual life-history and population dynamics of Daphnia

We present a model framework for the simulation of growth and reproduction of Daphnia at varying conditions of food concentration and temperature. The core of our framework consists of an individual level model that simulates allocation of assimilated carbon into somatic growth, maintenance costs, and reproduction on the basis of a closed carbon budget. A fixed percentage of assimilated carbon is allocated into somatic growth and maintenance costs. Special physiological adaptations in energy acquisition and usage allow realistic model performance even at very low food concentrations close to minimal food requirements. All model parameters are based on physiological measures taken from the literature. Model outputs were thoroughly validated on data from a life-table experiment with Daphnia galeata. For the first time, a successful model validation was performed at such low food concentrations. The escalator boxcar train (EBT) was used to integrate this individual level model into a stage-structured population model. In advance to previous applications of the EBT to Daphnia we included an additional clutch compartment into the model structure that accounts for the characteristic time delay between egg deposition and hatching in cladocerans. By linking two levels of biological organisation, this model approach represents a comprehensive framework for studying Daphnia both at laboratory conditions and in the field. We compared outputs of our stage-structured model with predictions by two other models having analogous parameterisation: (i) another individual level Daphnia model (Kooijman–Metz model) and (ii) a classical unstructured population model. In contrast to our Daphnia model, the Kooijman–Metz model lacks the structure to account for the optimisation of energy acquisition and maintenance requirements by individual daphnids. The unstructured population model showed different patterns of population dynamics that were not in concordance with typical patterns observed in the field. Thus, we conclude our model provides a comprehensive tool for the simulation of growth and reproduction of Daphnia and corresponding population dynamics.     

A hydrologically driven model of swamp water mosquito population dynamics

We develop a swamp water mosquito population model that is forced solely by environmental variability. Measured temperature and land surface wetness conditions are used to simulate Anopheles walkeri population dynamics in a northern New Jersey habitat. Land surface wetness conditions, which represent oviposition habitat availability, are derived from simulations using a dynamic hydrology model. Using only these two density-independent effects, population model simulations of biting Anoph. walkeri correlate significantly with light trap collections. These results suggest that prediction of mosquito populations and the diseases they transmit could be better constrained by inclusion of environmental variability.     

Dissecting the drivers of population cycles: Interactions between parasites and mountain hare demography

There is a growing awareness that cyclic population dynamics in vertebrate species are driven by a complex set of interactions rather than a single causal factor. While theory suggests that direct host-parasite interactions may destabilise population dynamics, the interaction between host and parasite may also influence population dynamics through indirect effects that result in delayed responses to either density or to life-history traits. Using empirical data on mountain hares (Lepus timidus) infected with a nematode parasite (Trichostrongylus retortaeformis), we developed an individual-based model (IBM) that incorporated direct effects and delayed life-history effects (DLHEs) of a macroparasite, alternative transmission mechanisms and seasonality in host population dynamics. The full model describes mean characteristics of observed mountain hare time series and parasite abundance, but by systematically removing model structure we dissect out dynamic influences of DLHEs. The DLHEs were weakly destabilising, increasing the propensity for cyclic dynamics and suggesting DLHEs could be important processes in host-parasite systems. Further, by modifying model structure we identify a strong influence of parasite transmission mechanism on host population stability, and discuss the implications for parasite aggregation mechanisms, host movement and natural geographical variation in host population dynamics. The effect of T. retortaeformis on mountain hares likely forms part of a complex set of interactions that lead to population cycles.     

Assessing the impact of biological control of Plutella xylostella through the application of Lotka–Volterra model

The Lotka–Volterra model was applied to the population densities of diamondback moth (DBM), Plutella xylostella (L.) and its exotic larval parasitoid Diadegma semiclausum (Hellen) data that was collected earlier by icipe's DBM biological control team. The collections were done for 15 months before the release and 36 months after release of the parasitoid in two areas; in Werugha, Coast Province of Kenya and Tharuni, Central Province of Kenya, respectively. For each area in pre- and post-release periods, we estimated Lotka–Volterra model parameters from the minimization of the loss function between the theoretical and experimental time-series datasets following the Nelder-Mead multidimensional method. The model estimated a reduction in the value of the steady state of DBM population from 4.86 to 2.17 in Werugha and from 6.11 to 3.76 and 3.45 (with and without exclusion of the time before D. semiclausum recovery) in Tharuni when transiting from the pre- and post-release periods, respectively. This change was a consequence of the newly introduced parasitoid, in the areas. The study presented a successful and detailed technique for non-linear model parameters restoration which was demonstrated by the correct mimicking of empirical datasets from the classical biological control with D. semiclausum, in different areas of Kenya. The applied model has measured the parasitoids impact on the DBM biological control through a quantitative estimate of the effectiveness of the newly introduced species D. semiclausum. These equations may therefore be used as tool for decision making in the implementation for such pests’ management system strategy.     

Influence of host migration between woodland and pasture on the population dynamics of the tick Ixodes ricinus: A modelling approach

Ticks act as vectors of pathogens that can be harmful to animals and/or humans. Epidemiological models can be useful tools to investigate the potential effects of control strategies on diseases such as tick-borne diseases. The modelling of tick population dynamics is a prerequisite to simulating tick-borne diseases and the corresponding spread of the pathogen. We have developed a dynamic model to simulate changes in tick density at different stages (egg, larva, nymph and adult) under the influence of temperature. We have focused on the tick Ixodes ricinus, which is widespread in Europe. The main processes governing the biological cycles of ticks were taken into account: egg laying, hatching, development, host (small, mainly rodents, or large, like deer and cattle, mammals) questing, feeding and mortality. This model was first applied to a homogeneous habitat, where simulations showed the ability of the model to reproduce the general patterns of tick population dynamics. We considered thereafter a multi-habitat model, where three different habitats (woodland, ecotone and meadow) were connected through host migration. Based on this second application, it appears that migration from woodland, via the ecotone, is necessary to sustain the presence of ticks in the meadow. Woodland can therefore be considered as a source of ticks for the meadow, which in turn can be regarded as a sink. The influence of woodland on surrounding tick densities increases in line with the area of this habitat before reaching a plateau. A sensitivity analysis to parameter values was carried out and demonstrated that demographic parameters (sex ratio, development, mortality during feeding and questing, host finding) played a crucial role in the determination of questing nymph densities. This type of modelling approach provides insight into the influence of spatial heterogeneity on tick population dynamics.     

Simulation modeling to understand how selective foraging by beaver can drive the structure and function of a willow community

Beaver–willow (Castor-Salix) communities are a unique and vital component of healthy wetlands throughout the Holarctic region. Beaver selectively forage willow to provide fresh food, stored winter food, and construction material. The effects of this complex foraging behavior on the structure and function of willow communities is poorly understood. Simulation modeling may help ecologists understand these complex interactions. In this study, a modified version of the SAVANNA ecosystem model was developed to better understand how beaver foraging affects the structure and function of a willow community in a simulated riparian ecosystem in Rocky Mountain National Park, Colorado (RMNP). The model represents willow in terms of plant and stem dynamics and beaver foraging in terms of the quantity and quality of stems cut to meet the energetic and life history requirements of beaver. Given a site where all stems were equally available, the model suggested a simulated beaver family of 2 adults, 2 yearlings, and 2 kits required a minimum of 4 ha of willow (containing about10 stems m⁻²) to persist in a steady-state condition. Beaver created a willow community where the annual net primary productivity (ANPP) was 2 times higher and plant architecture was more diverse than the willow community without beaver. Beaver foraging created a plant architecture dominated by medium size willow plants, which likely explains how beaver can increase ANPP. Long-term simulations suggested that woody biomass stabilized at similar values even though availability differed greatly at initial condition. Simulations also suggested that willow ANPP increased across a range of beaver densities until beaver became food limited. Thus, selective foraging by beaver increased productivity, decreased biomass, and increased structural heterogeneity in a simulated willow community.     

Modelling the effects of green macroalgae blooms on the population dynamics of Cyathura carinata (Crustacea: Isopoda) in an eutrophied estuary

A population dynamics model was developed to simulate the effects of benthic macroalgae blooms (mostly Enteromorpha spp.) on the productivity of Cyathura carinata (Crustacea: Isopoda), a possible keystone species in the benthic communities of the Mondego estuary. The model describes C. carinata population dynamics, as well as the relationships between Enteromorpha biomass, Enteromorpha decaying rates, organic matter content in the sediments and detritus consumption by C. carinata, a detritic feeder. Model results support the idea that seasonal blooms of Enteromorpha determine a significant increase of organic matter content in the sediments, due to macroalgae decay, which initially contributes to enhance C. carinata consumption and growth rates, determining a significant increase in the biomass. Nevertheless, later, following the algae bloom, C. carinata biomass decreases, and reaches its lowest value, close to 0, when the algae crash. This effect is probably related with strong anoxic conditions, especially during night, due to high algal decomposition rates. In accordance with the model, migration of new individuals from adjacent areas must occur in order to recolonise the area affected by the algae bloom. Therefore, it seems reasonable to conclude that macroalgae blooms that are limited in space may favour C. carinata populations, but extensive blooms affecting the whole area of distribution of this species will determine its disappearance.     

Evaluation of discrete host–parasitoid models for diamondback moth and Diadegma semiclausum field time population density series

The performance of discrete mathematical models to describe the population dynamics of diamondback moth (DBM) (Plutella xylostella L.) and its parasitoid Diadegma semiclausum was investigated. The parameter values for several well-known models (Nicholson–Bailey, Hassell and Varley, Beddington, Free and Lawton, May, Holling type 2, 3 and Getz and Mills functional responses) were estimated. The models were tested on 20 consecutive sets of time series data collected at 14 days interval for pest and parasitoid populations obtained from a highland cabbage growing area in eastern Kenya. Model parameters were estimated from minimized squared difference between the numerical solution of the model equations and the empirical data using Powell's method. Maximum calculated DBM growth rates varied between 0.02 and 0.07. The carrying capacity determined at 16.5 DBM/plant by the Beddington et al. model was within the range of field data. However, all the estimated parameter values relating to the parasitoid, including the instantaneous searching rate (0.07–0.28), per capita searching efficiency (0.20–0.27), search time (5.20–5.33), handling time (0.77–0.90), and parasitism aggregation index (0.33), were well outside the range encountered empirically. All models evaluated for DBM under Durbin–Watson criteria, except the May model, were not autocorrelated with respect to residuals. In contrast, the criteria applied to the parasitoid residuals showed strong autocorrelations. Thus, these models failed to estimate parasitoid dynamics. We conclude that the interactions of the DBM with its parasitoid cannot be explained by any of the models tested. Two factors may be associated with this failure. First, the parasitoid in this integrated biological control system may not be playing a major role in regulating DBM population. Second, and perhaps more likely, poor correlations reflect gross inadequacies in the theoretical assumptions that underlie the existing models.     

Habitat and population modelling of roe deer using an interactive geographic information system

Management of German roe deer (Capreolus capreolus) populations is a challenge for wildlife managers and foresters because population densities are difficult to estimate in forests and forest regeneration can be negatively affected when roe deer density is high. We describe a model to determine deer population densities compatible with forest management goals, and to assess harvest rates necessary to maintain desired deer densities. A geographic information system (GIS) was used to model wildlife habitat and population dynamics over time. Our model interactively incorporates knowledge of field biologists and foresters via a graphical user interface (GUI). Calibration of the model with deer damage maps allowed us to evaluate density dependence of a roe deer population. Incorporation of local knowledge into temporally dynamic and spatial models increases understanding of population dynamics and improves wildlife management.     

A methodological approach to develop “contaminant migration–population effects” models

The main aim of the present work is to discuss the methodological approaches that underpin the “contaminant migration–population effects” models for the evaluation of the detriment to populations of moving organisms in environmental systems with spatial and time dependent pollution levels. A technique to couple the equations controlling the population dynamics and the pollutant dispersion is described and discussed. The domain of application and the limitations of the methodology are analysed and illustrated by some examples. Possible alternative approaches are briefly presented.     

Temperature effects on vital rates of different life stages and implications for population growth of Baltic sprat

Baltic sprat (Sprattus sprattus balticus S.) is a key species in the pelagic ecosystem of the Baltic Sea. Most stocks of small pelagic species are characterized by natural, fishery-independent fluctuations, which make it difficult to predict stock development. Baltic sprat recruitment is highly variable, which can partly be related to climate-driven variability in hydrographic conditions. Results from experimental studies and field observations demonstrate that a number of important life history traits of sprat are affected by temperature, especially the survival and growth of early life stages. Projected climate-driven warming may impact important processes affecting various life stages of sprat, from survival and development during the egg and larval phases to the reproductive output of adults. This study presents a stage-based matrix model approach to simulate sprat population dynamics in relation to different climate change scenarios. Data obtained from experimental studies and field observations were used to estimate and incorporate stage-specific growth and survival rates into the model. Model-based estimates of population growth rate were affected most by changes in the transition probability of the feeding larval stage at all temperatures (+0, +2, +4, +6?°C). The maximum increase in population growth rate was expected when ambient temperature was elevated by 4?°C. Coupling our stage-based model and more complex, biophysical individual-based models may reveal the processes driving these expected climate-driven changes in Baltic Sea sprat population dynamics.     

Structural changes in lake functioning induced from nutrient loading and climate variability

Climate variability is increasingly recognized as an important regulatory factor, capable of influencing the structural properties of aquatic ecosystems. Lakes appear to be particularly sensitive to the ecological impacts of climate variability, and several long time series have shown a close coupling between climate, lake thermal properties and individual organism physiology, population abundance, community structure, and food web dynamics. Thus, understanding the complex interplay among meteorological forcing, hydrological variability, and ecosystem functioning is essential for improving the credibility of model-based water resources/fisheries management. Our objective herein is to examine the relative importance of the ecological mechanisms underlying plankton seasonal variability in Lake Washington, Washington State (USA), over a 35-year period (1964–1998). Our analysis is founded upon an intermediate complexity plankton model that is used to reproduce the limiting nutrient (phosphate)–phytoplankton–zooplankton–detritus (particulate phosphorus) dynamics in the lake. Model parameterization is based on a Bayesian calibration scheme that offers insights into the degree of information the data contain about model inputs and allows obtaining predictions along with uncertainty bounds for modeled output variables. The model accurately reproduces the key seasonal planktonic patterns in Lake Washington and provides realistic estimates of predictive uncertainty for water quality variables of environmental management interest. A principal component analysis of the annual estimates of the underlying ecological processes highlighted the significant role of the phosphorus recycling stemming from the zooplankton excretion on the planktonic food web variability. We also identified a moderately significant signature of the local climatic conditions (air temperature) on phytoplankton growth (r = 0.41), herbivorous grazing (r = 0.38), and detritus mineralization (r = 0.39). Our study seeks linkages with the conceptual food web model proposed by Hampton et al. [Hampton, S.E., Scheuerell, M.D., Schindler, D.E., 2006b. Coalescence in the Lake Washington story: interaction strengths in a planktonic food web. Limnol. Oceanogr. 51, 2042–2051.] to emphasize the “bottom-up” control of the Lake Washington plankton phenology. The posterior predictive distributions of the plankton model are also used to assess the exceedance frequency and confidence of compliance with total phosphorus (15 μg L⁻¹) and chlorophyll a (4 μg L⁻¹) threshold levels during the summer-stratified period in Lake Washington. Finally, we conclude by underscoring the importance of explicitly acknowledging the uncertainty in ecological forecasts to the management of freshwater ecosystems under a changing global environment.     

A Voronoi diagram based population model for social species of wildlife

A population model is presented that accounts for spatial structure within habitat patches. It is designed for social species of wildlife that form social group home ranges that are much smaller than patch size. The model represents social group home ranges by Voronoi regions that tessellate a patch to form a Voronoi diagram. Neighbouring social groups are linked with habitat-confined shortest paths and form a dispersal network. The model simulates population dynamics and makes use of Voronoi diagrams and dispersal networks as a spatial component. It then produces density maps as outputs. These are maps that show predicted animal densities across the patches of a landscape. A construction procedure for the particular Voronoi diagram type used by the model is described. As a test case, the model is run for the squirrel glider (Petaurus norfolcensis), a small arboreal marsupial native to Australia. A time series of density maps are produced that show squirrel glider density changing across a landscape through time.     

A population model for the peach fruit moth, Carposina sasakii Matsumura (Lepidoptera: Carposinidae), in a Korean orchard system

A population model for the peach fruit moth, Carposina sasakii Matsumura, was constructed to understand the population dynamics of this pest species and to develop an effective management strategy for various orchard (apple, peach, apple + peach) systems. The model was structured by the five developmental stages of C. sasakii: egg, larva, pupa, larval-cocoon (overwintering larva), and adult. The model consisted of a series of component models: (1) a bimodal spring adult emergence model, (2) an adult oviposition model, (3) stage emergence models of eggs, larvae, and pupae, (4) a larval survival rate model in fruits, (5) a larval-cocoon formation model, and (6) an insecticide effect model. Simulations using the model described the typical patterns of C. sasakii adult abundance in various orchard systems well, and was specific to the composition of host plants: three adult abundance peaks (first peak, mid-season peak, and last peak) a year with decreased peaks after the first peak in monoculture orchards of late apple, two adult peaks a year with a much higher last peak in monoculture orchards of early peach, and three adult peaks a year with much higher later peaks in mixed orchards of late apple and early peach. The average deviation between model outputs and actual records for first and second adult peak dates was 2.8 and 3.9 d, respectively, in simulations without an insecticide effect. The deviation decreased when insecticide effects were incorporated into the model. We also performed a sensitivity analysis of our model, and suggest possible applications of the model.