Mating disruption of the honeybee mite Varroa destructor under laboratory and field conditions

Mating in the mite Varroa destructor, an ectoparasite of the honeybee, takes place within the sealed brood cell of its host and is triggered by a female sex pheromone consisting of three fatty acids and their respective ethyl esters. In a laboratory bioassay, we observed interactions among offspring of a Varroa female at 11 days after host cell capping in the absence and in the presence of the sex pheromone and clearly demonstrated that male mites were not able to distinguish between receptive daughters and either older or immature and unreceptive females when exposed to the pheromone. In addition, mating attempts in the presence of the pheromone with otherwise receptive females were clearly of shorter duration and males often failed to select a receptive female. In order to evaluate the effect of pheromone exposure on successful copulations and the number of spermatozoa transferred under field conditions, we sprayed one of the pheromone components, oleic acid, on an empty brood comb before host egg-laying and Varroa infestation and counted the spermatozoa of daughter mites taken from this comb. We could show that the number of spermatozoa was indeed reduced, and 20 % of females lacked spermatozoa. Our results open up new possibilities and represent a promising step toward biological control of Varroa mites in beehives.     

Cuticular volatiles,attractivity of worker larvae and invasion of brood cells by Varroa mites. A comparison of Africanized and European honey bees

Summary. Africanized honey bees (AHBs) of Brazil and Mexico have proven to be tolerant to Varroa destructor mites. In contrast, European honey bees (EHBs: Apis mellifera carnica) at the same tropical study site are highly intolerant to these ectoparasites. A lower attractiveness of Varroa-tolerant AHB larvae has been hypothesised to be an important trait in reducing the susceptibitlity of AHBs to these mites. Thus, selection for EHB brood that is less attractive to mites is thought to be one possibility for limiting mite population growth and thus increase the tolerance of EHBs to the mite.?In Ribeir?o Preto, Brazil, European A. m. carnica bees and AHBs were tested with respect to their rate of brood infestation and brood attractiveness to Varroa mites. For the comparison of brood infestation rates, we introduced combs with pieces of EHB and AHB brood into honey bee colonies (18 repetitions). The relative infestation rate of EHB brood was significantly higher compared to AHB brood.?The preference behaviour of single Varroa mites was tested in a laboratory bioassay where either living host stages were offered or host extracts were presented on dummies. By these tests we could confirm the preference of Varroa females for certain developmental host stages and for their corresponding extracts. In contrast to the within-colony results, Varroa mites in the laboratory bioassay showed a slight preference for AHB compared to EHB larvae.?The gas chromatographic analysis revealed differences in the chemical spectrum of extracts obtained from different larvae. In accord with the results of the bioassays, we could detect stage-specific odour differences in larval cuticular compounds, including methyl esters and hydrocarbons that have been described as kairomones. None of these substances, however, revealed significant race-specific differences. Therefore, the quantity and composition of certain cuticular compounds seem to be responsible only for the recognition of a suitable host stage by Varroa females. The different infestation rates in the colonies, however, seem to be caused neither by race-specific differences in attractiveness of bee larvae nor by an extended attractive period of EHB larvae: both AHB and EHB larvae become attractive approximately 21 h before capping of the brood cell, and thus have the same window of time when they can be parasitised.?Therefore differential Varroa-infestation rates are not related to larval attraction but probably are determined by other race-specific and colony-related factors. Received 11 June 2001; accepted 19 November 2001.     

Volatiles of the honey bee larva initiate oogenesis in the parasitic mite Varroa destructor

Summary. Varroa reproduction is closely synchronized to the development of its host. In this study we present a new bioassay for field and laboratory tests to evaluate host factors triggering Varroa oogenesis. Female mites deprived of feeding activated oogenesis when perceiving larval volatiles. In laboratory assays the living L5-larva and pentane extracts of the larval cuticle had a clear activating effect. Wax and larval food did not elicit Varroa oogenesis. The activating components apparently are in the polar fraction of the cuticular volatiles. The consequences of this regulative mechanism for the host parasite relationship and prospects for further research are discussed.     

The effect of estimated PAR uncertainties on the physiological processes of biosphere models

Photosynthetically active radiation (PAR) energy reaching on the vegetated surface is a key determinant of plant physiological processes. Most of biosphere or crop models use the ratio of PAR to incoming solar radiation (R_s), PAR/R_s, to convert R_s into PAR in order to reduce weather data-input requirements. Several existing models simply specify a constant ratio, PAR/R_s = 0.5. However, some field experiments have reported that the ratio PAR/R_s may not be constant. Previous empirical equations of PAR/R_s were derived based on the data of monthly or daily timescales collected from only a few measurement sites, hence they may not be appropriate to be used in current global biosphere models usually with hourly simulation time steps. Here, we represent the exponential correlation between PAR/R_s and sky clearness index (0-1) using hourly data from 54 Ameriflux measurement sites. It is found that PAR/R_s increases up to 0.6 in cloudy conditions when the clearness index (CI) is below ∼0.2, whereas it is nearly constant at ∼0.42 when CI is above 0.2. When the identified empirical equation is used in the model simulation, it results in −4 to 2% difference in the stomatal conductance compared to that using the constant ratio PAR/R_s = 0.5.     

New hydroepidemiological models of indicator organisms and zoonotic pathogens in agricultural watersheds

Simple analytical models are derived to assess how a series of cattle animal farms affect the transport and fate of an indicator organism (Escherichia coli) and a zoonotic pathogen (Campylobacter) in a stream. Separate steady-state mass-balance models are developed and solved for the ultimate minimum and maximum concentrations for the two organisms. The E. coli model assumes that the organism is ubiquitous and abundant in the animals’ digestive tracts. In contrast, a simple dose-response model is employed to relate the Campylobacter prevalence to drinking water drawn from the stream. Because faecal indicators are commonly employed to assess the efficacy of best management practice (BMP) interventions, we also employ the models to assess how BMPs impact pathogen levels. The model provides predictions of (a) the relative removal efficacy for Campylobacter and (b) the prevalence of Campylobacter infection among farm animals after implementation of BMPs. Dimensionless numbers and simple graphs are developed to assess how prevalence is influenced by a number of factors including animal density and farm spacing. A significant outcome of this model development is that the numerous dimensional input and parameter variables are reduced to a group of just four dimensionless Campylobacter-related quantities, characterizing: animal density; in-stream attenuation; animal-to-animal transmission; and infection recovery. Calculations reveal that for some constellations of these four quantities there can be a greater-than-expected benefit in that the proportional reduction of stream Campylobacter concentrations post-BMP can substantially exceed the proportional reduction of concentrations of E. coli in that stream. In addition, a criterion for system sterility (i.e., the conditions required for the farm infection rate to decrease with downstream distance) is derived.     

Exploring the influence of lake water chemistry on chlorophyll a: A multivariate statistical model analysis

A multivariate statistical approach integrating the absolute principal components score (APCS) and multivariate linear regression (APCS-MLR), along with structural equation modeling (SEM), was used to model the influence of water chemistry variables on chlorophyll a (Chl a) in Lake Qilu, a severely polluted lake in southwestern China. Water quality was surveyed monthly from 2000 to 2005. APCS-MLR was used to identify key water chemistry variables, mine data for SEM, and predict Chl a. Seven principal components (PCs) were determined as eigenvalues >1, which explained 68.67% of the original variance. Four PCs were selected to predict Chl a using APCS-MLR. The results showed a good fit between the observed data and modeled values, with R² = 0.80. For SEM, Chl a and eight variables were used: NH₄-N (ammonia-nitrogen), total phosphorus (TP), Secchi disc depth (SD), cyanide (CN), arsenic (As), cadmium (Cd), fluoride (F), and temperature (T). A conceptual model was established to describe the relationships among the water chemistry variables and Chl a. Four latent variables were also introduced: physical factors, nutrients, toxic substances, and phytoplankton. In general, the SEM demonstrated good agreement between the sample covariance matrix of observed variables and the model-implied covariance matrix. Among the water chemistry factors, T and TP had the greatest positive influence on Chl a, whereas SD had the largest negative influence. These results will help researchers and decision-makers to better understand the influence of water chemistry on phytoplankton and to manage eutrophication adaptively in Lake Qilu.     

Application of a Random Forest algorithm to predict spatial distribution of the potential yield of Ruditapes philippinarum in the Venice lagoon, Italy

We present a modelling framework that combines machine learning techniques and Geographic Information Systems to support the management of an important aquaculture species, Manila clam (Ruditapes philippinarum). We use the Venice lagoon (Italy), the first site in Europe for the production of R. philippinarum, to illustrate the potential of this modelling approach. To investigate the relationship between the yield of R. philippinarum and a set of environmental factors, we used a Random Forest (RF) algorithm. The RF model was tuned with a large data set (n = 1698) and validated by an independent data set (n = 841). Overall, the model provided good predictions of site-specific yields and the analysis of marginal effect of predictors showed substantial agreement among the modelled responses and available ecological knowledge for R. philippinarum. The most influent environmental factors for yield estimation were percentage of sand in the sediment, salinity, and water depth. Our results agree with findings from other North Adriatic lagoons. The application of the fitted RF model to continuous maps of all the environmental variables allowed estimates of the potential yield for the whole basin. Such a spatial representation enabled site-specific estimates of yield in different farming areas within the lagoon. We present a possible management application of our model by estimating the potential yield under the current farming distribution and comparing it to a proposed re-organization of the farming areas. Our analysis suggests a reduction of total yield is likely to result from the proposed re-organization.     

Comparison of exergy found by a classical thermodynamic approach and by the use of the information stored in the genome

It is possible to calculate the exergy for organisms based on classic thermodynamics as already demonstrated by Mejer and Jorgensen [Mejer, H., Jorgensen, S.E., 1979. Exergy and ecological buffer capacity. State-of-the-art in Ecol. Model. 7, 829–846]. The calculation of exergy as eco-exergy, which is based on the information stored in the genome, has lately been proposed by Jørgensen and co-workers. Recently, Ludovisi [Ludovisi, A., 2009. Exergy vs information in ecological successions: interpreting community changes by a classical thermodynamic approach. Ecol. Model. 220, 1566–1577] has put forward a method based on classical thermodynamics, which leads to the calculation of “virtual” values of concentration at equilibrium for a number of organic compounds (VEC) and freshwater organisms (VECE). This paper compares the two approaches by analysing the correlation existing between the VECE- and the β-values derived by Jørgensen et al. [Jørgensen, S.E., Ladegaard, N., Debeljak, M., Marques, J.C., 2005. Calculations of exergy for organisms. Ecol. Model. 185, 165–175]. It was found that there was a good correlation, which can be useful for estimating β-values for organisms whose genome is not known in a sufficient detail. The relationship between VECE- and β-values suggests that two proposed thermodynamic orientors based on these quantities – the eco-exergy index and the structural information – should lead to coherent results when applied to the evaluation of the development state of ecosystems. A numerical simulation shows that this expectation is verified in a major case, but also that different, even opposite, responses can arise, depending on the biological composition of the biocoenosis investigated.     

Sensitivity analysis of the asymptotic behavior of a model for the environmental movement of radionuclides

The asymptotic behavior of a linear compartment model for the environmental movement of radionuclides is investigated. Here, the expression asymptotic behavior is used to designate the behavior of q(t) as t → ∞, where q is the solution of a vector differential equation of the form dq/dt = h + Kq. The asymptotic behavior of such equations is described. For the model and conditions under consideration, each element of q converges monotonically to a steady-state value. A hydrologic system is defined and used to illustrate this behavior. An approach to sensitivity analysis employing Latin hypercube sampling, rank transformations and stepwise regression is presented and then applied to this system. A total of 20 independent variables is introduced and the following dependent variables are investigated for the various components of the system: amount of radionuclide present at steady state. concentration of radionuclide at steady state, and time required to reach 90% of steady state. Finally, an application of asymptotic behavior in the analysis of a hypothetical site for the geologic isolation of high-level radioactive waste is described and a brief discussion of differential sensitivity analysis is given.     

Estimation of annual potential evapotranspiration at regional scale based on the effect of moisture on soil respiration

Potential evapotranspiration (PET) is an important component of water cycle. For traditional models derived from the principle of aerodynamics and the surface energy balance, its calculation always includes many parameters, such as net radiation, water vapor pressure, air temperature and wind speed. We found that it can be acquired in an easier way in specific regions. In this study, a new PET model (PETP model) derived from two empirical models of soil respiration was evaluated using the Penman-Monteith equation as a standard method. The results indicate that the PETP model estimation concur with the Penman-Monteith equation in sites where annual precipitation ranges from 717.71 mm to 1727.37 mm (R² = 0.68, p = 0.0002), but show large discrepancies in all sites (R² = 0.07, p = 0.1280). Then we applied our PETP model at the global scale to the regions with precipitation higher than 700 mm using 2.5° CMAP data to obtain the annual PET for 2006. As expected, the spatial pattern is satisfactory overall, with the highest PET values distributed in the lower latitudes or coastal regions, and with an average of 1292.60 ± 540.15 mm year⁻¹. This PETP model provides a convenient approach to estimate PET at regional scales.     

A discrete model for estimating the development time from egg to infecting larva of Ostertagia ostertagi parametrized using a fuzzy rule-based system

Ostertagia ostertagi is a nematode, predominantly affecting cattle in the Pampean region of Argentina. A mathematical model parametrized using fuzzy rule-based systems of the Takagi-Sugeno-Kant type (FTSK) for estimating the development time from egg to infecting larval stage L3 of the gastrointestinal parasite O. ostertagi is here proposed. The estimation of development time of O. ostertagi is essential for the generation of appropriate control mechanisms, since this provides information about the time when parasites are ready to migrate to pastures. For the purpose of reflecting the natural environmental conditions, the mean daily temperature is taken as the main and only regulator of the development time. Humidity conditions are considered to be sufficient for the normal development of the larvae. Hence the individual's daily growth is a function of its length and the mean temperature recorded on the previous day. It is expressed in terms of a difference equation with fuzzy parameters, which are defined using laboratory data. Model outputs are tested against results of field experiments. Simulation results are very satisfactory, yielding a mean estimation error (MEE) of 0.64 weeks, with variance 0.34, and a determination coefficient R² = 0.74. The model clearly exhibits an inverse relationship between development time and temperature both in controlled and in field conditions. It also exhibits a very sensitive response both to the order in which the temperature sequence occurs, - reproducing the differences observed between spring and autumn - and to the amplitude of the temperature range.     

Modeling amphibian energetics, habitat suitability, and movements of western toads, Anaxyrus (=Bufo) boreas, across present and future landscapes

Effective conservation of amphibian populations requires the prediction of how amphibians use and move through a landscape. Amphibians are closely coupled to their physical environment. Thus an approach that uses the physiological attributes of amphibians, together with knowledge of their natural history, should be helpful. We used Niche Mapper™ to model the known movements and habitat use patterns of a population of Western toads (Anaxyrus (=Bufo) boreas) occupying forested habitats in southeastern Idaho. Niche Mapper uses first principles of environmental biophysics to combine features of topography, climate, land cover, and animal features to model microclimates and animal physiology and behavior across landscapes. Niche Mapper reproduced core body temperatures (T_c) and evaporation rates of live toads with average errors of 1.6 ± 0.4 °C and 0.8 ± 0.2 g/h, respectively. For four different habitat types, it reproduced similar mid-summer daily temperature patterns as those measured in the field and calculated evaporation rates (g/h) with an average error rate of 7.2 ± 5.5%. Sensitivity analyses indicate these errors do not significantly affect estimates of food consumption or activity. Using Niche Mapper we predicted the daily habitats used by free-ranging toads; our accuracy for female toads was greater than for male toads (74.2 ± 6.8% and 53.6 ± 15.8%, respectively), reflecting the stronger patterns of habitat selection among females. Using these changing to construct a cost surface, we also reconstructed movement paths that were consistent with field observations. The effect of climate warming on toads depends on the interaction of temperature and atmospheric moisture. If climate change occurs as predicted, results from Niche Mapper suggests that climate warming will increase the physiological cost of landscapes thereby limiting the activity for toads in different habitats.     

Modelling habitat overlap among sympatric mesocarnivores in southern Illinois,USA

Few researchers have developed large-scale habitat models for sympatric carnivore species. We created habitat models for red foxes (Vulpes vulpes), coyotes (Canis latrans) and bobcats (Lynx rufus) in southern Illinois, USA, using the Penrose distance statistic, remotely sensed landscape data, and sighting location data within a GIS. Our objectives were to quantify and spatially model potential habitat differences among species. Habitat variables were quantified for 1-km² buffered areas around mesocarnivore sighting locations. Following variable reduction procedures, five habitat variables (percentage of grassland patches, interspersion–juxtaposition of forest patches, mean fractal dimension of wetland patches and the landscape, and road density) were used for analysis. Only one variable differed (P < 0.05) between red fox and coyote sighting areas (road density) and bobcat and coyote sighting areas (mean fractal dimension of the landscape). However, all five variables differed between red fox and bobcat sighting areas, indicating considerable differences in habitat affiliation between this pair-group. Compared to bobcats, red fox sightings were affiliated with more grassland cover and larger grassland patches, higher road densities, lower interspersion and juxtaposition of forest patches, and lower mean fractal dimension of wetland patches. These differences can be explained by different life history requirements relative to specific cover types. We then used the Penrose distance statistic to create habitat models for red foxes and bobcats, respectively, based on the five-variable dataset. An independent set of sighting locations were used to validate these models; model fit was good with 65% of mesocarnivore locations within the top 50% of Penrose distance values. In general, red foxes were affiliated with mixtures of agricultural and grassland cover, whereas bobcats were associated with a combination of grassland, wetland, and forest cover. The greatest habitat overlap between red foxes and bobcats was found at the interface between forested areas and more open cover types. Our study provides insight into habitat overlap among sympatric mesocarnivores, and the distance-based modelling approach we used has numerous applications for modelling wildlife–habitat relationships over large scales.     

Design of a Domain Specific Language for modelling processes in landscapes

The modelling of processes that occur in landscapes is often confronted to issues related to the representation of space and the difficulty of properly handling time and multiple scales. In order to investigate these issues, a flexible modelling environment is required. We propose to develop such a tool based on a Domain Specific Language (DSL) that capitalises on the service-oriented architecture (SOA) paradigm. The modelling framework around the DSL is composed of a model building environment, a code generator and compiler, and a program execution platform. The DSL introduces five language elements (entity, service, relation, scenario and datafacer) that can be combined to offer a wide range of possibilities for modelling in space and time at different scales. When developing a model, model parts are either built using the DSL or taken from libraries of previously built ones, and adapted to the specific model. The practical usage of the DSL is illustrated first with the Lotka–Volterra model, and then with a landscape modelling experiment on the spread of a mosquito-borne disease in the Sahelian region of West Africa. An interesting characteristic of this approach is the possibility of adding new elements into an existing model, and replacing others with more appropriate ones, thus allowing potentially complex models to be built from simpler parts.     

Evaluating weather effects on interannual variation in net ecosystem productivity of a coastal temperate forest landscape: A model intercomparison

Forest productivity is strongly affected by seasonal weather patterns and by natural or anthropogenic disturbances. However weather effects on forest productivity are not currently represented in inventory-based models such as CBM-CFS3 used in national forest C accounting programs. To evaluate different approaches to modelling these effects, a model intercomparison was conducted among CBM-CFS3 and four process models (ecosys, CN-CLASS, Can-IBIS and 3PG) over a 2500 ha landscape in the Oyster River (OR) area of British Columbia, Canada. The process models used local weather data to simulate net primary productivity (NPP), net ecosystem productivity (NEP) and net biome productivity (NBP) from 1920 to 2005. Other inputs used by the process and inventory models were generated from soil, land cover and disturbance records. During a period of intense disturbance from 1928 to 1943, simulated NBP diverged considerably among the models. This divergence was attributed to differences among models in the sizes of detrital and humus C stocks in different soil layers to which a uniform set of soil C transformation coefficients was applied during disturbances. After the disturbance period, divergence in modelled NBP among models was much smaller, and attributed mainly to differences in simulated NPP caused by different approaches to modelling weather effects on productivity. In spite of these differences, age-detrended variation in annual NPP and NEP of closed canopy forest stands was negatively correlated with mean daily maximum air temperature during July-September (T_amax) in all process models (R² = 0.4-0.6), indicating that these correlations were robust. The negative correlation between T_amax and NEP was attributed to different processes in different models, which were tested by comparing CO₂ fluxes from these models with those measured by eddy covariance (EC) under contrasting air temperatures (T_a). The general agreement in sensitivity of annual NPP to T_amax among the process models led to the development of a generalized algorithm for weather effects on NPP of coastal temperate coniferous forests for use in inventory-based models such as CBM-CFS3: NPP′ = NPP − 57.1 (T_amax − 18.6), where NPP and NPP′ are the current and temperature-adjusted annual NPP estimates from the inventory-based model, 18.6 is the long-term mean daily maximum air temperature during July-September, and T_amax is the mean value for the current year. Our analysis indicated that the sensitivity of NPP to T_amax was nonlinear, so that this algorithm should not be extrapolated beyond the conditions of this study. However the process-based methodology to estimate weather effects on NPP and NEP developed in this study is widely applicable to other forest types and may be adopted for other inventory based forest carbon cycle models.     

Behavioral attributes and parental care of Varroa mites parasitizing honeybee brood

Varroa jacobsoni, an ectoparasite of the Asian honeybeeApis cerana, has been introduced world-wide, and is currently decimating colonies of the European honeybeeApis mellifera.Varroa's reproductive cycle is tuned to that of drone cells, those mainly parasitized in the original host. We describe here how a single fertilized female, infesting a brood cell, can produce two to four adult fertilized females within the limited time span of bee development (270 h in worker and 320 h in drone cells), despite the disturbance caused by cocoon spinning and subsequent morphological changes of the bee. From observations on transparent artificial cells we were able to show how the mite combats these problems with specialized behaviors that avoid destruction by the developing bee, prepares a feeding site for the nymphs on the bee pupa, and constructs a fecal accumulation on the cell wall which serves as a rendezvous site for matings between its offspring. The proximity of the fecal accumulation to the feeding site facilitates feeding by the maturing progeny. However, communal use of the feeding site leads to competition between individuals, and protonymphs are most disadvantaged. This competition is somewhat compensated by the timing of oviposition by the mites. Use of a common rendezvous and feeding site by two or moreVarroa mothers in multiinfested cells may have developed from the parental care afforded to them as nymphs.     

Estimating dyad association probability under imperfect and heterogeneous detection

In animal behaviour studies, association indices estimate the proportion of time two individuals (i.e. a dyad) spend in association. In terms of dyads, all association indices can be interpreted as estimators of the probability that a dyad is associated. However, traditional indices rely on the assumptions that the probability to detect a particular individual (p) is either approximately one and/or homogeneous between associated and not associated individuals. Based on marked individuals we develop a likelihood based model to estimate the probability a dyad is associated (ψ) accounting for p < 1 and possibly varying between associated and not associated individuals. The proposed likelihood based model allows for both individual and dyadic missing observations. In addition, the model can easily be extended to incorporate covariate information for modeling p and ψ. A simulation study showed that the likelihood based model approach yield reasonably unbiased estimates, even for low and heterogeneous individual detection probabilities, while, in contrast, traditional indices showed moderate to strong biases. The application of the proposed approach is illustrated using a real data set collected from a population of Commerson's dolphin (Cephalorhynchus commersonii) in Patagonia Argentina. Finally, we discuss possible extensions of the proposed model and its applicability in animal behaviour and ecological studies.     

Modelling coupled peach tree-aphid population dynamics and their control by winter pruning and nitrogen fertilization

Nitrogen fertilization and winter pruning are commonly used to control crop production in peach [Prunus persica (L.) Batsch] orchards. They are also known to affect the dynamics of Myzus persicae (Sulzer) (Homoptera: Aphididae) aphid populations via bottom-up regulation processes. Interactions between crops and pests can cause complex system behaviour in response to management practices. An integrated approach will therefore improve the understanding of the effects of these two cultural practices on aphid and peach performances.We developed a simulation model that describes the cultural control of interacting peach tree and aphid population dynamics. It uses the principles of common trophic models while gathering available knowledge and explicit assumptions on peach and aphid functioning and the effects of cultural practices.The model was able to qualitatively reproduce the system behaviour observed in the field. It accounted for actions and feedback such as stimulation of foliar growth by winter pruning, consecutive aphid population increase, subsequent damage to foliage, and partial compensatory growth of foliage. The model also reproduced low losses in fruit production due to aphid infestations. However, it called for further integration of ‘long-term’ effects. Analysis of the model showed the complexity of peach tree and aphid responses to leaf N × winter pruning interactions. Simulations indicated that fruit production losses remained low within a range of realistic values of leaf N and pruning intensity, whereas manipulating peach and aphid dynamics, their interactions and their relationships to practices could result in higher losses.The model is useful to evaluate the relevance of cultural practices for a bottom-up regulation of aphid dynamics in crop-pest management. After considering other control methods and fruit quality, it can be used to find a combination of practices that optimises trade-offs between fruit production and environmental conservation goals. A modelling approach that links crop growth and pest population dynamics and integrates management practice effects has strong potential for improving crop-pest management in an integrated crop production context.     

Catch equations: restoring the missing terms in the nominally generalized Baranov catch equation

Observational models for the catch of fish at age a (or size) at time t are fundamental equations in fisheries science, linking a population model with data. The well known Baranov catch equation (which assumes that fishing and natural mortalities are constant over both age and time) is a nominal basis of those most commonly used in fish stock assessment and fish population models (which assume that fishing and natural mortalities vary with both age and time). But, what should a catch equation look like, if the instantaneous rates of fishing and natural mortalities of fish of age a at time t vary with age a and time t? Without answering this question, use of those catch equations in fish stock assessment and population models renders their results uncertain. In this paper, I derive a general catch in number or in biomass equation as observational models of an age- and time-dependent model for a fish population by Taylor series expansion of, and by directly manipulating, a general catch integral, reduce it to commonly used catch equations, and compare the performance of 11 of them using data on the western king prawn Penaeus latisulcatus. I show that the nominal generalization of the Baranov catch equation misses several terms. In so doing, I derive the catch equations more accurately and restore these missing terms. Although almost all approximations overestimate the catch per recruit for older prawns, all commonly used catch equations and their extensions perform worse than theoretically sound representations of the general catch equation and their approximations. The age-specific bias of all models is <2.5, <18 and <90% for a time interval of sampling of 1, 7 and 30 days, respectively. Such large biases even for moderate values of the length of the time interval of sampling highlight a need for assessing the utility of commonly used catch equations for individual species.     

A simple and precise method for fitting a von Bertalanffy growth curve

The parameter K of the von Bertalanffy equation, as developed by Beverton and Holt (1957), is first estimated by the relation $$\log _e \left( {dL_t /dt} \right) = A - Kt$$ where dLt/dt denotes growth increments per a unit of age, t denotes age, and A is a constant. The K estimate is used to evaluate L∞; $$L_\infty = \left( {e^K \sum\limits_2^n {L_t - \sum\limits_1^{n - 1} {L_t } } } \right)/\left( {n - 1} \right)\left( {e^K - 1} \right)$$ The L∞ estimate is used to estimate t _o, and to obtain a better estimate for K; $$\log _e \left( {1 - L_t /L_\infty } \right) = - Kt + Kt_0 $$ The K estimate may be used to obtain another estimate for L∞. Solved examples show that a single iteration is sufficient to obtain fitted equations which are, on the average, as precise as equations fitted by the least squares method shown by Tomlinson and Abramson (1961). This new method can be used, with a slight modification, for the second equation given above, if growth data have unequal age intervals. The variance of K, t _o and log _e L∞ can be estimated by applying the simple methods used in the case of straight-line relationships.