Simulating the temporal pattern of waste production in farmed gilthead seabream (Sparus aurata), European seabass (Dicentrarchus labrax) and Atlantic bluefin tuna (Thunnus thynnus)

Most fish farming waste output models provide gross waste rates as a function of stocked or produced biomass for a year or total culture cycle, but without contemplating the temporality of the discharges. This work aims to ascertain the temporal pattern of waste loads by coupling available growth and waste production models and developing simulation under real production rearing conditions, considering the overlapping of batches and management of stocks for three widely cultured species in the Mediterranean Sea: gilthead seabream (Sparus aurata), European seabass (Dicentrarchus labrax) and Atlantic bluefin tuna (Thunnus thynnus). For a similar annual biomass production, the simulations showed that waste output and temporal dumping patterns differ between the three species as a result of the disparities in growth velocity, nutrient digestibility, maintenance metabolic budget and husbandry. The simulations allowed the temporal patterns including the periods of maximum discharge and the dissolved and particulate nitrogen and phosphorus content in the wastes released to be determined, both of which were seen to be species-specific.     

Development of an individual-based model to evaluate elk (Cervus elaphus nelsoni) movement and distribution patterns following the Cerro Grande Fire in north central New Mexico, USA

Though studies have modeled the effects of fires on elk, no studies have related the effects of post-fire landscape succession on ungulate movements and distribution using dynamic modeling techniques. The purpose of this study was to develop and test a spatially-explicit, stochastic, individual-based model (IBM) to evaluate potential movement and distribution patterns of elk (Cervus elaphus nelsoni) in relation to spatial and temporal aspects of the Cerro Grande Fire that burned north central New Mexico in May of 2000. Following extensive literature review, the SAVANNA Ecosystem Model was selected to simulate the underlying post-fire successional processes driving elk movement and distribution. Standard logisitic regression was used to analyze habitat-use patterns of ten elk from data collected using global positioning system radio collars while an additional five animals were used as an independent test set during model validation. Static variables in the form of roads, buildings, fences, and habitual use/memory were used to modify a map of impedance values based on the logistic regression of slope, aspect, and elevation. Integration with SAVANNA came through the application of a habitat suitability index (HSI), which combined movement rules written for the IBM and variables modified and produced by the dynamic ecological processes run in SAVANNA. Overall pattern analysis indicated that realistic migrational processes and habitat-use patterns emerged from movement rules incorporated into the IBM in response to advancing and receding snow when compared to the independent test set. Primary and secondary movement pathways emerged from the collective responses of simulated individuals. Using regression analyses, no significant differences between simulated animals and animals used in either model development or an independent test set revealed any differences in response to snow patterns. These considerations suggest the model was adequately corroborated based on existing data and outlined objectives.     

Modeling the impacts of hunting on the population dynamics of red howler monkeys (Alouatta seniculus)

Overexploitation of wildlife populations occurs across the humid tropics and is a significant threat to the long-term survival of large-bodied primates. To investigate the impacts of hunting on primates and ways to mitigate them, we developed a spatially explicit, individual-based model for a landscape that included hunted and un-hunted areas. We used the large-bodied neotropical red howler monkey (Alouatta seniculus) as our case study species because its life history characteristics make it vulnerable to hunting. We modeled the influence of different rates of harvest and proportions of landscape dedicated to un-hunted reserves on population persistence, population size, social dynamics, and hunting yields of red howler monkeys. In most scenarios, the un-hunted populations maintained a constant density regardless of hunting pressure elsewhere, and allowed the overall population to persist. Therefore, the overall population was quite resilient to extinction; only in scenarios without any un-hunted areas did the population go extinct. However, the total and hunted populations did experience large declines over 100 years under moderate and high hunting pressure. In addition, when reserve area decreased, population losses and losses per unit area increased disproportionately. Furthermore, hunting disrupted the social structure of troops. The number of male turnovers and infanticides increased in hunted populations, while birth rates decreased and exacerbated population losses due to hunting. Finally, our results indicated that when more than 55% of the landscape was harvested at high (30%) rates, hunting yields, as measured by kilograms of biomass, were less than those obtained from moderate harvest rates. Additionally, hunting yields, expressed as the number of individuals hunted/year/km², increased in proximity to un-hunted areas, and suggested that dispersal from un-hunted areas may have contributed to hunting sustainability. These results indicate that un-hunted areas serve to enhance hunting yields, population size, and population persistence in hunted landscapes. Therefore, spatial regulation of hunting via a reserve system may be an effective management strategy for sustainable hunting, and we recommend it because it may also be more feasible to implement than harvest quotas or restrictions on season length.     

Dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain)

In this study we developed a dynamic growth model for Scots pine (Pinus sylvestris L.) plantations in Galicia (north-western Spain). The data used to develop the model were obtained from a network of permanent plots, of between 10 and 55-year-old, which the Unidade de Xestión Forestal Sostible (Sustainable Forest Management Unit) of the University of Santiago de Compostela has set up in pure plantations of this species of pine in its area of distribution in Galicia. In this model, the initial stand conditions at any point in time are defined by three state variables (number of trees per hectare, stand basal area and dominant height), and are used to estimate stand volume, classified by commercial classes, for a given projection age. The model uses three transition functions expressed as algebraic difference equations of the three corresponding state variables used to project the stand state at any point in time. In addition, the model incorporates a function for predicting initial stand basal area, which can be used to establish the starting point for the simulation. This alternative should only be used when the stand is not yet established or when no inventory data are available. Once the state variables are known for a specific moment, a distribution function is used to estimate the number of trees in each diameter class, by recovering the parameters of the Weibull function, using the moments of first and second order of the distribution (arithmetic mean diameter and variance, respectively). By using a generalized height–diameter function to estimate the height of the average tree in each diameter class, combined with a taper function that uses the above predicted diameter and height, it is then possible to estimate total or merchantable stand volume.     

Application of a temperature-dependent von Bertalanffy growth model to bullhead (Cottus gobio)

The most studied and commonly applied model of fish growth is the von Bertalanffy model. However, this model does not take water temperature into account, which is one of the most important environmental factors affecting the life cycle of fish, as many physiological processes that determine growth, e.g. metabolic rate and oxygen supply, are directly influenced by temperature. In the present study we propose a version of the von Bertalanffy growth model that includes mean annual water temperatures by correlating the growth coefficient, k, explicitly and the asymptotic length, L_∞, implicitly to water temperature. All relationships include parameters with an obvious biological relevance that makes them easier to identify. The model is used to fit growth data of bullhead (Cottus gobio) at different locations in the Bez River network (Drme, France). We show that temperature explains much of the growth variability at the different sampling sites of the network.     

Assessing environmental factors in red spruce (Picea rubens Sarg.) growth in the Great Smoky Mountains National Park, USA: From conceptual model, envirogram, to simulation model

This study provides a method for assessing a multiplicity of environmental factors in red spruce growth in the Great Smoky Mountains National Park (GSMNP) of Southeastern USA. Direct and indirect factors in the annual growth increment are first organized into a schematic input-output envirogram (ARIRS), and this information is then used to construct a simulation model (ARIM). The envirogram represents a structured conceptualization of most environmental factors involved in growth, as developed from relevant literature. This interdisciplinary synthesis distinguishes direct vs. indirect factors in growth and takes account of the systems ecology concept that indirect factors may be as important as or more important than direct ones in regulating growth. The ARIRS envirogram summarizes hierarchically organized, within- and cross-scale, local-to-global interactions, and its construction makes it obvious that growth is influenced by many cross-scale spatiotemporal interactions. More research on genecology is still needed to clarify the role of phenotypic plasticity and adaptive capacity in nutrient cycling, global change, and human disturbance.     

A simulation model for Japanese sardine (Sardinops melanostictus) migrations in the western North Pacific

A two-dimensional individual-based model coupled with fish bioenergetics was developed to simulate migration and growth of Japanese sardine (Sardinops melanostictus) in the western North Pacific. In the model, fish movement is controlled by feeding and spawning migrations with passive transport by simulated ocean current. Feeding migration was assumed to be governed by search for local optimal habitats, which is estimated by the spatial distribution of net growth rate of a sardine bioenergetics model. The forage density is one of the most important factors which determines the geographical distributions of Japanese sardine during their feeding migrations. Spawning migration was modeled by an artificial neural network (ANN) with an input layer composed of five neurons that receive environmental information (surface temperature, temperature change experienced, current speed, day length and distance from land). Once the weight of the ANN was determined, the fish movement was solved by combining with the feeding migration model. To obtain the weights of the ANN, three experiments were conducted in which (1) the ANN was trained with back propagation (BP) method with optimum training data, (2) genetic algorithm (GA) was used to adjust the weights and (3) the weights of the ANN were decided by the GA with BP, respectively. BP is a supervised learning technique for training ANNs. GA is a search technique used in computing to find approximate solutions, such as optimization of parameters. Condition factor of sardine in the model is used as a factor of optimization in the GA works. The methods using only BP or GA did not work to search the appropriate weights in the ANN for spawning migration. In the third method, which is a combined approach of GA with BP, the model reproduced the most realistic spawning migration of Japanese sardine. The changes in temperature and day length are important factors for the orientation cues of Japanese sardine according to the sensitivity analysis of the weights of the ANN.     

Integrating farming techniques in an ecological matrix model: Implementation on the primrose (Primula vulgaris)

Several studies have proven the importance of field margins in sustaining biodiversity and other work has been done on the effect of field management on field margin flora. However few models have been built to predict the effects of field management on the flora. Our project addresses this need for a model capable of predicting the effect of cropping techniques and their timing on the flora of field margins. Primula vulgaris is a biodiversity indicator, characteristic of undisturbed flora and found in field margins and woodlands: its population has been declining for several years. We created a temporal matrix model of P. vulgaris populations on field margins, taking into account the effects of field, field margin and roadside management based on literature and expert knowledge. We then analysed its sensitivity to demographic parameters by comparing lambda (growth rate) sensitivity and elasticity. We compared the management parameter effect using the relative growth rate of the population after 6 years of simulation. Sensitivity analysis to biological parameters showed the importance of adult survival and seed production and germination. Results show that P. vulgaris is particularly sensitive to broad-spectrum herbicides and that other management techniques like early mowing, scything and scrub-killer (diluted broad-spectrum herbicide or specific herbicide) are less aggressive. Our simulations show that management of cash crops in Brittany is too aggressive for P. vulgaris populations and that 4-5 years of grassland in the adjacent field are necessary to maintain populations.     

Waterfowls habitat modeling: Simulation of nest site selection for the migratory Little Tern (Sterna albifrons) in the Nakdong estuary

This paper aims to find patterns in nest site selection by Little Terns Sterna albifrons, in the Nakdong estuary in South Korea. This estuary is important waterfowl stopover and breeding habitat, located in the middle of the East Asia-Australasian Flyway. The Little Tern is a common species easily observed near the seashore but their number is gradually declining around the world. We investigated their nests and eggs on a barrier islet in the Nakdong estuary during the breeding season (May to June, 2007), and a pattern for the nest site selection was identified using genetic programming (GP). The GP generated a predictive rule-set model for the number of Little Tern nests (training: R² = 0.48 and test: 0.46). The physical features of average elevation, variation of elevation, plant coverage, and average plant height were estimated to determine the influence on nest numbers for Little Tern. A series of sensitivity analyses stressed that mean elevation and vegetation played an important role in nest distribution for Little Tern. The influence of these two variables could be maximized when elevation changed moderately within the sampled quadrats. The study results are regarded as a good example of applying GP to vertebrate distribution patterning and prediction with several important advantages compared to conventional modeling techniques, and can help establish a management or restoration strategy for the species.     

The response of the woodpigeon (Columba palumbus) to relaxation of intraspecific competition: A hybrid modelling approach

The recent rapid growth of the woodpigeon population in the British Isles is a cause for concern for environmental managers. It is unclear what has driven their increase in abundance. Using a mathematical model, we explored two possible mechanisms, reduced intraspecific competition for food and increased reproductive success. We developed an age-structured hybrid model consisting of a system of ordinary differential equations that describes density-dependent mortality and a discrete component, which represents the birth-pulse. We investigated equilibrium population dynamics using our model. The two hypotheses predict contrasting population age profiles at equilibrium. We adapted the model to examine the impacts of control measures. We showed that an annual shooting season that follows the period of density-dependent mortality is the most effective control strategy because it simultaneously removes adult and juvenile woodpigeons. The model is a first step towards understanding the processes that influence the dynamics of woodpigeon populations.     

A system dynamics model for the management of the Manila clam, Ruditapes philippinarum (Adams and Reeve, 1850) in the Bay of Arcachon (France)

The Manila clam Ruditapes philippinarum (Adams and Reeve, 1850) is one of the mollusc species that, driven mainly by the shellfish market industry, has extended throughout the world, far beyond the limits of its original habitat. The Manila clam was introduced into France for aquaculture purposes, between 1972 and 1975. In France, this venerid culture became increasingly widespread and, since 1988, this species has colonised most of the embayments along the French Atlantic coast. In 2004, this development resulted in a fishery of ca. 520 t in Arcachon Bay.     

Population dynamics of splitnose rockfish (Sebastes diploproa) in the Northeast Pacific Ocean

We developed an age-structured population model of splitnose rockfish, Sebastes diploproa, in the Northeast Pacific Ocean. Splitnose rockfish is a bycatch species that co-occurs with several commercially important species that are currently declared overfished. Bycatch species are typically not the focus of stock assessment efforts because of their limited economic importance, but they may suffer the same population declines as species with which they co-occur. To examine the dynamics of splitnose rockfish for the first time, we analyzed data from three groundfish fisheries and four research surveys conducted in the Northeast Pacific Ocean. To develop a model, we used Stock Synthesis, a statistical framework for the construction of a population dynamics models utilizing both fishery-dependent and fishery-independent data. In the model, we reconstructed the total catch of the species back to 1900, estimated the dynamics of the stock spawning output and recruitment and evaluated biomass depletion relative to the stock's unfished state, as well as sources of uncertainty in model outputs. The results indicate that the splitnose rockfish is currently not overfished even though it has experienced several periods of abrupt decline in its biomass. Revisiting age data from earlier years, monitoring fishery discard, and investigating the spatial dynamics of splitnose rockfish is important to further improve the understanding of this species’ population dynamics, and decrease uncertainty in model results.     

Modeling effects of toxin exposure in fish on long-term population size, with an application to selenium toxicity in bluegill (Lepomis macrochirus)

A primary goal in ecotoxicology is the prediction of population-level effects of contaminant exposure based on individual-level response. Assessment of toxicity at the population level has predominately focused on the population growth rate (PGR), but the PGR may not be a relevant toxicological endpoint for populations at equilibrium. Equilibrium population size may be a more meaningful endpoint than the PGR because a population with smaller equilibrium size is more susceptible to the negative effects of environmental variability. We address the individual-to-population extrapolation problem with modeling utilizing classical mathematical theory. We developed and analyzed a general model applicable to many freshwater fish species, that includes density-dependent juvenile survival and additional juvenile mortality due to toxicity exposure, and we quantified effect on equilibrium population size as a means of assessing toxicity. Individual-level effects are typically greater than population-level effects until the individual effect is large, due to compensatory density-dependent relationships. These effects are sensitive to the recruitment potential of a population, in particular the low-density first-year survival rate S_b. Assuming high S_b could result in underestimating effects of population-level toxicity. The equilibrium size depends directly on S_b, the reproductive potential, the toxin concentration at which mean mortality is 50% (LC₅₀), and the rate at which individual mortality increases with increasing toxin concentration. More experimental data are needed to decrease the uncertainty in estimating these parameters. We then used existing data for selenium toxicity in bluegill sunfish to parameterize a simulation version of the model as an example to assess the effects of environmental stochasticity on toxicity response. Effects of environmental variability resulted in simulated extinctions at much lower toxin concentrations than predicted deterministically.     

Analysis of behavioral changes of zebrafish (Danio rerio) in response to formaldehyde using Self-organizing map and a hidden Markov model

Two computational methods were applied to classification of movement patterns of zebrafish (Danio rerio) to elucidate Markov processes in behavioral changes before and after treatment of formaldehyde (0.1 mg/L) in semi-natural conditions. The complex data of the movement tracks were initially classified by the Self-organizing map (SOM) to present different behavioral states of test individuals. Transition probabilities between behavioral states were further evaluated to fit Markov processes by using the hidden Markov model (HMM). Emission transition probability was also obtained from the observed variables (i.e., speed) for training with the HMM. Experimental transition and emission probability matrices were successfully estimated with the HMM for recognizing sequences of behavioral states with accuracy rates in acceptable ranges at central and boundary zones before (77.3-81.2%) and after (70.1-76.5%) treatment. A heuristic algorithm and a Markov model were efficiently combined to analyze movement patterns and could be a means of in situ behavioral monitoring tool.     

An individual-based model to study the reproduction of egg bearing copepods: Application to Eurytemora affinis (Copepoda Calanoida) from the Seine estuary,France

Limited empirical studies have elucidated the daily egg production and associated reproductive processes of egg bearing copepod. Herein, we present an individual-based model which constitutes a realistic representation of the reproduction in egg bearing copepods. The model has been parameterized using an extensive set of experimental data obtained from the literature and from the laboratory and field experiments on the estuarine copepod Eurytemora affinis. The proposed model takes into account the adult female longevity, the clutch size and interclutch duration, which is a function of egg maturation time and latency time required by the female after egg hatching to produce a new clutch. The embryonic development time and hatching success are also taken into account. The effect of temperature on the means and variances of above-mentioned reproductive parameters has been also incorporated. A multi agent system based generic platform “Mobidyc” has been used to generate and calibrate the model. The model demonstrates the reproductive parameters of females of E. affinis which is validated through individual based experiments. Temperature specific simulations provide a dynamical explanation of temperature effect on the cumulative egg production. The daily survival principally affects the number of clutches produced per female during its life span. The results obtained in the present study by combining temperature and survival effects reveal the relatively greater importance of the first factor on the daily egg production of egg-carrying copepods. The present model is generic and hence easily applicable to other animals with comparable reproductive strategy.     

GIS-based modeling of the geographic distribution of Quercus emoryi Torr. (Fagaceae) in México and identification of significant environmental factors influencing the species’ distribution

The greatest concentration of oak species in the world is believed to be found in Mexico. These species are potentially useful for reforestation because of their capacity to adapt to diverse environments. Knowledge of their geographic distribution and of species–environment relations is essential for decision-making in the management and conservation of natural resources. The objectives of this study were to develop a model of the distribution of Quercus emoryi Torr. in Mexico, using geographic information systems and data layers of climatic and other variables, and to determine the variables that significantly influence the distribution of the species. The study consisted of the following steps: (A) selection of the target species from a botanical scientific collection, (B) characterization of the collecting sites using images with values or categories of the variables, (C) model building with the overlay of images that meet the habitat conditions determined from the characterization of sites, (D) model validation with independent data in order to determine the precision of the model, (E) model calibration through adjustment of the intervals of some variables, and (F) sensitivity analysis using precision and concordance non-parametric statistics applied to pairs of images. Results show that the intervals of the variables that best describe the species’ habitat are the following: altitude from 1650 to 2750 amsl, slope from 0 to 66°; average minimum temperature of January from −12 to −3 °C; mean temperature of June from 11 to 25 °C; mean annual precipitation from 218 to 1225 mm; soil units: lithosol, eutric cambisol, haplic phaeozem, chromic luvisol, rendzina, luvic xerosol, mollic planosol, pellic vertisol, eutric regosol; type of vegetation: oak forest, oak–pine forest, pine forest, pine–oak forest, juniperus forest, low open forest, natural grassland and chaparral. The resulting model of the geographic distribution of Quercus emoryi in Mexico had the following values for non-parametric statistics of precision and agreement: Kappa index of 0.613 and 0.788, overall accuracy of 0.806 and 0.894, sensitivity of 0.650 and 0.825, specificity of 0.963, positive predictive value of 0.945 and 0.957 and negative predictive value of 0.733 and 0.846. Results indicate that the variable average minimum temperature of January, with a maximum value of −3 °C, is an important factor in limiting the species’ distribution.     

Application of a spatial meta-population model with stochastic parameters to the management of the invasive grass Nassella trichotoma in North Canterbury, New Zealand

Optimising the management of invasive plants requires the identification of the population size outcomes for alternative management strategies. Mathematical models can be useful tools for making such management strategy comparisons. In this paper we develop a generic landscape meta-population model and apply it to the weedy grass, Nassella trichotoma, an invasive species occupying approximately 800 land parcels, predominantly pastoral farms, in the Hurunui district, North Canterbury, New Zealand. Empirical evidence reveals that this meta-population is currently stable (at a median density of 6 plants ha⁻¹) under a community strategy requiring manual removal (termed ‘grubbing’) of plants annually from all land parcels. Reduction in population size requires an alternative management strategy. Field data, collected over a 12 year period, were used to provide stochastic parameter values for land parcel size, carrying capacity, rates of local population growth and grubbing.The model reveals that at steady state, the most significant contribution to population growth on a land parcel comes from within the land parcel itself; the expected annual per capita growth on an individual land parcel is 4 orders of magnitude greater than the expected annual contribution from plants arising from other land parcels. This result implies that many of the farms currently supporting N. trichotoma may pose little or no threat to, nor are threatened themselves by, other farms infested by the weed. However, the steady state distribution (of the weed's population density) was sensitive to the spread rate, revealing a need for data on this process. It was also sensitive to how any increase in the grubbing rate is distributed; increasing it via a uniform distribution U(0, 1) where all rates between 0 and 100% year⁻¹ are equally probable did not affect the steady state, whereas increasing the rates via the uniform distribution U(0.25, 0.75) resulted in fewer farms with high population densities. In general the model provides a basis for exploring the effects of a wide range of alternative grubbing strategies on population growth in N. trichotoma.     

A distributed-delay model to predict ageing and survival rates of adults of Cryptolestes ferrugineus (Stephens) (Coleoptera: Laemophloeidae) in granaries filled with wheat

A time-varying distributed-delay model simulating effects of multifactors was developed. Prediction of the ageing rate and survival distribution of adults of the rusty grain beetle, Cryptolestes ferrugineus (Stephens) (Coleoptera: Laemophloeidae) in various environments found in wheat-filled granaries was conducted as an example to illustrate the application of this developed model. Published adult mortalities, determined at different temperatures, relative humidities, and food sources, were directly used to find the average ageing rate and family of cumulative function of adult mortality. The developed model could predict the adult survival rate at constant or transient temperatures with different relative humidities. This model could also simulate the effect of adult acclimation to their environment when they experience temperature and moisture fluctuations inside granaries. To validate the developed model, the simulation results were compared with available experimental data from the literature. There was no difference between predicted and measured mortalities in two granaries in which the mortalities were determined in a 4-month experiment.