Simulation of small bird populations. II. Reduced breeding in two British raptor species

A computer model was developed to simulate the fate of small populations of birds. It uses general and easily available data as input. Monte-Carlo techniques are used and a survival probability is calculated for every population member four times per simulated year. The model allows for density-dependence in winter survival and also in fecundity.Simulation results are used to compile standard age-specific life-tables for all complete cohorts generated. A mean life-table is also made. The survivor functions, both accumulated and mean, are contrasted with control functions and tested for significance.The model has been applied to classical population data in ornithology, namely those for the great tit and the tawny owl in Wytham Woods (Oxford, UK). There was a fair agreement between simulation results and field data.     

On interacting bee/mite populations: a stochastic model with analysis using cumulant truncation

Parasitism by the Varroa mite has had recent drastic impact on both managed and feral bee colonies. This paper proposes a stochastic population dynamics model for interacting African bee colony and Varroa mite populations. Cumulant truncation procedures are used to obtain approximate transient cumulant functions, unconstrained by the usual assumption of bivariate Normality, for an assumed large-scale model. The apparent size of the variance and skewness functions suggest the importance of the proposed truncation procedure which retains some higher-order cumulants, but determining the accuracy of the approximations is problematical. A smaller-scale bee/Varroa mite model is hence proposed and investigated. The accuracy for the means is exceptional, for the second-order cumulants is moderate, and for some third-order cumulants is poor. Notwithstanding the poor accuracy of a skewness approximation, the saddlepoint approximations for the marginal transient population size distributions are excellent. The cumulant truncation methodology is very general, and research is continuing in its application to this new class of host-parasite models.     

Integral projection models for finite populations in a stochastic environment

Continuous types of population structure occur when continuous variables such as body size or habitat quality affect the vital parameters of individuals. These structures can give rise to complex population dynamics and interact with environmental conditions. Here we present a model for continuously structured populations with finite size, including both demographic and environmental stochasticity in the dynamics. Using recent methods developed for discrete age-structured models we derive the demographic and environmental variance of the population growth as functions of a continuous state variable. These two parameters, together with the expected population growth rate, are used to define a one-dimensional diffusion approximation of the population dynamics. Thus, a substantial reduction in complexity is achieved as the dynamics of the complex structured model can be described by only three population parameters. We provide methods for numerical calculation of the model parameters and demonstrate the accuracy of the diffusion approximation by computer simulation of specific examples. The general modeling framework makes it possible to analyze and predict future dynamics and extinction risk of populations with various types of structure, and to explore consequences of changes in demography caused by, e.g., climate change or different management decisions. Our results are especially relevant for small populations that are often of conservation concern.     

Climate change threatens polar bear populations: a stochastic demographic analysis

The polar bear (Ursus maritimus) depends on sea ice for feeding, breeding, and movement. Significant reductions in Arctic sea ice are forecast to continue because of climate warming. We evaluated the impacts of climate change on polar bears in the southern Beaufort Sea by means of a demographic analysis, combining deterministic, stochastic, environment-dependent matrix population models with forecasts of future sea ice conditions from IPCC general circulation models (GCMs). The matrix population models classified individuals by age and breeding status; mothers and dependent cubs were treated as units. Parameter estimates were obtained from a capture-recapture study conducted from 2001 to 2006. Candidate statistical models allowed vital rates to vary with time and as functions of a sea ice covariate. Model averaging was used to produce the vital rate estimates, and a parametric bootstrap procedure was used to quantify model selection and parameter estimation uncertainty. Deterministic models projected population growth in years with more extensive ice coverage (2001-2003) and population decline in years with less ice coverage (2004-2005). LTRE (life table response experiment) analysis showed that the reduction in lambda in years with low sea ice was due primarily to reduced adult female survival, and secondarily to reduced breeding. A stochastic model with two environmental states, good and poor sea ice conditions, projected a declining stochastic growth rate, log lambdas, as the frequency of poor ice years increased. The observed frequency of poor ice years since 1979 would imply log lambdas approximately - 0.01, which agrees with available (albeit crude) observations of population size. The stochastic model was linked to a set of 10 GCMs compiled by the IPCC; the models were chosen for their ability to reproduce historical observations of sea ice and were forced with "business as usual" (A1B) greenhouse gas emissions. The resulting stochastic population projections showed drastic declines in the polar bear population by the end of the 21st century. These projections were instrumental in the decision to list the polar bear as a threatened species under the U.S. Endangered Species Act.     

Analytical methods for a stochastic mainland-island metapopulation model

We study a class of chain-binomial metapopulation models, giving special attention to the ‘mainland-island’ configuration, where patches receive immigrants from an external source. We evaluate the distribution of the number n_t of occupied patches at any census time t and establish a law of large numbers that identifies a deterministic trajectory which can be used to approximate the process when the number of patches is large. We also establish a central limit law, which shows that the fluctuations about this trajectory are approximately normally distributed. We describe briefly much finer results that can be used for model calibration.     

Duplex auditory distance assessment in a small passerine bird (Pipilo erythrophthalmus)

Eastern towhees, Pipilo erythrophthalmus, (Emberizidae, Passeriformes) in Florida estimate source sound-pressure level (SPL; i.e., sound amplitude) and often misjudge speaker distance in the field when vocalization source SPL is varied experimentally. Sound frequencies below ~3.5 kHz attenuate reliably with distance in comparison with higher sound frequencies in Florida scrub habitat. As a result, I predicted that towhees should use SPL as an auditory distance cue when they hear stimuli produced with sound frequencies below ~3.5 kHz but use another cue when they hear stimuli produced with sound frequencies above ~3.5 kHz. Subjects often misjudged speaker distance when approaching playbacks of SPL-altered stimuli produced with sound frequencies below ~3.5 kHz but rarely misjudged speaker distance when played SPL-altered stimuli produced with sound frequencies above ~3.5 kHz. I discuss the possibility that towhees employ a duplex sound localization strategy.     

A stochastic model for the use of a country park

The subject of this theoretical study is a country park with a very delicate natural environment, located near large urban areas, as a result of which it receives a heavy inflow of visitors.The problem is that of determining the best organization of the park to achieve a distribution of visitors which is compatible with the protection of the natural environment. Therefore a mathematical model is sought which describes the distribution of visitors in relation to the various zones within the park.In this paper the mathematical model and its subsequent calibration are described.     

Assessment of nitrogen leaching from arable land in large river basins: Part I. Simulation experiments using a process-based model

A two-step procedure for analysing nitrogen leaching from arable land in large river basins is suggested: (1) application of a process-based dynamic model for a set of representative conditions in a large river basin to simulate water and nitrogen fluxes and (2) development of a fuzzy-rule based metamodel using the simulated nitrogen fluxes in Step 1 as a training set. After that the metamodel can be used for rapid assessment of water quality inside the considered ranges of parameters, describing natural conditions and management practices. This paper describes Step 1 of the procedure. Step 2 is described in an accompanying paper (Haberlandt et al., Ecological Modelling 150 (3) (2002) 277–294). The advantage of this approach is that it combines the ‘process-based foundation’ with the resulting simplicity of the metamodel. Simulation experiments for analysing nitrogen (N) leaching from arable land were performed using the Soil and Water Integrated Model (SWIM) for a set of representative conditions in the Saale basin (23 687 km²) in Central Europe. The Saale River is one of the main tributaries of the Elbe. In advance, hydrological validation of the model was done for the whole Saale basin and validation of nitrogen dynamics was fulfilled in two mesoscale sub-basins of the Elbe. For the simulation experiments the drainage basin area was sub-divided into five climate zones and nine representative soil classes were chosen. The basic rotation and fertilisation schemes were established using regional information obtained from literature. In addition, the effects of changing the basic rotation to more/less intensive ones and changing fertilisation rates by 50% increase/decrease were studied. The ranges of simulated nitrogen fluxes for the basic rotation and fertilisation schemes are comparable to available regional estimates and differences between sub-regions and soils are plausible. The relative importance of natural and anthropogenic factors affecting nitrogen leaching for the Saale River basin was as follows: (1) soil, (2) climate, (3) fertilisation rate and (4) crop rotation. The simulation experiments provide a basis for a fuzzy-rule based metamodel approach, which aims at rapid water quality assessment of large regions.     

Habitat fragmentation lowers survival of a tropical forest bird.

Population ecology research has long been focused on linking environmental features with the viability of populations. The majority of this work has largely been carried out in temperate systems and, until recently, has examined the effects of habitat fragmentation on survival. In contrast, we looked at the effect of forest fragmentation on apparent survival of individuals of the White-ruffed Manakin (Corapipo altera) in southern Costa Rica. Survival and recapture rates were estimated using mark-recapture analyses, based on capture histories from 1993 to 2006. We sampled four forest patches ranging in size from 0.9 to 25 ha, and four sites in the larger 227-ha Las Cruces Biological Station Forest Reserve (LCBSFR). We found a significant difference in annual adult apparent survival rates for individuals marked and recaptured in forest fragments vs. individuals marked and recaptured in the larger LCBSFR. Contrary to our expectation, survival and recapture probabilities did not differ between male and female manakins. Also, there was no support for the existence of annual variation in survival within each study site. Our results suggest that forest fragmentation is likely having an effect on population dynamics for the White-ruffed Manakin in this landscape. Therefore, populations that appear to be persisting in fragmented landscapes might still be at risk of local extinction, and conservation action for tropical birds should be aimed at identifying and reducing sources of adult mortality. Future studies in fragmentation effects on reproductive success and survival, across broad geographical scales, will be needed before it is possible to achieve a clear understanding of the effects of habitat fragmentation on populations for both tropical and temperate regions.     

The application of a multiple-recapture technique for the study of relatively small fish populations

Expressions are given for the estimation of catchability of untagged fish using the type of multiple-recapture experiments suited to relatively small fish populations. in these experiments all captured fish are released after tagging untagged fish. The realistic assumption that fish populations suffer from different causes of mortality during the sampling surveys is adopted here. The catchability estimate for untagged fish is used to evaluate instantaneous fishing mortality, abundance, survival, instantaneous total mortality and instantaneous natural mortality rates of untagged fish. These estimates are free from Types A and B tagging errors, and take into consideration that catchabilities of tagged and untagged fish are different.     

Migration effects in a stochastic multipopulation model for African bee population dynamics

The rate of northern migration of the Africanized honey bee (AHB) in the United States has recently slowed dramatically. This paper investigates the impact of migration on the equilibrium size distributions of a particular stochastic multipopulation model, namely a coupled logistic power law model. The bivariate equilibrium size distribution of the model is derived and illustrated with parameter values used to describe AHB population dynamics. In the model, the difference between the equilibrium sizes of the two populations is a measure of the effect of migration. The distribution of this difference may be approximated by a normal distribution. The mean and variance parameters for the normal are predicted accurately by a second-order regression model based on the migration rate and the maximum size of the first population. The methodology is general, and should be useful in studying the migration effect in many other applications with one-way migration.     

An atmospheric—terrestrial heavy metal transport model. I. model theory

A general model TOHM was developed to predict the terrestrial fate of zinc, cadmium, chromium, lead and mercury emitted by the operation of a coal-fired electric generating facility. The general model consisted of interfacing submodels describing atmospheric dispersion, precipitation, soil chemistry, and soil erosion. The models were developed from input data from a semi-arid region of the southwest United States, and except for the climatic and topographic constraints, are not site specific. TOHM was found to predict no substantial increase in indigenous levels of zinc, chromium and lead in the impact (deposition) area. However, both mercury and cadmium were predicted to be emitted and eroded to the environmental sink (receiving lake) in concentrations exceeding that naturally present in the system. TOHM is currently unvalidated, though comparison of soil erosion predictions with erosion quantities measured in the impact area gives good agreement.     

A simulation model for the management of vicuña populations

The population dynamics of the vicuña was modelled based on field data from the Central Galeras Sector, Perú. Rains were simulated in order to obtain net primary productivity and grass availability which act upon density-dependent fecundity and mortality. The model produces a population growth curve that tends to stabilize at densities around 100 vicuñas per km². Harvest and shearing processes were simulated as part of the vicuña population management model. Harvest was based upon a fixed threshold density D_e below which no harvest occurs; for densities above D_e harvesting is applied at a rate proportional to the difference between D_e and the current population density (fixed escapement or ‘bang-bang’ harvest rule). Management optimization was analyzed by determining the optimal escapement density D_e, which maximized either net profits or the number of animals harvested. Analyzing the results as cumulative totals over 20 years of simulation, an optimum harvest production was obtained for a D_e of about 40 vicuñas per km², and maximum profit was obtained for a D_e around 70 vicuñas per km². Analyzing the results of 20 years of simulation as annual averages with an original population density of 40 vicuñas per km², the harvest production and profits were maximized for a D_e of 40 and 60 vicuñas per km², respectively.The model was validated using data from the Reserva Nacional San Guillermo, Argentina, where vicuña and guanaco populations coexist (although their interaction was not modelled). The sensitivity analysis was performed with three different techniques: (a) stepwise multiple linear regression, (b) visual graphic analysis based on a polar coordinates system, and (c) direct evaluation of the effect on management decisions. The curve shape parameters of the fecundity and mortality functions proved to be the most important ones in determining the outcome of the model.     

A two-dimensional stochastic model of downy mildew of radish

A two-dimensional stochastic model that simulates the spread of disease over space and time was recently proposed by Xu and Ridout [Xu, X.M., Ridout, M.S., 1998. Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. Phytopathology 88, 1000–1012]. In a theoretical study, the authors showed the ability of their model to generate a broad range of disease patterns and disease progress rates. The objective of our study was to test if this theoretical approach was able to describe disease progress and the disease pattern of a specific disease, downy mildew (Peronospora parasitica) of radish (Raphanus sativus L.). Two field experiments with artificial inoculation were carried out and disease incidence and spatial pattern were assessed twice a week until disease incidence was greater than 0.25. Four model parameters were estimated by an algorithm that uses a least square regression together with an evolutionary optimisation strategy. Moran's I indices of spatial autocorrelation calculated both for measured und simulated data were significantly correlated (α = 0.05, r = 0.61). Also observed variances in measurements and in simulations were closely and significantly correlated (α = 0.05, r = 0.95). Thus, disease pattern (as assessed in terms of variance inflation and spatial autocorrelation) was well described by the model. The model accounted for 94% of the variation in the disease incidence data. It has, therefore, the potential to be developed into a forecast model for risk analysis and for decision support in plant protection. However, in the specific case of downy mildew on radish more experimental data are required for model validation and to parameterise the effects of environment on infection, sporulation and spore dispersal.     

Biosystematic studies of the red algal genus Eucheuma. I. Electrophoretic variation among Florida populations

Electrophoretic techniques were used to assess the degree of genetic differentiation among 4 species of the seaweed Eucheuma; E. isiforme, E. nudum, E. gelidium and E. acanthocladum. Nine Floridian populations were surveyed for 5 enzymes (14 loci), and compared using both phenotypic identity (I _p )and Nei's genetic identity (I) statistics. Results suggest there is a very high degree of genetic similarity between E. isiforme and E. nudum (=0.904), and between E. gelidium and E. acanthocladum (=0.857), but a very low degree of similarity between these two pairs of species (=0.372). These findings are in agreement with an earlier report which recommended the removal of E. gelidium and E. acanthocladum from the genus based on differences in reproductive anatomy. Greater genetic similarity was observed among the E. isiforme populations than among the E. nudum populations, the latter being ecologically more diverse and geographically or hydrographically more isolated. The proportion of polymorphic loci per population ranged from 0.25 to 0.36. Heterozygote deficiencies were observed at two acid phosphatase loci in offshore populations of E. nudum which showed a propensity for vegetative reproduction.     

Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g., aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed or modeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.     

Microbial associations in sponges. I. Ecology,physiology and microbial populations of coral reef sponges

Illumination, current strength and physical turbulence influence the distribution of 4 tropical sponges. Three sponges with cyanobacteria in exposed tissues grow only in poen shallow habitats: Pericharax heteroraphis in moderate-current, lowturbulence regions on the reef slope; Jaspis stellifera in low-current, moderate-turbulence regions of the outer reef flat; and Neofibularia irata in moderate-current, high-turbulence areas below the reef crest. Ircinia wistarii contains no cyanobacteria and occurs in deeper, strong-current, high-turbulence regions. N. irata agressively overgrows neighbouring corals and its growth form is influenced by the current strength. The sponges efficiently filter bacteria from the water. The efficiency is related to the aquiferous structure, particularly the size of choanocyte chambers, and is unrelated to the existing bacterial populations in sponge tissue. The numbers of bacteria associated with the sponges are proportional to the sponge mesohyl density, with the dense sponges J. stellifera and I. wistarii containing many bacteria whereas P. heteroraphis is not dense and has few bacteria.     

Two-compartment model of radionuclide accumulation into marine organisms. I. Accumulation from a medium of constant activity

The interpretation of kinetics of radionuclide accumulation into biological organisms can be performed by using the well-known multicompartment models. The application of a two-compartment model in the interpretation of radionuclide accumulation into marine organisms, when this does not markedly deplete the medium, is considered. It has been found that most of the loss experiments cannot be interpreted without the use of uptake data. The agreement between the uptake and loss parameters is discussed. Explicit expressions for different kinds of two-compartment models are evaluated. The interpretation of irreversible and other special cases is proposed.     

A stochastic bioeconomic model for the management of clam farming

The Manila clam Tapes philippinarum is one of the most important commercial mollusc species in Europe. Intensive clam farming takes place in several coastal lagoons of the Northern Adriatic Sea, supporting local economy but raising the problem of the environmental sustainability of this activity. In this work, we propose a bioeconomic model that provides guidelines for an efficient management of intensive clam farming. Clam demography is described by a stochastic model of growth and survival, accounting for the effect of water temperature, seeding substratum and density dependence of vital rates. The model is calibrated on and applied to the case of Sacca di Goro, a lagoon located in the Po River Delta (Northern Italy). We consider two distinct management criteria: the optimisation of the marketable yield and the optimisation of monetary benefits, respectively. The use of a stochastic formulation allows us to reveal the existing trade-off between maximizing the median yield or profit and minimizing its variance. A Pareto analysis shows that seeding in spring or fall on sandy substrata and harvesting 18 months later provides the best compromise between these two contrasting objectives, maximizing profits while minimizing the associated uncertainty level. Finally, we show that seeding clams at high densities (more than 750 clams m⁻² on muddy substrata and more than 1500 elsewhere) can have not only a potentially negative impact on the ecological sustainability of clam farming, but also a negative economic effect.