Evaluating estimators of the numbers of females with cubs-of-the-year in the yellowstone grizzly bear population

Current management of the grizzly bear (Ursus arctos) population in Yellowstone National Park and surrounding areas requires annual estimation of the number of adult female bears with cubs-of-the-year. We examined the performance of nine estimators of population size via simulation. Data were simulated using two methods for different combinations of population size, sample size, and coefficient of variation of individual sighting probabilities. We show that the coefficient of variation does not, by itself, adequately describe the effects of capture heterogeneity, because two different distributions of capture probabilities can have the same coefficient of variation. All estimators produced biased estimates of population size with bias decreasing as effort in creased. Based on the simulation results we recommend the Chao estimator for model M _h be used to estimate the number of the female bears with cubs of the year; however, the estimator of Chao and Shen may also be useful depending on the goals of the research.     

Insights Into the Latent Multinomial Model Through Mark-Resight Data on Female Grizzly Bears With Cubs-of-the-Year

Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for female grizzly bears with cubs-of-the-year (FCOY), and inference suffers from both limitations. To overcome difficulties due to sparseness, we assume homogeneity in sighting probabilities over 16 years of bi-annual aerial surveys. We model counts of marked and unmarked animals as multinomial random variables, using the capture frequencies of marked animals for inference about the latent multinomial frequencies for unmarked animals. We discuss undesirable behavior of the commonly used discrete uniform prior distribution on the population size parameter and provide OpenBUGS code for fitting such models. The application provides valuable insights into subtleties of implementing Bayesian inference for latent multinomial models. We tie the discussion to our application, though the insights are broadly useful for applications of the latent multinomial model.     

Differentiation of nitrogen and microbial community in the littoral and limnetic sediments of a large shallow eutrophic lake (Chaohu Lake,China)

Purpose

Nitrogen (N) is one of the major elements causing eutrophication in freshwater lakes, and the N cycle is mainly driven by microorganisms. Lake littoral zones are found to be “hotspots” for N removal from both the basin and receiving waters. However, the environmental factors that drive the distribution of microorganisms are diverse and unclear. Here, we examined the differentiation of nitrogen and microbial community between the littoral and limnetic sediments to explore their interactions.

Materials and methods

Sediment samples were collected in the littoral and limnetic zones of Chaohu Lake in winter (ca. 7 °C) and autumn (ca. 22 °C). Abundances of the bacterial and archaeal genes amoA (ammoxidation), nirS and nirK (denitrification), hzsB (anaerobic ammonium oxidation; anammox), and nrfA (dissimilatory nitrate reduction to ammonium; DNRA) were measured via quantitative real-time polymerase chain reaction (qPCR). Clone libraries were constructed for further phylogenetic analysis to study the community composition.

Results and discussion

We observed significant higher concentration values in terms of sedimentary NH₄⁺-N and NO₃^?-N in the limnetic zone than littoral zone (p?<?0.05; n?=?12). In general, abundance values of the above six genes in the littoral zone were all higher than those in the limnetic zone, while higher in winter (7 °C) than in autumn (22 °C) (p?<?0.05; n?=?6). The spatial heterogeneity had the most significant effect on the distribution of ammonia-oxidizing archaea (AOA) and anammox bacteria abundance. Both temporal (temperature) and spatial heterogeneity affected the abundance of ammonia-oxidizing bacteria (AOB). The variation in the abundance of denitrifying bacteria and DNRA bacteria mainly reflected the temporal (temperature) heterogeneity.

Conclusions

The six N-cycle-related microorganisms were affected by different environmental factors and presented different distribution patterns. The lower nitrogen content and the higher microbial abundance and diversity showed that the littoral zone was the “hotspot” of N-cycling-related microorganisms in a large, eutrophic, and turbid lake. It is suggested that increasing the area and restoring the ecological function of the littoral zone was effective and significant in eutrophic lake management.

     

Using regression models in design‐based estimation of spatial means of soil properties

The precision of design‐based sampling strategies can be increased by using regression models at the estimation stage. A general regression estimator is given that can be used for a wide variety of models and any well‐defined sampling design. It equals the π estimator plus an adjustment term that accounts for the differences between the π estimators for the spatial means of the auxiliary variables and the true spatial means of these variables. The regression estimator and ratio estimator follow from certain assumptions on the model and the sampling design. These are compared with the π estimator in two case studies. In one study a bivariate field of linearly related variables was simulated and repeatedly sampled by Simple Random Sampling without replacement and sample sizes 10, 25, 50, 100 and 200. For all sample sizes the ratio of the standard error of the simple regression estimator to that of the π estimator was approximately 55%. The bias of the simple regression estimator was negligibly small. The confidence interval estimators were valid for all sample sizes except for n = 10. Also the ratio estimator was approximately unbiased, and the confidence interval estimators were valid for all sample sizes, even for n = 10. This is remarkable because the ratio estimator assumes that the intercept of the regression line is 0 which was incorrect for the simulated field. On the other hand, only approximately 55% of the potential gain was achieved because the model was inappropriate. In a second study the spatial means of the Mean Highest Watertable of map units were estimated by Stratified Simple Random Sampling and the combined (multiple) regression estimator. The NAP elevation, the local elevation, the Easting and the Northing were used as auxiliary variables. For all map units except one the combined (multiple) regression estimator was more precise than the π estimator. The ratio of the standard errors varied from 0.36 to 1.04. The domain for which the regression estimator was less precise than the π estimator showed strong variation between strata. For this domain it was more efficient to group the strata into two groups and to fit simple models for these groups separately.     

西北旱区石羊河流域作物耗水点面尺度转化方法的研究

基于DEM与GIS空间分析功能研究了石羊河流域主要农作物春小麦需水量ET_c的时空分异规律。根据8个气象站近50年气象资料,应用1998年FAO推荐的Penman-Monteith公式计算参考作物蒸发蒸腾量ET₀,由收集到的春小麦需水量试验资料获得多年平均作物系数K_c。近50年来流域上游的古浪、天祝春小麦全生育期ET_c呈微弱的增加趋势,中游的凉州区表现出极显著的减少趋势,其他站减少趋势不显著。确立了ET_c与海拔高度、纬度、坡向的多元回归关系,借助Arcview3.3、ArcGIS9.0与Visual Basic6.0软件实现了春小麦ET_c的空间尺度转换,并分析了石羊河流域25%、50%、75%三个不同水文年春小麦ET_c的空间变异情况。石羊河流域春小麦ET_c由山区向绿洲平原递增,多年平均值为270～591 mm。估计值与计算值相差在11.1%以内。     

Analysis of the variable charge of two organic soils by means of the NICA-Donnan model

We have tested to see if the generic set of NICA‐Donnan model parameters, used to describe isolated humic substances, can also describe soil humic substances in situ. A potentiometric back‐titration technique was used to determine the variable surface charge of two organic peat soils at three different ionic strengths. The non‐ideal, competitive‐adsorption NICA‐Donnan model was used to simulate the surface charge, by assuming a bimodal distribution of H⁺ affinity on the soil solid phase. The model provided an excellent fit to the experimental data. The Donnan volume, V_D, varied slightly with ionic strength, although the variation was less than for humic substances in solution. The values obtained for the parameters that define the affinity distributions, the intrinsic proton binding constant (log K_i^int) and the heterogeneity of the site (m_i), were similar to those observed for isolated soil humic acids. The abundance of carboxylic groups in the whole soil represented 30% of the typical value for isolated soil humic acids. The composition of the organic matter of the whole soils, obtained by ¹³C CPMAS NMR, was comparable to the characteristic composition of soil humic acids.     

The relationship between structure and the hydraulic conductivity of soil

A random fractal matrix comprising a hierarchical aggregation of primary structural elements is used to capture the characteristics of a heterogeneous soil structure with a tortuous pore space. The influence of heterogeneity of both the solid matrix and the pore space, as well as the shape of the pore boundary, on the saturated and unsaturated hydraulic conductivity is studied. For such random structures, the fractal (Hausdorff) dimension alone is not enough to characterize the structure from the point of view of fluid flow and additional characterizations are introduced. The porosity, ρ_p, of the primary elements has a critical value, ρ_c. With probability 1, both the saturated and unsaturated conductivities are found to be dependent as a power law on the length scale, L, at which the measurement is made when ρ_p>ρ_c. When ρ_p<ρ_c, only the unsaturated conductivity is scaling in length scale, while the saturated conductivity becomes dominated, with probability close to 1, by the conductivity of the largest connecting pores in the structure, i.e. preferential pathways. The relationships between the parameters of the power laws and structure are derived and are found to depend on the fractal (Hausdorff) and spectral dimensions of the solid matrix, denoted d_m and respectively. A discussion of the importance of these results for the interpretation and extrapolation of measurements is presented, and the implications for variability and predictability of the hydraulic properties of soil is discussed.     

Closed mark-recapture models to estimate species richness: An example using data on epigeal spiders

Species richness is a fundamental ecological property. The problem of estimating the number of species is quite similar to that of estimating the population size of a single species. Some authors of mark-recapture statistics have proposed using some of these methods to estimate species richness. This necessitates understanding how the recording probabilities of individuals differ from those of species. In particular, the species of a species pool are likely to exhibit a wide range of recording probabilities. Depending on sampling conditions, temporal or spatial variation in species detection probability may also occur, making model M _th estimators particularly useful. Empirical detection probabilities and estimates of species numbers using three coverage, one point, and two jackknife estimators are presented for series of spatial and temporal trapping occasions of epigeal spiders.     

Bayesian Calibration of Blue Crab (<Emphasis Type="Italic">Callinectes sapidus</Emphasis>) Abundance Indices Based on Probability Surveys

Abundance and standard error estimates in surveys of fishery resources typically employ classical design-based approaches, ignoring the influences of non-design factors such as varying catchability. We developed a Bayesian approach for estimating abundance and associated errors in a fishery survey by incorporating sampling and non-sampling variabilities. First, a zero-inflated spatial model was used to quantify variance components due to non-sampling factors; second, the model was used to calibrate the estimated abundance index and its variance using pseudo empirical likelihood. The approach was applied to a winter dredge survey conducted to estimate the abundance of blue crabs (Callinectes sapidus) in the Chesapeake Bay. We explored the properties of the calibration estimators through a limited simulation study. The variance estimator calibrated on posterior sample performed well, and the mean estimator had comparable performance to design-based approach with slightly higher bias and lower (about 15% reduction) mean squared error. The results suggest that application of this approach can improve estimation of abundance indices using data from design-based fishery surveys.     

我国水蚀区坡耕地土壤分离能力的空间分布与影响因素

我国水蚀区不同区域自然地理环境和土壤理化性质存在巨大差异,可能会引起土壤分离能力(Dc)的差异。然而目前大尺度上(如水蚀区)Dc的空间分布及其影响因素的研究尚未见报道。在水蚀区依据土壤类型和土壤质地不同布设了36个采样点,用扰动土(代表新耕坡耕地)测定其Dc并分析其影响因素。结果表明,水蚀区沙漠风沙土Dc最大,红壤Dc最小,Dc呈强度空间变异。西北黄土高原地区和南方山地丘陵区Dc最大。黏粒和砂粒含量适中的土壤质地Dc最大。水流剪切力与水流功率在模拟Dc方面无显著差异。Dc与粉粒、土壤粒径参数、阳离子交换量和土壤有机质存在显著的负相关关系,与砂粒、中值粒径、平均几何粒径和交换性纳百分比存在显著的正相关关系。水蚀区Dc可用水流剪切力、粉粒、阳离子交换量和土壤有机质很好地模拟(R^2=0.71,NSE=0.71)。     

Evapotranspiration and regional probabilities of soil moisture stress in rainfed crops, southern India

The long-term probability of soil moisture stress in rainfed crops was mapped at 0.5° resolution over the Krishna River basin in southern India (258,948 km²). Measurements of actual evapotranspiration (E_a) from 90 lysimeter experiments at four locations in the basin were used to calibrate a non-linear regression model that predicted the combined crop coefficient (K_cK_s) as a function of the ratio of seasonal precipitation (P) to potential evapotranspiration (E_p). Crops included sorghum, pulses (mung bean, chickpea, soybean, pigeonpea) and oilseeds (safflower and sunflower). E_p was calculated with the Penman–Monteith equation using net radiation derived from two methods: (1) a surface radiation budget calculated from satellite imagery (E_pSRB) and (2) empirical equations that use data from meteorological stations (E_pGBE). The model of K_s as a function P/E_p was combined with a gridded time series of precipitation (0.5° resolution, 1901–2000) and maps of E_pSRB to define the probability distributions of P, P/E_p and K_s for sorghum at each 0.5° cell over the basin. Sorghum, a C4 crop, had higher E_a and K_s values than the C3 plants (oilseeds, pulses) when precipitation was low (P < 1 mm d⁻¹) but lower maximum E_a rates (3.3–4.5 mm d⁻¹) compared with C3 crops (oilseeds and pulses, 4.3–4.9 mm d⁻¹). The crop coefficient under adequate soil moisture (K_c) was higher than the FAO-56 crop coefficients by up to 56% for oilseeds and pulses. The seasonal soil moisture coefficient (K_s) for sorghum ranged from 1.0 under high rainfall (July–October) to 0.45 in dry seasons (November–March), showing strong soil moisture controls on E_a. E_pSRB calculated at the lysimeter stations was 4–20% lower than E_pGBE, with the largest difference in the dry season. K_c derived from E_pSRB was only slightly (2–4%) higher than K_c derived from E_pSRB, because the maximum E_a occurred during the monsoon when the differences between E_pSRB and E_pGBE were small. Approximately 20% of the basin area was expected to experience mild or greater soil moisture stress (K_s < 0.80) during the monsoon cropping season 1 year in every 2 years, while 70% of the basin experienced mild or greater stress 1 year in 10. The maps of soil moisture stress provide the basis for estimating the probability of drought and the benefits of supplemental irrigation.     

Empirical binomial sampling plans: model calibration and testing using Williams’ method III for generalized linear models with overdispersion

Binomial sampling plans that use presence/absence data for estimating pest population density are commonly used in cropprotection when counting individual pest units is not cost effective. These plans are often based on the empirical relationship between the proportion of presences, p, and a count-based estimate of the mean population density, [(m)\tilde]\tilde \mu , given by ln{ - ln(1 - p) } = a₀ + a₁ ln([(m)\tilde] )\ln \left\{ { - \ln (1 - p)} \right\} = \alpha _0 + \alpha _1 ln(\tilde \mu ), which is typically fitted as a simple linear regression. However, correctly incorporating all of (i) binomial sampling errors, (ii) biological errors (i.e., overdispersion), and (iii) errors in variables is not possible using linear regression. Here, model calibration and testing is carried out using William’s method III for fitting a binomial generalized linear model with overdispersion (GLMw) in order to handle (i) and (ii), and simulation is used to study the effect of using the sample estimate of μ as the predictor variable. Calculation of the operating characteristics function of the decision rule for an action threshold of p ₀ is compared for linear and GLM_w models, with the former shown to substantially underestimate the probability of correct decisions and overestimate the probability of incorrect decisions. A binomial sampling plan for populations of the leaf beetle Chrysophtharta bimaculata, a defoliator of Eucalyptusnitens plantations, is used to demonstrate the methods.     

Estimating the number of true null hypotheses from a histogram of p values

In an earlier article, an intuitively appealing method for estimating the number of true null hypotheses in a multiple test situation was proposed. That article presented an iterative algorithm that relies on a histogram of observed p values to obtain the estimator. We characterize the limit of that iterative algorithm and show that the estimator can be computed directly without iteration. We compare the performance of the histogram-based estimator with other procedures for estimating the number of true null hypotheses from a collection of observed p values and find that the histogram-based estimator performs well in settings similar to those encountered in microarray data analysis. We demonstrate the approach using p values from a large microarray experiment aimed at uncovering molecular mechanisms of barley resistance to a fungal pathogen.     

Lead sorption to selected Portuguese soils

We studied the interaction of lead with seven Portuguese soils with different physical and chemical properties in order to elucidate more fully the behaviour of Pb in soil. We studied these adsorption phenomena by voltammetric titrations with differential pulse polarography (DPP) at different pH (6.0–7.2) and ionic strengths, I (0.010–0.50 m ) in order to clarify some of the factors that might control soil sorption capacity for Pb. From the voltammetric data, average formation constants, , and binding capacity, C_c, have been estimated according to a surface complexation model based on Scatchard and van den Berg–R?zic methods. Linear Scatchard and van den Berg–R?zic plots (r≥ 0.99) indicated that the results can be interpreted according to the existence of just one predominant active site for Pb(II) adsorption. The values from both procedures () agreed in all cases (r= 0.938, n= 66, P < 0.001). The same happened with C_c values that were statistically equivalent (r= 0.9998; n= 66; P < 0.001). The C_c values were found to depend on the pH and I, as well as on the soil properties. Either Langmuir or Freundlich isotherms fitted the experimental data well (r > 0.90, P < 0.05). The lead binding capacities were strongly and significantly correlated (P < 0.05) with pH, cation exchange capacity, organic carbon, loss‐on‐ignition, total Al₂O₃ content, extractable forms of Al and pyrophosphate extractable Fe, [Fe_p]. From a forward, stepwise regression model we concluded that [Al₂O₃], [Pb′] (concentration of labile lead in solution), [Fe_p], pH and I are able to explain more than 99.7% of the variation in lead sorption in our soils. The soils’ surface groups with special affinity to Pb(II) are in the inorganic fraction associated with aluminium.     

Predicting bare soil temperature. I. Theory and models for the multi-day mean diurnal variation

The energy balance equation for the soil-air interface is expressed, by suitable approximations, in a form linear in the surface temperature T₀. This forms the basis of two predictive models for the diurnal variation of T₀, averaged over a many-day interval, for potentially evaporating bare soil. Input data include total solar radiation, air temperature and vapour pressure, windspeed u_a, cloud cover c, and soil radiative, aerodynamic and thermal properties (the latter assumed uniform). In the simpler model, based on harmonic analysis, u_a and c are assumed constant. For N_t observations per day, an algebraic solution is found as a set of equations for the parameters of up to the first N_t/2 harmonics. In the second model, dynamic wind-speed is introduced, and a more complicated linear algebraic method of solution is required. The models have agroclimatic value, since by averaging they predict the thermal ‘climate’ of soil, in contrast to instantaneous models which describe the time-specific thermal ‘weather’.     

Estimating Disease Prevalence Using Inverse Binomial Pooled Testing

Monitoring populations of hosts as well as insect vectors is an important part of agricultural and public health risk assessment. In applications where pathogen prevalence is likely low, it is common to test pools of subjects for the presence of infection, rather than to test subjects individually. This technique is known as pooled (group) testing. In this paper, we revisit the problem of estimating the population prevalence p from pooled testing, but we consider applications where inverse binomial sampling is used. Our work is unlike previous research in pooled testing, which has largely assumed a binomial model. Inverse sampling is natural to implement when there is a need to report estimates early on in the data collection process and has been used in individual testing applications when disease incidence is low. We consider point and interval estimation procedures for p in this new pooled testing setting, and we use example data sets from the literature to describe and to illustrate our methods.     

Equations to describe the amount and rate of sorption

The partition of materials that react with soil between the solid and the solution phase, and how this changes with time, can often be described by a simple equation: S = a c^b1t^b2 where S is the amount sorbed, c is the solution concentration, t the time of contact, and a, b₁ and b₂ are parameters. However, when the range of values for sorption is large, it is apparent that both b₁ and b₂ increase with decreasing sorption. At low values for sorption, b₁ approaches 1, and sorption plots are nearly linear. These observations are consistent with a mechanistic model in which it is postulated that the materials react with heterogenous sites. As the amount of sorption decreases, the heterogeneity of the occupied sites decreases. This is why b₁ increases. Because there is heterogeneity of occupied sites, there is a range of rates for the subsequent reaction. This is why the rates are proportional to a fractional index of time. It is better to describe the effects of time this way than by using several first-order equations.     

Optimal sample size for composite sampling with subsampling, when estimating the proportion of pecky rice grains in a field

The proportion of pecky rice grains has been estimated empirically using composite sampling with subsampling. The procedure can be summarized as follows: (1) A fixed number of rice plants, n ₁, are drawn at random in the paddy field; (2) all of the rice grains in the collected rice plants are mixed well to form a composite; (3) a portion of the grains, n ₂, is drawn at random from the composite; and (4) the collected grains are examined by eye to estimate the proportion of pecky rice grains. We propose a method for determining the optimal sample size in estimating the proportion of defective items by this type of composite sampling with subsampling. Spatial heterogeneity in the proportion of defective items is included in the estimation. We use Taylor’s power law to describe the density-dependent change of spatial heterogeneity. In controlling the precision of the estimate, we use the relative precision, D, which is defined by the coefficient of variation of the estimated proportion. We propose a rejection procedure in which the product is rejected if the estimate of proportion with D=0.25 is larger than a predetermined tolerable threshold of proportion. We also consider another control criterion in which the consumer’s risk, \, is controlled by a zero-tolerance method. Finally, we examine the relationship between the two control criteria.     

Modeling vertical movement of organic matter in a soil incubated for 41 years with C labeled straw

The distribution of organic matter (OM) in the soil profile reflects the balance between inputs and decomposition at different depths as well as transport of OM within the profile. In this study we modeled movement of OM in the soil profile as a result of mechanisms resulting in dispersive and advective movement. The model was used to interpret the distribution of ¹⁴C in the soil profile 41 years after the labeling event. The model fitted the observed distribution of ¹⁴C well (R²=0.988, AIC_c=−82.6), with a dispersion constant of D=0.71 cm² yr⁻¹ and an advection constant of v=0.0081 cm yr⁻¹. However, the model consistently underestimated the amount of OM in the soil layers from 27 to 37 cm depth. A possible explanation for this is that different fractions of OM are transported by different mechanisms. For example, particulate OM, organomineral colloids and dissolved OM are not likely to be transported by the same mechanisms. A model with two OM fractions, one moving exclusively by dispersive processes (D=0.26 cm² yr⁻¹) and another moving by both dispersive (D=0.99 cm² yr⁻¹) and advective (v=0.23 cm yr⁻¹) processes provided a slightly better fit to the data (R²=0.995, AIC_c=−83.6). More importantly, however, this model did not show the consistent underestimation from 27 to 37 cm soil depth. This corroborates the assumption that differing movement mechanisms for different OM fractions are responsible for the observed distribution of ¹⁴C in the profile. However, varying dispersion, advection, and decay of OM with depth are also possible explanations.     

Simulating site-specific nitrogen mineralization dynamics in a Swedish arable field

Abstract

The objective of this work was to test whether a dynamic soil C and N model using site-specific information improved estimates of apparent net N mineralization compared with regressions only based on static soil properties. This comparison was made using data from a 34-point sampling grid within a Swedish arable field during two growing seasons, using a simple carbon balance and nitrogen mineralization model (ICBM/N) for the dynamic approach. Three free model parameters were simultaneously optimized using non-linear regression to obtain the best model fit to the data from all grid points and both years. Calculated annual mean net mineralization (Nm_sim) matched the measured Nm mean exactly, and was 44 and 71 kg N ha^?1 for the two growing seasons 1999 and 2000, respectively. However, the variability in calculated Nm_sim values among the 34 grid points was smaller than that measured, and only a small proportion of the variation within a single year was explained by the model. Despite this, the model explained 56% of the total variation in Nm during the two growing seasons, mainly due to the good fit to the seasonal overall difference. Significant factors influencing net mineralization included the soil environment controlling mineralization, total N in soil organic matter and N in crop residues. Uncertainties in estimation of θ _fc and θ _wp (soil water content at saturation and wilting point) and the possible influence of unknown horizontal and vertical water flows made high-precision calculations of soil water content difficult. The precision and general applicability of the actual measurements thus set limits for estimating critical parameters, and the limitations of both the experimental design and the model are discussed. It is concluded that improvements in precision in sampling and analysis of data from the grid points are needed for more critical hypothesis testing.