Compound Poisson-gamma vs. delta-gamma to handle zero-inflated continuous data under a variable sampling volume

Bayesian estimation of rainfall dispersion in Thailand using gamma distribution with excess zeros

The gamma distribution is commonly used to model environmental data. However, rainfall data often contain zero observations, which violates the assumption that all observations must be positive in a gamma distribution, and so a gamma model with excess zeros treated as a binary random variable is required. Rainfall dispersion is important and interesting, the confidence intervals for the variance of a gamma distribution with excess zeros help to examine rainfall intensity, which may be high or low risk. Herein, we propose confidence intervals for the variance of a gamma distribution with excess zeros by using fiducial quantities and parametric bootstrapping, as well as Bayesian credible intervals and highest posterior density intervals based on the Jeffreys', uniform, or normal-gamma-beta prior. The performances of the proposed confidence interval were evaluated by establishing their coverage probabilities and average lengths via Monte Carlo simulations. The fiducial quantity confidence interval performed the best for a small probability of the sample containing zero observations (δ) whereas the Bayesian credible interval based on the normal-gamma-beta prior performed the best for large δ. Rainfall data from the Kiew Lom Dam in Lampang province, Thailand, are used to illustrate the efficacies of the proposed methods in practice.

Bayesian estimation for the mean of delta-gamma distributions with application to rainfall data in Thailand

Precipitation and flood forecasting are difficult due to rainfall variability. The mean of a delta-gamma distribution can be used to analyze rainfall data for predicting future rainfall, thereby reducing the risks of future disasters due to excessive or too little rainfall. In this study, we construct credible and highest posterior density (HPD) intervals for the mean and the difference between the means of delta-gamma distributions by using Bayesian methods based on Jeffrey's rule and uniform priors along with a confidence interval based on fiducial quantities. The results of a simulation study indicate that the Bayesian HPD interval based on Jeffrey's rule prior performed well in terms of coverage probability and provided the shortest expected length. Rainfall data from Chiang Mai province, Thailand, are also used to illustrate the efficacies of the proposed methods.

Proportion of Grassland at Landscape Scale Drives Natural Pest Control Services in Agricultural Landscapes

Managing regulating ecosystem services delivered by biodiversity in farmland is a way to maintain crop yields while reducing the use of agrochemicals. Because semi-natural habitats provide shelter and food for pest enemies, a higher proportion of semi-natural habitats in the landscape or their proximity to crops may enhance pest control in arable fields. However, the ways in which the spatial arrangement of these habitats affects the delivery of this beneficial ecosystem service to crops remains poorly known. Here, we investigated the relative effects of the amount of grassland in the landscape versus the distance to the nearest grassland on the predation rates of weed seeds and aphids into 52 cereal fields. We found that both seed and aphid predation levels increased with the proportion of grassland in a 500 m radius buffer while the distance to the nearest grassland displayed no effect. We show that increasing from 0 to 50% the proportion of grasslands in a 500 m radius, respectively, increased seed and aphid predation by 38 and 20%. In addition to the strong effect of the proportion of grassland, we found that seed predation increased with the proportion of forest fragments while aphid predation increased with the proportion of organic farming in the landscape. Overall, our results reveal that natural pest control in cereal crops is not related to the distance to the nearest grassland, suggesting that natural enemies are not limited by their dispersal ability. Our study indicates that maintaining key semi-natural habitats, such as grasslands, is needed to ensure natural pest control and support food production in agricultural landscapes.

Effects of Natura 2000 on nontarget bird and butterfly species based on citizen science data

The European Union's Natura 2000 (N2000) is among the largest international networks of protected areas. One of its aims is to secure the status of a predetermined set of (targeted) bird and butterfly species. However, nontarget species may also benefit from N2000. We evaluated how the terrestrial component of this network affects the abundance of nontargeted, more common bird and butterfly species based on data from long-term volunteer-based monitoring programs in 9602 sites for birds and 2001 sites for butterflies. In almost half of the 155 bird species assessed, and particularly among woodland specialists, abundance increased (slope estimates ranged from 0.101 [SD 0.042] to 3.51 [SD 1.30]) as the proportion of landscape covered by N2000 sites increased. This positive relationship existed for 27 of the 104 butterfly species (estimates ranged from 0.382 [SD 0.163] to 4.28 [SD 0.768]), although most butterflies were generalists. For most species, when land-cover covariates were accounted for these positive relationships were not evident, meaning land cover may be a determinant of positive effects of the N2000 network. The increase in abundance as N2000 coverage increased correlated with the specialization index for birds, but not for butterflies. Although the N2000 network supports high abundance of a large spectrum of species, the low number of specialist butterflies with a positive association with the N2000 network shows the need to improve the habitat quality of N2000 sites that could harbor open-land butterfly specialists. For a better understanding of the processes involved, we advocate for standardized collection of data at N2000 sites.

Predicting cyanobacterial biovolume from water temperature and conductivity using a Bayesian compound Poisson-Gamma model

Eutrophication and climate change scenarios engender the need to develop good predictive models for harmful cyanobacterial blooms (CyanoHABs). Nevertheless, modeling cyanobacterial biomass is a challenging task due to strongly skewed distributions that include many absences as well as extreme values (dense blooms). Most modeling approaches alter the natural distribution of the data by splitting them into zeros (absences) and positive values, assuming that different processes underlie these two components. Our objectives were (1) to develop a probabilistic model relating cyanobacterial biovolume to environmental variables in the Río de la Plata Estuary (35°S, 56°W, n = 205 observations) considering all biovolume values (zeros and positive biomass) as part of the same process; and (2) to use the model to predict cyanobacterial biovolume under different risk level scenarios using water temperature and conductivity as explanatory variables. We developed a compound Poisson-Gamma (CPG) regression model, an approach that has not previously been used for modeling phytoplankton biovolume, within a Bayesian hierarchical framework. Posterior predictive checks showed that the fitted model had a good overall fit to the observed cyanobacterial biovolume and to more specific features of the data, such as the proportion of samples crossing three threshold risk levels (0.2, 1 and 2 mm³ L^-1) at different water temperatures and conductivities. The CPG model highlights the strong control of cyanobacterial biovolume by nonlinear and interactive effects of water temperature and conductivity. The highest probability of crossing the three biovolume levels occurred at 22.2 °C and at the lowest observed conductivity (∼0.1 mS cm^-1). Cross-validation of the fitted model using out-of-sample observations (n = 72) showed the model's potential to be used in situ, as it enabled prediction of cyanobacterial biomass based on two readily measured variables (temperature and conductivity), making it an interesting tool for early alert systems and management strategies. Furthermore, this novel application demonstrates the potential of the Bayesian CPG approach for predicting cyanobacterial dynamics in response to environmental change.

Developing and assessing a density surface model in a Bayesian hierarchical framework with a focus on uncertainty: insights from simulations and an application to fin whales (Balaenoptera physalus)

Density surface models (DSMs) are an important tool in the conservation and management of cetaceans. Most previous applications of DSMs have adopted a two-step approach to model fitting (hereafter referred to as the Two-Stage Method), whereby detection probabilities are first estimated using distance sampling detection functions and subsequently used as an offset when fitting a density-habitat model. Although variance propagation techniques have recently become available for the Two-Stage Method, most previous applications have not propagated detection probability uncertainty into final density estimates. In this paper, we describe an alternative approach for fitting DSMs based on Bayesian hierarchical inference (hereafter referred to as the Bayesian Method), which is a natural framework for simultaneously propagating multiple sources of uncertainty into final estimates. Our framework includes (1) a mark-recapture distance sampling observation model that can accommodate two team line transect data, (2) an informed prior for the probability a group of animals is at the surface and available for detection (i.e. surface availability) (3) a density-habitat model incorporating spatial smoothers and (4) a flexible compound Poisson-gamma model for count data that incorporates overdispersion and zero-inflation. We evaluate our method and compare its performance to the Two-Stage Method with simulations and an application to line transect data of fin whales (Balaenoptera physalus) off the east coast of the USA. Simulations showed that both methods had low bias (<1.5%) and confidence interval coverage close to the nominal 95% rate when variance was propagated from the first step. Results from the fin whale analysis showed that density estimates and predicted distribution patterns were largely similar among methods; however, the coefficient of variation of the final abundance estimate more than doubled (0.14 vs 0.31) when detection variance was correctly propagated into final estimates. An analysis of the variance components demonstrated that overall detectability as well as surface availability contributed substantial amounts of variance in the final abundance estimates whereas uncertainty in mean group size contributed a negligible amount. Our method provides a Bayesian alternative to DSMs that incorporates much of the flexibility available in the Two-Stage Method. In addition, these results demonstrate the degree to which uncertainty can be underestimated if certain components of a DSM are assumed fixed.

Scaling in the Local Strain-Rate Field during Jerky Flow in an Al-3%Mg Alloy

Jerky flow in alloys, or the Portevin-Le Chatelier effect, presents an outstanding example of self-organization phenomena in plasticity. Recent acoustic emission investigations revealed that its microscopic dynamics is governed by scale invariance manifested as power-law statistics of intermittent events. As the macroscopic stress serrations show both scale invariance and characteristic scales, the micro-macro transition is an intricate question requiring an assessment of intermediate behaviors. The first attempt of such an investigation is undertaken in the present paper by virtue of a one-dimensional (1D) local extensometry technique and statistical analysis of time series. The data obtained complete the missing link and bear evidence to a coexistence of characteristic large events and power laws for smaller events. The scale separation is interpreted in terms of the phenomena of self-organized criticality and synchronization in complex systems. Furthermore, it is found that both the stress serrations and local strain-rate bursts agree with the so-called fluctuation scaling related to general mathematical laws and unifying various specific mechanisms proposed to explain scale invariance in diverse systems. Prospects of further investigations including the duality manifested by a wavy spatial organization of the local bursts of plastic deformation are discussed.