Spatial modeling of data with excessive zeros applied to reindeer pellet‐group counts

We analyze a real data set pertaining to reindeer fecal pellet‐group counts obtained from a survey conducted in a forest area in northern Sweden. In the data set, over 70% of counts are zeros, and there is high spatial correlation. We use conditionally autoregressive random effects for modeling of spatial correlation in a Poisson generalized linear mixed model (GLMM), quasi‐Poisson hierarchical generalized linear model (HGLM), zero‐inflated Poisson (ZIP), and hurdle models. The quasi‐Poisson HGLM allows for both under‐ and overdispersion with excessive zeros, while the ZIP and hurdle models allow only for overdispersion. In analyzing the real data set, we see that the quasi‐Poisson HGLMs can perform better than the other commonly used models, for example, ordinary Poisson HGLMs, spatial ZIP, and spatial hurdle models, and that the underdispersed Poisson HGLMs with spatial correlation fit the reindeer data best. We develop R codes for fitting these models using a unified algorithm for the HGLMs. Spatial count response with an extremely high proportion of zeros, and underdispersion can be successfully modeled using the quasi‐Poisson HGLM with spatial random effects.     

A novel method for quantifying overdispersion in count data and its application to farmland birds

The statistical modelling of count data permeates the discipline of ecology. Such data often exhibit overdispersion compared with a standard Poisson distribution, so that the variance of the counts is greater than that of the mean. Whereas modelling to reveal the effects of explanatory variables on the mean is commonplace, overdispersion is generally regarded as a nuisance parameter to be accounted for and subsequently ignored. Instead, we propose a method that models the overdispersion as a biologically interesting property of a data set and show how novel inference is provided as a result. We adapted the double hierarchical generalized linear model approach to create an easily extendible model structure that quantifies the influence of explanatory variables on the overdispersion of count data, and apply it to farmland birds. These data were from a study within Irish agricultural ecosystems, in which total bird species abundance and the abundance of farmland indicator species were compared on dairy and non‐dairy farms in the winter and breeding seasons. In general, overdispersion in bird counts was greater on dairy farms than on non‐dairy farms, and for total bird numbers, overdispersion was greatest on dairy farms in winter. Our code is fitted using the Bayesian package Rstan, and we make all code and data available in a GitHub repository. Within a Bayesian framework, this approach facilitates a meaningful quantification of the effects of categorical explanatory variables on any response variable with a tendency to overdispersion that has a meaningful biological or ecological explanation.     

Assessing overdispersion and dose-response in the male dominant lethal assay.

In dominant lethal studies the primary variables of interest are typically expressed as discrete counts or proportions (e.g., live implants, resorptions, percent pregnant). Simple statistical sampling models for discrete data such as binomial or Poisson generally do not fit this type of data because of extra-binomial or extra-Poisson departures from variability predicted under these simple models. Extra-variability in the fetal response may originate from parental contributions. These can lead to over- or under-dispersion seen as, e.g., extra-binomial variability in the proportion response. Utilizing a large control database, we investigated the relative impact of extra-variability from male or female contributions on the endpoints of interest. Male-related effects did not seem to contribute to overdispersion in our database; female-related effects were, however, evidenced. Various statistical methods were considered to test for significant treatment differences under these forms of sampling variability. Computer simulations were used to evaluate these methods and to determine which are most appropriate for practical use in the evaluation of dominant lethal data. Our results suggest that distribution-free statistical methods such as a nonparametric permutation test or rank-based tests for trend can be recommended for use.     

Testing approaches for overdispersion in poisson regression versus the generalized poisson model

Overdispersion is a common phenomenon in Poisson modeling, and the negative binomial (NB) model is frequently used to account for overdispersion. Testing approaches (Wald test, likelihood ratio test (LRT), and score test) for overdispersion in the Poisson regression versus the NB model are available. Because the generalized Poisson (GP) model is similar to the NB model, we consider the former as an alternate model for overdispersed count data. The score test has an advantage over the LRT and the Wald test in that the score test only requires that the parameter of interest be estimated under the null hypothesis. This paper proposes a score test for overdispersion based on the GP model and compares the power of the test with the LRT and Wald tests. A simulation study indicates the score test based on asymptotic standard Normal distribution is more appropriate in practical application for higher empirical power, however, it underestimates the nominal significance level, especially in small sample situations, and examples illustrate the results of comparing the candidate tests between the Poisson and GP models. A bootstrap test is also proposed to adjust the underestimation of nominal level in the score statistic when the sample size is small. The simulation study indicates the bootstrap test has significance level closer to nominal size and has uniformly greater power than the score test based on asymptotic standard Normal distribution. From a practical perspective, we suggest that, if the score test gives even a weak indication that the Poisson model is inappropriate, say at the 0.10 significance level, we advise the more accurate bootstrap procedure as a better test for comparing whether the GP model is more appropriate than Poisson model. Finally, the Vuong test is illustrated to choose between GP and NB2 models for the same dataset.     

Increased competition does not lead to increased phylogenetic overdispersion in a native grassland

That competition is stronger among closely related species and leads to phylogenetic overdispersion is a common assumption in community ecology. However, tests of this assumption are rare and field‐based experiments lacking. We tested the relationship between competition, the degree of relatedness, and overdispersion among plants experimentally and using a field survey in a native grassland. Relatedness did not affect competition, nor was competition associated with phylogenetic overdispersion. Further, there was only weak evidence for increased overdispersion at spatial scales where plants are likely to compete. These results challenge traditional theory, but are consistent with recent theories regarding the mechanisms of plant competition and its potential effect on phylogenetic structure. We suggest that specific conditions related to the form of competition and trait conservatism must be met for competition to cause phylogenetic overdispersion. Consequently, overdispersion as a result of competition is likely to be rare in natural communities.     

Hatching plasticity in a Southeast Asian tree frog mitigates submergence-induced mortality

Environmentally cued hatching has been well-documented in amphibians in response to a wide range of abiotic and biotic factors. The hatching of terrestrial amphibian eggs in response to flooding may be basal within the group, but amphibian lineages in tropical Asia and sub-Saharan Africa have not received as much attention as their Neotropical counterparts. We investigated submergence-induced hatching in Feihyla hansenae, a Rhacophorid tree frog with terrestrial eggs. We quantified natural rates of clutch submergence at our study site in Thailand. Using submergence experiments, we found that embryos are capable of hatching early to escape flooding, and that failure to hatch results in mortality. Among the embryos that were able to hatch early, only the earliest, youngest hatchlings experienced a trade-off in body size that persisted for 6 days, while later, older hatchlings were not significantly smaller than spontaneous hatchlings under control conditions. By incorporating our natural and experimental data into Monte Carlo methods to simulate and compare survival probabilities with and without hatching plasticity, we found an overall 3.1% increase in submergence survival due to hatching plasticity. Our findings support the idea that flooding-induced hatching is widespread across amphibians with terrestrial eggs and highlight the importance of researching understudied tropical regions. As climate change is projected to affect rainfall patterns, the ability of embryos to escape abiotic egg-stage threats may be an indicator of species' ability to flexibly navigate a changing environment.     

Moderated statistical tests for assessing differences in tag abundance

MOTIVATION: Digital gene expression (DGE) technologies measure gene expression by counting sequence tags. They are sensitive technologies for measuring gene expression on a genomic scale, without the need for prior knowledge of the genome sequence. As the cost of sequencing DNA decreases, the number of DGE datasets is expected to grow dramatically. Various tests of differential expression have been proposed for replicated DGE data using binomial, Poisson, negative binomial or pseudo-likelihood (PL) models for the counts, but none of the these are usable when the number of replicates is very small. RESULTS: We develop tests using the negative binomial distribution to model overdispersion relative to the Poisson, and use conditional weighted likelihood to moderate the level of overdispersion across genes. Not only is our strategy applicable even with the smallest number of libraries, but it also proves to be more powerful than previous strategies when more libraries are available. The methodology is equally applicable to other counting technologies, such as proteomic spectral counts. AVAILABILITY: An R package can be accessed from http://bioinf.wehi.edu.au/resources/     

Variation in the hatching response of Ochlerotatus albifasciatus egg batches (Diptera: Culicidae) in temperate Argentina

Egg hatching of winter-collected Ochlerotatus albifasciatus was studied for six months. Batches of eggs were divided into two groups, one of them was stored in the laboratory at 23 degrees C and 12:12 photoperiod, and the other in the field under dead leaves. Every month, from July to December, eggs from the two groups were flooded under both laboratory and field conditions. Unhatched eggs were returned to the original condition and flooded two more times separated by ten-day intervals. Results show that egg diapause is expressed in different intensities, not only on eggs exposed to different conditions but also in those exposed to the same condition, even when they were laid by the same female. Successive inundations yielded incomplete hatches of eggs, and favored the hatching response in the next flooding. Low environmental temperatures before and during the flooding depressed hatching response. This shows that eggs need a warm period before flooding as well as warm temperatures during flooding, to hatch. As drought period was longer hatching response increased, but this was also accompanied by warmer environmental conditions. The experiment performed in laboratory did not show that increment. Field studies showed that a layer of dead leaves protected eggs from extreme temperatures.     

Overdispersion of the molecular clock: temporal variation of gene-specific substitution rates in Drosophila

Simple models of molecular evolution assume that sequences evolve by a Poisson process in which nucleotide or amino acid substitutions occur as rare independent events. In these models, the expected ratio of the variance to the mean of substitution counts equals 1, and substitution processes with a ratio greater than 1 are called overdispersed. Comparing the genomes of 10 closely related species of Drosophila, we extend earlier evidence for overdispersion in amino acid replacements as well as in four-fold synonymous substitutions. The observed deviation from the Poisson expectation can be described as a linear function of the rate at which substitutions occur on a phylogeny, which implies that deviations from the Poisson expectation arise from gene-specific temporal variation in substitution rates. Amino acid sequences show greater temporal variation in substitution rates than do four-fold synonymous sequences. Our findings provide a general phenomenological framework for understanding overdispersion in the molecular clock. Also, the presence of substantial variation in gene-specific substitution rates has broad implications for work in phylogeny reconstruction and evolutionary rate estimation.     

Population trends from count data: Handling environmental bias,overdispersion and excess of zeroes

The assessment of population trends is a key point in wildlife conservation. Survey data collected over long period may not be comparable due to the presence of environmental biases (i.e. inadequate representation of the variability of environmental covariates in the study area). Moreover, count data may be affected by both overdispersion (i.e. the variance is larger than the mean) and excess of zero counts (potentially leading to zero inflation). The aim of this study was to define a modelling procedure to assess long-term population trends that addressed these three issues and to shed light on the effects of environmental bias, overdispersion, and zero inflation on trend estimates. To test our procedure, we used six bird species whose data were collected in northern Italy from 1992 to 2019. We designed a multi-step approach. First, using generalised additive models (GAMs), we implemented a full factorial design of models (eight models per species) taking or not into account the environmental bias (including or not including environmental covariates, respectively), overdispersion (using a negative binomial distribution or a Poisson distribution, respectively), and zero inflation (using or not using zero-inflated models, respectively). Models were ranked according to the Akaike Information Criterion. Second, annual population indices (median and 95% confidence interval of the number of breeding pairs per point count) were predicted through a parametric bootstrap procedure. Third, long-term population trends were assessed and tested for significance fitting weighted least square linear regression models to the predicted annual indices. To evaluate the effect of environmental bias, overdispersion, and zero inflation on trend estimates, an average discrepancy index was calculated for each model group. The results showed that environmental bias was the most important driver in determining different trend estimates, although overlooking overdispersion and zero inflation could lead to misleading results. For five species, zero-inflated GAMs resulted the best models to predict annual population indices. Our findings suggested a mutual interaction between zero inflation and overdispersion, with overdispersion arising in non-zero-inflated models. Moreover, for species having flocking foraging and/or colonial breeding behaviours, overdispersed and zero-inflated models may be more adequate. In conclusion, properly handling environmental bias, which may affect several data sets coming from long-term monitoring programs, is crucial to obtain reliable estimates of population trends. Furthermore, the extent to which overdispersion and zero inflation may affect trend estimates should be assessed by comparing different models, rather than presumed using statistical assumption.     

Temperature-controlled under-water egg dormancy and postflood hatching in Isotoma viridis (Collembola) as forms of adaptation to annual long-term flooding

Summary Incubation experiments with eggs of a population of Isotoma viridis, which is exposed to annual long-term flooding from about April to July, as well as field observations show that temperature controls both, underwater egg dormancy and immediate postflood hatching. The population is located at the Eder Freshwater Reservoir in Germany.If constant experimental temperatures are above 14°C, almost all eggs are nondormant. Dormancy is established at temperatures below 15°C, but embryonic development is completed. Experiments indicate that of the environmental factors that change drastically at the end of submergence (light, turgor pressure, oxygen, a.o.), only temperature acts as a hatching trigger. Hatching of the previously dormant eggs occurs at a constant threshold temperature of 16°C, mainly within 2 to 20 days after temperature elevation, but most of these eggs need even higher temperatures to hatch. Remaining eggs were partly stimulated to hatch by recooling them at 7°C for some days and then rewarming them again.The threshold temperatures observed are unusually high for Collembola and seem to be the result of selection by the special floodplain conditions. During normal years, the surface temperatures of submerged soil usually do not exceed threshold limits before summer drainage. This allows both, protection from under-water hatching and an optimal timing of hatching at the very beginning of the main terrestrial period. The experiments show that above the threshold temperature (in warm summers), individuals can hatch under water and survive submerged for 10–15 days. They can survive even longer in the water habitat, if emergent structures enable them to climb onto the water surface. Furthermore, a considerable polymorphism observed in some hatching properties improves the chance to survive under the unpredictable floodplain conditions.     

Some covariance models for longitudinal count data with overdispersion

A family of covariance models for longitudinal counts with predictive covariates is presented. These models account for overdispersion, heteroscedasticity, and dependence among repeated observations. The approach is a quasi-likelihood regression similar to the formulation given by Liang and Zeger (1986, Biometrika 73, 13-22). Generalized estimating equations for both the covariate parameters and the variance-covariance parameters are presented. Large-sample properties of the parameter estimates are derived. The proposed methods are illustrated by an analysis of epileptic seizure count data arising from a study of progabide as an adjuvant therapy for partial seizures.     

The combined effects of temperature and salinity on hatching success and the survival,growth, and development of the larval stages of Metapenaeus bennettae (Racek & Dall)

During the spawning season of the estuarine prawn Metapenaeus bennettae (Racek & Dall), laboratory and field experiments were conducted to examine the combined effects of temperature and salinity on hatching success of eggs and the survival, growth and development of larvae. Response surface analysis showed that optimal levels of temperature and salinity for maximum hatching success varied depending on conditions during spawning. Similarly, temperature and salinity conditions that produced maximum survival and growth of larvae depended on conditions during rearing prior to experimental temperature/salinity treatments. At the onset of feeding, larvae showed the lowest tolerance to changes in temperature and salinity. Supplementary feeding experiments in the laboratory, and survival rates in field experiments indicated that starvation was a more potent factor than the effects of temperature and salinity in determining survival through the protozoeal larval stages. Late larval stages were relatively indifferent to the effects of temperature and salinity. It is suggested that, during early development, adaptive response to the prevailing physical conditions enhances survival in an estuarine environment.     

Estimation and testing with overdispersed proportions using the beta-logistic regression model of Heckman and Willis

Methods are presented for modeling dose-related effects in proportion data when extra-binomial variability is a concern. Motivation is taken from experiments in developmental toxicology, where similarity among conceptuses within a litter leads to intralitter correlations and to overdispersion in the observed proportions. Appeal is made to the well-known beta-binomial distribution to represent the overdispersion. From this, an exponential function of the linear predictor is used to model the dose-response relationship. The specification was introduced previously for econometric applications by Heckman and Willis; it induces a form of logistic regression for the mean response, together with a reciprocal biexponential model for the intralitter correlation. Large-sample, likelihood-based methods for estimating and testing the joint proportion-correlation response are studied. A developmental toxicity data set illustrates the methods.     

Sensitivity analysis of common statistical models used to study the short-term effects of air pollution on health

The relationship between photochemical air pollutants (nitrogen dioxide and ozone) and emergency room admissions for asthma in Madrid (Spain) for the period 1995-1998 was analysed using the statistical models commonly used to studying the short-term effects of air pollution on health: linear and Cochrane-Orcutt regression, standard Poisson and Poisson corrected by overdispersion, Poisson autoregressive models, and generalised additive models. Linear regression models presented residual autocorrelation, Poisson regression models also showed overdispersion, and generalised additive models did not show residual autocorrelation and overdispersion was substantially reduced. Linear models provided biased estimates because our health outcome is non-normally distributed. Estimates from Poisson regression allowing for overdispersion and autocorrelation did not differ substantially from those reported by generalised additive models, which present the best model fit in terms of the absence of autocorrelation and reduction of overdispersion.     

Interrelationship of the serum lysozyme level to the leukocyte count in the blood]

The leucocyte counts in the peripheral blood and titers of the serum lysozyme under conditions of various experimental models were compared. Albino rats, mice, guinea pigs and rabbits exposed to the effect of various factors of a biological and chemical nature were used in the experiments. In addition, observations on humans immunized with bacterial and viral vaccines were analyzed. Development of 3 reaction types was shown to be possible. In the 1st type the dynamics of the lysosome activity and blood leucocyte counts changed in the same way (immunization with smallpox vaccine, listeria infection). Decreased counts of the leucocytes due to the use of cytostatic drugs were accompanied by a parallel decrease in the lysozyme activity. Such variant of the reaction was predominating. The 2nd type of the shifts characterized by an impaired synchronous pattern of the dynamics of the indices was not so frequent (the use of high doses of cytostatics). The 3rd type of the reactions with an exactly opposite character of the shifts in the leucocyte counts and lysozyme activity was observed only as an exclusion. It is concluded that the quantitative dynamics of the leucocytes is not enough by itself for creating an opinion on the nature of the changes in the serum lysozyme. The possible role of macrophages in the above processes is discussed.     

Semi‐parametric analysis of overdispersed count and metric data with varying follow‐up times: Asymptotic theory and small sample approximations

Count data are common endpoints in clinical trials, for example magnetic resonance imaging lesion counts in multiple sclerosis. They often exhibit high levels of overdispersion, that is variances are larger than the means. Inference is regularly based on negative binomial regression along with maximum‐likelihood estimators. Although this approach can account for heterogeneity it postulates a common overdispersion parameter across groups. Such parametric assumptions are usually difficult to verify, especially in small trials. Therefore, novel procedures that are based on asymptotic results for newly developed rate and variance estimators are proposed in a general framework. Moreover, in case of small samples the procedures are carried out using permutation techniques. Here, the usual assumption of exchangeability under the null hypothesis is not met due to varying follow‐up times and unequal overdispersion parameters. This problem is solved by the use of studentized permutations leading to valid inference methods for situations with (i) varying follow‐up times, (ii) different overdispersion parameters, and (iii) small sample sizes.     

AN ACCOUNT OF THE HATCHING STRATEGIES OF BIRDS

1. Three basic hatching methods are described together with one subsidiary method. The symmetrical method is characterized by rotation of the chick in the egg during hatching climax; a line of damage around the circumference of the egg is evident at the beginning of a pushing phase which causes a fairly symmetrical cap to be broken from the shell. The asymmetrical method is used by a few long-billed species; it involves little or no rotation of the chick in the egg, and produces asymmetrical shell remains. The megapodes have developed a unique hatching method in response to their unusual incubation conditions. Parental assistance has been observed in some species, but only as an auxiliary to either the symmetrical or asymmetrical method. Approximately 150 species have been categorized according to the hatching method(s) they use. 2. Among those species adopting the symmetrical method, there is considerable variability as to how far the chick turns in the egg during hatching climax. On this basis, a spectrum of behaviour, expressed in terms of angle of rotation (θ), has been proposed. At one end lie species such as the bobwhite quail and little owl (θ≥ 360°), and at the other, the ostrich and rhea (θ≤ 90°). 3. The theory that, with the exception of the megapodes, there is only one basic hatching method is examined. The tenets of this theory are found to be inconsistent with recent observations of species differences in hatching behaviour. It is concluded that hatching behaviour is governed by an intrinsic species-specific programme, in turn influenced by mechanical or other external factors. 4. The literature contains several suggestions as to the external factors that might influence hatching technique, but only one detailed investigation. It is proposed that interspecific differences in the mechanical properties of the egg integument (the shell and its underlying membranes) can be regarded as forming a spectrum from very brittle to comparatively tough. The amount of climax rotation by the chick is seen as an adaptive response to brittleness or toughness of the egg integument. The hatching technique of the chick is further modified as a response to the effect of moisture content on the integument. 5. The selective pressures leading to the evolution of the symmetrical and asymmetrical hatching methods are discussed. The previous model for the development of the asymmetrical method is amended to account for those species of gull which may adopt either method.