Response surfaces for overdispersion in the study of the conditions for fish eggs hatching

Response surface methodology, originally developed for determining optimal conditions in industrial experiments, was early adapted to experiments in marine ecology. However, these involved studying the shape of the complete response surface, not only detecting the optimum, and often had counts or durations as the response variable. Thus, nonlinear, nonnormal response models were required. For counts, binomial and beta-binomial models have been used, the latter because of substantial overdispersion. In closely controlled experiments, overdispersion among units held under the same conditions might indicate that some mishap has occurred in conducting the study. One possible check is to model the dispersion as a second response surface. This procedure is used to show that overdispersion in fish egg hatching experiments has a biological explanation in that it occurs only under suboptimal hatching conditions.     

青海湖裸鲤寄生舌状绦虫的空间格局研究

舌状绦虫裂头蚴只寄生在体长小于２２０ｍｍ的青海湖裸鲤中,其种群在宿主种群中呈聚集分布。其聚集分布的强度随寄生虫种群平均密度的增加而降低。由于舌状绦虫在宿主体腔生长,产生明显的空间拥挤效应,可能导致宿主死亡或被食鱼鸟类捕食而转移到终末宿主中。在体长小于１２０ｍｍ的宿主中,密度依赖的死亡过程可能是使聚集强度降低的原因;而体长１４０－２００ｍｍ的鱼中,则是非密度依赖的全死过程使聚集强度增加．     

Distribution of the infection by Camallanus corderoi (Nemata: Spiruroidea) in different autochthonous hosts and localities of the Valdivia river basin, Chile

Six hundred and thirty nine autochthonous fish were examined in 1986-1987 in search for Camallanus corderoi infection on different biotopes from Valdivia River basin (between 39 degrees 30'-40 degrees 00'S, 73 degrees 30'-71 degrees 45' W). Brachigalaxias bullocki, Galaxias maculatus, Galaxias platei, Aplochiton taeniatus, Cheirodon australe, Basilichthys australis and Cauque mauleanum are new hosts for C. corderoi. Infection by C. corderoi in fish is acquired by ingestion of infected copepods and prevalence and intensity of infection showed differences between host fish and biotopes. In general, infrapopulations of C. corderoi showed overdispersion in different hosts.     

Population biology of the metacercariae of Centrocestus formosanus (Trematoda: Heterophyidae) on the gills of Aplocheilus panchax

The population biology of metacercariae of Centrocestus formosanus (Nishigori, 1924) on the gills of the larvivorous fish, Aplocheilus panchax (Hamilton) was investigated based on data from examination of monthly samples of fish collected from a stream at Visakhapatnam during the period December 1983 to April 1986. The seasonal dynamics, dispersion pattern and long-term changes were studied. No seasonality in prevalence and density of infection with metacercariae was observed. The recruitment of metacercariae occurred throughout the year. An increase in density of infection with increase in size of the fish was noted. Possible reasons for the observed distribution are discussed. The frequency distribution of the metacercariae followed the negative binomial at different times of the year. The data indicated an increase in degree of overdispersion with increase in size offish except for a slight drop in the largest size class. Long-term changes in the abundance of metacercariae are given and a decline in parasite population abundance is noted.     

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.     

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.     

The ecological interaction between arctic charr, Salvelinus alpinus (L.), and the plerocercoid stage of Diphyllobothrium ditremum

Six hundred and two arctic charr, Salvelinus alpinus , from a small lake (30 ha) were examined for infection with plerocercoids of Diphyllobothrium ditremum the only species of this genus present; 466 (77.4%) harboured the parasite in an overdispersed infection. The prevalence of infection increased with age and reached 100% at 7+ years for males and 8+ years for females. The rate of infection appeared to be related to the feeding biology of the charr which did not change within the age span studied. The rate of increase in density of infection (plerocercoids per fish) decreased with age as did the degree of overdispersion. It is concluded that the infection probably induces mortality in the fish population, and that such mortality is dependent on parasite density.     

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.     

Mortalities induced by the copepod Sinergasilus polycolpus in farmed silver and bighead carp in a reservoir

The frequency distributions of the parasitic copepod Sinergasilus polycolpus were examined in silver carp Hypophthalmichthys molitrix and bighead carp Aristichthys nobilis during a disease outbreak of the 2 species of fish in a reservoir in China. The mean abundance of the copepod was positively related with host length and age, and the overdispersion of the copepod in both silver and bighead carp was fitted well with negative binomial distribution. Although parasite-induced host mortality was observed, a peaked age-parasite abundance curve was not detected in the present parasite-host system. It is also proposed that this peaked age-abundance curve is unlikely to be observed in its natural host populations.     

Ecological aspects between Contracaecum sp. (Nematoda, Anisakidae) and the host Serrasalmus spilopleura Kner, 1860 (Pisces, Characidae) in natural populations of northeastern Argentina

From February 1987 to February 1989, the populational biology of Contraceacum sp. (larvae) in its paratenic host, the fish Serrasalmus spilopleura Kner, 1860, was studied in two ponds in a subtropical permanent habitat northeastern of Argentina. Fishes from Ramada Paso pond presented 80% of prevalence and 1 to 132 larvae per fish while fishes from Aeroclub pond presented 63% of prevalence and 1 to 184 larvae per fish. Fishes collected from Aeroclub pond have shown a high prevalence of infection during the first period of study (1987), diminishing the following year. In fishes from Ramada Paso pond the prevalence varied not significatively during the two years. Prevalence and mean intensity of infection increase with body length and weight of the hosts. Sex of hosts is not an influential factor in parasitic level. The lenitic "closed" environmental (Ramada Paso pond) evidenced the greatest larvae mean intensity and prevalence. Although, the lenitic "open" environmental (Aeroclub pond) showed the greatest parasitic number of individuals in an infrapopulation. The spatial dispersion in both ponds were aggregated and fit well a negative binomial model. Nevertheless, the Aeroclub pond presented the greatest overdispersion.     

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.     

Overdispersion of the molecular clock varies between yeast, Drosophila and mammals

Although protein evolution can be approximated as a "molecular evolutionary clock," it is well known that sequence change departs from a clock-like Poisson expectation. Through studying the deviations from a molecular clock, insight can be gained into the forces shaping evolution at the level of proteins. Generally, substitution patterns that show greater variance than the Poisson expectation are said to be "overdispersed." Overdispersion of sequence change may result from temporal variation in the rate at which amino acid substitutions occur on a phylogeny. By comparing the genomes of four species of yeast, five species of Drosophila, and five species of mammals, we show that the extent of overdispersion shows a strong negative correlation with the effective population size of these organisms. Yeast proteins show very little overdispersion, while mammalian proteins show substantial overdispersion. Additionally, X-linked genes, which have reduced effective population size, have gene products that show increased overdispersion in both Drosophila and mammals. Our research suggests that mutational robustness is more pervasive in organisms with large population sizes and that robustness acts to stabilize the molecular evolutionary clock of sequence change.     

Epidemiology of Cryptosporidium molnari in Spanish gilthead sea bream (Sparus aurata L.) and European sea bass (Dicentrarchus labrax L.) cultures: from hatchery to market size

A long-term epidemiological study of Cryptosporidium molnari in aquacultured European sea bass (ESB) and gilthead sea bream (GSB) was performed in different types of facilities on the Atlantic, Cantabric, and Mediterranean coasts. Four types of studies were carried out. In study A, fish raised from juveniles to marketable size (ongrowing stage) were periodically sampled in three different types of cultures. Studies B and C focused on hatchery and nursery facilities. In study D, occasional samplings were performed during mortality or morbidity outbreaks. As a general trend, C. molnari was more prevalent in GSB than in ESB. Data on the distribution pattern of C. molnari in total sampled GSB (studies A, B, and D) had a variance higher than the mean (overdispersion). In GSB (study A), the type of ongrowing system (sea cages, earth ponds, or indoor tanks) was found to have no significant effect. There was a significant relationship between the presence of the parasite and both fish weight and season. The highest infection values were recorded in spring. Prevalence and intensity had convex weight profiles, with a peak in 30- to 100-g fish. In study D, the prevalence of infection was higher in fish recently introduced in sea cages and in preongrowing systems. In studies B and C, fish were almost never infected before entering the postlarval and nursery facilities. The parasite seems to enter the host mainly through the water in production steps with less stringent water treatment. Recirculation systems and fish cannibalism could contribute to oocyst concentration and dispersion in aquaculture facilities.     

Long-term stability in the population levels of the eyefluke Tylodelphys podicipina (Digenea: Diplostomatidae) in perch

Annual changes in the population size of the metacercariae of Tylodelphys podicipina in the eyes of perch in a small eutrophic lake were studied over ten years by following changes in prevalence, abundance and overdispersion of parasites throughout the life of each year class of fish. The population increased rapidly in the first two years after its introduction to the lake, but for the next six years fluctuated within very narrowly constrained limits before declining as a result of a catastrophic decline in the perch population. No evidence of parasite-induced host mortality was found: the decline in parasite abundance throughout the life of each year class was due to density-independent parasite mortality within the fish as a result of natural variation in the life span of the metacercariae. Levels of infection in the first year of a year class were determined principally by transmission processes, as transmission could only occur over a very brief period when release of cercariae from parent generation snails coincided with the presence of perch fry. Transmission appeared to be density-independent, and infection levels in perch to be determined by the dimensions of the transmission' window' and subsequently modified by parasite mortality. No evidence of host responses or any other regulatory factor of fish origin was found, and the infrapopulations in perch appear to be non-equilibrial and unstable. Although the possibility of regulatory processes acting on infrapopulations of the parasite in other hosts remains, the importance of transmission windows in determining infrapopulation levels in fish is emphasized.     

Gyrodactyloides bychowskii (Monogenea: Gyrodactylidae) from sea-caged Atlantic salmon Salmo salar in Scotland: occurrence and ribosomal RNA sequence analysis

Gyrodactyloides bychowskii has been recorded in Scottish waters for the first time. The parasite was found on the gills of Atlantic salmon reared in seawater. An integrated morphological and molecular examination of the parasite was carried out. Prevalence of the parasite was greatest in February and declined to 0 by June in 1999. During 2000, parasites were located in March and November. An overdispersion of parasites was recorded, with intensity of infection reaching over 200 parasites per gill arch in some fish. Parasitised gill tissue showed hyperplasia and hypertrophy but not always at the site of parasite attachment. The internal transcribed spacer of the ribosomal RNA gene array was amplified by PCR and sequenced. This sequence shared greatest similarity with the internal transcribed spacer of Gyrdicotylus gallieni, followed by Gyrodactylus species. This is the first molecular analysis of this parasite and provides sequence data that may be used in comparison of G. bychowskii from other locations or in phylogenetic analysis of this group of Monogenea.     

A note on overdispersion as an index of behavioural synchrony: a pilot study in dairy cows

We developed a method for studying the synchrony of behaviour based on calculations of overdispersion of a binomial process. The lying behaviour of cows was investigated under two different housing units inside the same barn. The first unit housed 30 cows undergoing conventional milking and the second unit housed 27 cows undergoing automatic milking. The lying behaviour of the cows was observed over 3 weeks in 12 periods of 6 h each. Every 5 min, we counted the number of cows lying down in the cubicles. As external cues, like feeding and conventional milking, can promote synchrony in dairy cows, we expected that cows conventionally milked would show more behavioural synchrony than automatically milked cows. Cows lied down synchronously in both units (overdispersion 1.67, P < 0.01). Lying synchrony tended to be slightly bigger in automatically than in conventionally milked cows (overdispersion 1.76 v. 1.58, P = 0.09), although the proportion of cows lying down was on average greater in conventionally than in automatically milked cows (60.7% v. 45.6%). This suggests that synchronized lying behaviour in cows is a constant phenomenon that depends on social facilitation rather than on external cues. The overdispersion index appears to be a useful tool for studying the synchrony of animal behaviour when observations are made at the group level.     

Epidemiology of Cryptosporidium molnari in Spanish Gilthead Sea Bream (Sparus aurata L.) and European Sea Bass (Dicentrarchus labrax L.) Cultures: from Hatchery to Market Size

A long-term epidemiological study of Cryptosporidium molnari in aquacultured European sea bass (ESB) and gilthead sea bream (GSB) was performed in different types of facilities on the Atlantic, Cantabric, and Mediterranean coasts. Four types of studies were carried out. In study A, fish raised from juveniles to marketable size (ongrowing stage) were periodically sampled in three different types of cultures. Studies B and C focused on hatchery and nursery facilities. In study D, occasional samplings were performed during mortality or morbidity outbreaks. As a general trend, C. molnari was more prevalent in GSB than in ESB. Data on the distribution pattern of C. molnari in total sampled GSB (studies A, B, and D) had a variance higher than the mean (overdispersion). In GSB (study A), the type of ongrowing system (sea cages, earth ponds, or indoor tanks) was found to have no significant effect. There was a significant relationship between the presence of the parasite and both fish weight and season. The highest infection values were recorded in spring. Prevalence and intensity had convex weight profiles, with a peak in 30- to 100-g fish. In study D, the prevalence of infection was higher in fish recently introduced in sea cages and in preongrowing systems. In studies B and C, fish were almost never infected before entering the postlarval and nursery facilities. The parasite seems to enter the host mainly through the water in production steps with less stringent water treatment. Recirculation systems and fish cannibalism could contribute to oocyst concentration and dispersion in aquaculture facilities.     

Evaluating Dependence Among Mule Deer Siblings in Fetal and Neonatal Survival Analyses

Abstract: The assumption of independent sample units is potentially violated in survival analyses where siblings comprise a high proportion of the sample. Violation of the independence assumption causes sample data to be overdispersed relative to a binomial model, which leads to underestimates of sampling variances. A variance inflation factor, c, is therefore required to obtain appropriate estimates of variances. We evaluated overdispersion in fetal and neonatal mule deer (Odocoileus hemionus) datasets where more than half of the sample units were comprised of siblings. We developed a likelihood function for estimating fetal survival when the fates of some fetuses are unknown, and we used several variations of the binomial model to estimate neonatal survival. We compared theoretical variance estimates obtained from these analyses with empirical variance estimates obtained from data-bootstrap analyses to estimate the overdispersion parameter, c. Our estimates of c for fetal survival ranged from 0.678 to 1.118, which indicate little to no evidence of overdispersion. For neonatal survival, 3 different models indicated that ĉ ranged from 1.1 to 1.4 and averaged 1.24–1.26, providing evidence of limited overdispersion (i.e., limited sibling dependence). Our results indicate that fates of sibling mule deer fetuses and neonates may often be independent even though they have the same dam. Predation tends to act independently on sibling neonates because of dam-neonate behavioral adaptations. The effect of maternal characteristics on sibling fate dependence is less straightforward and may vary by circumstance. We recommend that future neonatal survival studies incorporate additional sampling intensity to accommodate modest overdispersion (i.e., ĉ = 1.25), which would facilitate a corresponding ĉ adjustment in a model selection analysis using quasi-likelihood without a reduction in power. Our computational approach could be used to evaluate sample unit dependence in other studies where fates of individually marked siblings are monitored.     

A common tendency for phylogenetic overdispersion in mammalian assemblages

Competition has long been proposed as an important force in structuring mammalian communities. Although early work recognized that competition has a phylogenetic dimension, only with recent increases in the availability of phylogenies have true phylogenetic investigations of mammalian community structure become possible. We test whether the phylogenetic structure of 142 assemblages from three mammalian clades (New World monkeys, North American ground squirrels and Australasian possums) shows the imprint of competition. The full set of assemblages display a highly significant tendency for members to be more distantly related than expected by chance (phylogenetic overdispersion). The overdispersion is also significant within two of the clades (monkeys and squirrels) separately. This is the first demonstration of widespread overdispersion in mammal assemblages and implies an important role for either competition between close relatives where traits are conserved, habitat filtering where distant relatives share convergent traits, or both.     

Matched Case Control Studies with Random Exposure Effects

A method for analysing matched case control data in presence of overdispersion or correlation between observations within matched sets is presented. A generalised linear mixed model approach is adapted to account for overdispersion by allowing random exposure effects. Expressions for the elements of the estimation equation are derived and a strategy for achieving efficiency in computing is discussed. Results from simulation studies and two applications are presented.