Resource limitation in natural populations of phytophagous insects. A long-term study case with the chestnut weevil

The chestnut weevil, Curculio elephas (Gyll.), is a non-outbreaking species whose populations and food resources, the European chestnut, Castanea sativa, can be precisely defined. Thirteen and 17 generations of this insect were studied in two isolated sites. Field observations and experiments allowed us to estimate the absolute abundance, availability and use of chestnuts for weevil oviposition, and the number of weevil females emerging per site. Unavailable chestnuts were defined as the fruits either infested first by the chestnut moth (Cydia splendana) larvae (because of competition between the two species) or those avoided by chestnut weevil females when selecting their egg-laying sites, independently of chestnut moth presence. From a third to a half of the chestnuts were not available on the average for weevil infestation. Only one-fourth, on the average, of those available for oviposition were actually used by chestnut weevil females. Regardless of year and site, the number of available chestnuts per weevil female was higher than that of weevil-infested fruits per female, considering global food resources independently of their temporal variation in quality. However, realized fecundity of weevil females was positively correlated with the mean number of available chestnuts per female. We concluded that food resources can be limiting without being fully exploited by females because of temporal variation in chestnut quality.     

Generalized Poisson distribution: the property of mixture of Poisson and comparison with negative binomial distribution

We prove that the generalized Poisson distribution GP(theta, eta) (eta > or = 0) is a mixture of Poisson distributions; this is a new property for a distribution which is the topic of the book by Consul (1989). Because we find that the fits to count data of the generalized Poisson and negative binomial distributions are often similar, to understand their differences, we compare the probability mass functions and skewnesses of the generalized Poisson and negative binomial distributions with the first two moments fixed. They have slight differences in many situations, but their zero-inflated distributions, with masses at zero, means and variances fixed, can differ more. These probabilistic comparisons are helpful in selecting a better fitting distribution for modelling count data with long right tails. Through a real example of count data with large zero fraction, we illustrate how the generalized Poisson and negative binomial distributions as well as their zero-inflated distributions can be discriminated.     

Clutch size manipulations in the chestnut weevil, Curculio elephas: fitness of oviposition strategies

We test the adaptive value of clutch size observed in a natural population of the chestnut weevil Curculio elephas. Clutch size is defined as the number of immatures per infested chestnut. In natural conditions, clutch size averages 1.7 eggs. By manipulating clutch size in the field, we demonstrate that deviations from the theoretical ”Lack clutch size”, estimated as eight immatures, are mainly due to proximate and delayed effects of clutch size on offspring performance. We show the existence of a trade-off between clutch size and larval weight. The latter, a key life-history trait, is highly correlated with fitness because it is a strong determinant of larval survival and potential fecundity of offspring females. The fitness of different potential oviposition strategies characterized by their clutch sizes, ranging from one to nine immatures, was calculated from field- estimated parameters. Chestnut weevil females obtain an evolutionary advantage by laying their eggs singly, since, for instance, fitness of single-egg clutches exceeds fitness of two-egg clutches and four-egg clutches by 8.0% and 15.1% respectively. Received 4 August 1999 / Accepted: 7 October 1999     

Distribution of Polymorphus minutus among its intermediate hosts

Hirsch R. P. 1979. Distribution of Polymorphus minutus among its intermediate hosts. International journal for Parasitology10: 243–248. In 1971, Crofton investigated patterns of distribution of Polymorphus minutus in the intermediate host, Gammarus pulex. Among his conclusions were: (1) P. minutus populations occur in patterns similar to negative binomial distributions, and (2) parasite-induced host mortality results in patterns similar to truncated (high end) negative binomial distributions. Those conclusions, however, were not tested by statistical analyses. To test Crofton's observations, Chi-square goodness of fit tests were applied to data used by Crofton and an additional two stations sampled by Hynes & Nicholas in 1963. Analyses were expanded to include five theoretical distributions, four patterns of host mortality and various rates of host mortality. Truncated forms of negative binomial, positive binomial and Poisson distributions were also investigated where nontruncated distributions failed to fit observed distributions. It was found that negative binomial distributions most frequently describe patterns of P. minutus distribution with the exception of one population described by Poisson and another by positive binomial distributions. Crofton's assumption that truncated distributions result from parasite-induced host mortality seems unlikely in light of those analyses.     

A Stochastic Process and Generalized Distributions for the Study of Oviposition Evolution of a Parasite

This paper considers a generalized birth process {X^m(t), t > 0} and presents a new stochastic model for the number of eggs laid by a parasite on a host. Also, given an underlying distribution for the number of visits between parasites and a host, this distribution is generalized by the distribution of the number of eggs per visit laid on the host. If a certain number of eggs are already present on the host, a parasite such as a Japanese weevil, may avoid oviposition in subsequent visits (see JANARDAN (1980)) to the same host. A class of generalized distributions are presented to model such situations. The case of a single egg laying parasite and a Poisson distribution for the number of visits of the parasite to the same host yields a distribution of particular interest. In order to develop this model, certain lemmas are derived. Finally a characteristic property of this stochastic model is presented.     

Population dynamics of the chestnut gall-wasp,Dryocosmus kuriphilus Yasumatsu (Hymenoptera: Cynipidae)

Summary As a part of serial study on population dynamics of the chestnut gall-wasp,Dryocosmus kuriphilus, analyses of the distribution of eggs, gall-cells and emergent holes were made from the statistical point of view. Many of distributions of the eggs per bud could be described by the truncated Poisson, but some cases showed slight overdispersion than expected by chance. Because of no linear increase of with increasing (expected mean for complete sample), however, the truncated negative binomial seemed to be not so available for whole series. Distributions of the gall-cells and the emergent holes were, on the other hand, well described by the truncated Poisson distribution when the observed frequency was calculated for respective trees. Negative-binomial tendency found in distributions from some stations consisted of a certain number of trees would be resulted from mixture of Poisson populations with different means. Random or slightly concentrated oviposition and random mortality within galls was thus supposed for future study unless the proof favouring other distribution models would appear.     

Some Approximations of the Borel-Tanner or the Generalized Poisson Distribution

This paper considers some approximations for the Borel-Tanner (Generalized Poisson) sums by using (i) Gram-Charlier Poisson expansion, (ii) Mixture of two Poisson distributions, (iii) Variance stabilizing technique, and (iv) negative binomial distribution. It has been found that the approximation obtained by using the negative binomial distribution seems to be more efficient than the other approximation.     

Seedling dynamics of <Emphasis Type="Italic">Acer mono</Emphasis> and <Emphasis Type="Italic">Fagus crenata</Emphasis>: an environmental filter limiting their adult distributions

Spatial pattern of a biotic population may change over time as its component individuals grow or die out, but whether this is the case for desert annual plants is largely unknown. Here we examined seasonal changes in spatial patterns of two annuals, Eriogonum abertianum and Haplopappus gracilis, in initial (winter) and final (summer) densities. The density was measured as the number of individuals from 384 permanent quadrats (each 0.5 m × 0.5 m) in the Chihuahuan Desert near Portal, Arizona, USA. We used three probability distributions (binomial, Poisson, and negative binomial or NB) that represent three basic spatial patterns (regular, random, and clumped) to fit the observed frequency distributions of densities of the two annuals. Both species showed clear clumped patterns as characterized by the NB and had similar inverse J-shaped frequency distribution curves in two density categories. Also, both species displayed a reduced degree of aggregation from winter to summer after the spring drought (massive die-off), as indicated by the increased k-parameter of the NB and decreased values of another NB parameter p, variance/mean ratio, Lloyd’s Index of Patchiness, and David and Moore’s Index of Clumping. Further, we hypothesized that while the NB (i.e., Poisson-logarithmic) well fits the distribution of individuals per quadrat, its components, the Poisson and logarithmic, may describe the distributions of clumps per quadrat and of individuals per clump, respectively. We thus obtained the means and variances for (1) individuals per quadrat, (2) clumps per quadrat, and (3) individuals per clump. The results showed that the decrease of the density from winter to summer for each plant resulted from the decrease of individuals per clump, rather than from the decrease of clumps per quadrat. The great similarities between the two annuals indicate that our observed temporal changes in spatial patterns may be common among desert annual plants.     

大兴安岭塔河地区林火发生的优势预测模型选择

选取在经济学和社会科学领域广泛应用的零膨胀模型(zero-inflated models)和栅栏模型(Hurdle models)对大兴安岭地区林火发生进行模拟,应用赤池准则(AIC)、似然比检验(LR)和模型残差平方和(SSR)对两类共4个回归模型——零膨胀泊松模型(ZIP)、零膨胀负二项模型(ZINB)、栅栏泊松模型(PH)、栅栏负二项模型(NBH)进行拟合分析,最终选取适合此林火发生特性的预测模型.模型的AIC和SSR值表明,ZINB模型对当地林火数据的拟合度最高.运用LR检验对嵌套模型(ZINB与ZIP,NBH与PH)进行检验,结果显示: ZINB和NBH均优于各自的嵌入模型,说明负二项(NB)模型对数据结构中的过度离散现象可以很好地模拟和解释.根据研究区林火实际发生规律和两类不同模型的应用假设条件判断,零膨胀模型更适合塔河地区的林火特性.     

Two New Discrete Distributions

CONSUL and JAIN (1973a) introduced a generalized Poisson distribution, which has applications in reliability theory and many biometric studies, and described some of its properties. Here we obtain two new distributions treating two of the parameters of the above distribution as random variables having gamma and absolute value distributions. One of the new distributions is related to the negative binomial distribution. Their moments also have been obtained.     

Selection,caching, and consumption of hardwood seeds by forest rodents: implications for restoration of American chestnut

Recent field trials on blight‐resistant hybrids (BC₃F₃) of American chestnut (Castanea dentata) and Chinese chestnut (C. mollissima) have intensified planning for widespread restoration of Castanea to eastern U.S. forests. Restoration will likely rely on natural seed dispersal from sites planted with chestnut; however, we do not know how dispersal agents such as granivorous rodents will respond to hybrid chestnuts. At one extreme, excessive seed consumption may impede restoration. Alternatively, scatter‐hoarding rodents might facilitate the spread of chestnut by dispersal of seeds from restoration plantings. We conducted trials with five rodent species to quantify foraging preferences and to evaluate the potential role of granivores in chestnut restoration. Specifically, we presented seeds from American and hybrid chestnuts (BC₃F₂) with other common mast species and recorded the proportion of seeds removed and the fates of tagged seeds. Mice, chipmunks, and flying squirrels harvested both chestnut types preferentially over larger, tougher black walnut, hickory, and red oak seeds, but fox squirrels and eastern gray squirrels preferred larger seeds to chestnuts. All rodents consumed a greater proportion of the chestnuts than other seed types. American and hybrid chestnut also differed in important ways: except for fox squirrels, rodents preferentially removed American chestnuts over hybrid chestnuts, but we estimated that fox squirrels carried a greater proportion of hybrid chestnuts beyond our tag search area, suggesting that hybrids may be dispersed farther and cached more often than American chestnut. These differences indicate that hybrid chestnut may not be functionally equivalent to American chestnut with regard to seed–granivore interactions.     

Multivariate Polya and Inverse Polya Distributions of Order k

Multivariate Polya and inverse Polya distributions of order k are derived by means of generalized urn models and by compounding the type II multinomial and multivariate negative binomial distributions of order k of PHILIPPOU , ANTZOULAKOS and TRIPSIANNIS (1990, 1988), respectively, with the Dirichlet distribution. It is noted that the above two distributions include as special cases a multivariate hypergeometric distribution of order k, a negative one, an inverse one, a negative inverse one and a discrete uniform of the same order. The probability generating functions, means, variances and covariances of the new distributions are obtained and five asymptotic results are established relating them to the above-mentioned multinomial and multivariate negative binomial distributions of order k, and to the type II negative binomial and the type I multivariate Poisson distributions of order k of PHILIPPOU (1983), and PHILIPPOU , ANTZOULAKOS and TRIPSIAN-NIS (1988), respectively. Potential applications are also indicated. The present paper extends to the multivariate case the work of PHILIPPOU , TRIPSIANNIS and ANTZOULAKOS (1989) on Polya and inverse Polya distributions of order k..     

Distribution of foundress group size in Ropalidia fasciata and R. plebeiana (Hymenoptera: Vespidae): an analysis using zero-truncated distribution models

Distribution patterns of the number of foundresses per newly established nest (foundress group size, FGS) of two primitively eusocial, independent-founding wasps, Ropalidia fasciata and R. plebeiana, were studied using zero-truncated distribution models. The distribution pattern of the FGS of R. fasciata is significantly different from a zero-truncated Poisson distribution but fits the zero-truncated negative binomial distribution well, indicating a strongly contagious distribution. R. plebeiana sometimes establishes new colonies by reusing old nests. In this case, distributions are strongly contagious. Competition among foundresses may be one reason for the contagious distribution of FGS in R. fasciata and in cases of old-nest reuse by R. plebeiana, but further studies, especially on the behaviour of foundresses in relation to FGS, are necessary. Electronic Publication     

Interference at several temporal and spatial scales between two chestnut insects

Detection of interspecific competition between insects is often sensitive to scaling. We give an example of scale-dependent interference between the weevil Curculio elephas and the moth Cydia splendana, which both have larvae that develop in the fruits of chestnut Castanea sativa. Measures at three scales were considered: chestnut, husk (with one to three fertile fruits) and tree. Data come from observations in the field over 14 years, complemented by experiments done directly in trees. Data on individual chestnut fruits revealed a marked statistical interference between the two insects. Experiments demonstrated that presence of a moth larva in a fruit usually inhibits weevil egg-laying. Conversely, weevil presence does not strongly modify moth larval behavior. Cases of double infestation often correspond to fruits first attacked by the weevil. With measures on husks, interference between the two insects was observed only in some trees; its intensity was always weaker than in the chestnuts themselves. At the scale of entire trees, rates of infestation by each insect are not correlated. Interference in chestnut fruits is interpreted by assuming that the weevil female either is sensitive to a repellent molecule originating from a moth larva or its frass, or can detect moth larval sounds. Mechanisms governing infestation rates from data per tree are discussed in relation to those found at fruit scale and to plant-insect interactions. The need to estimate available resources both from quantitative and qualitative points of view is emphasized.     

Spatial Distribution of Adult <Emphasis Type="Italic">Anthonomus grandis</Emphasis> Boheman (Coleoptera: Curculionidae) and Damage to Cotton Flower Buds Due to Feeding and Oviposition

The cotton boll weevil Anthonomus grandis Boheman (Coleoptera: Curculionidae) is the main pest in cotton crop around the world, directly affecting cotton production. In order to establish a sequential sampling plan, it is crucial to understand the spatial distribution of the pest population and the damage it causes to the crop through the different developmental stages of cotton plants. Therefore, this study aimed to investigate the spatial distribution of adults in the cultivation area and their oviposition and feeding behavior throughout the development of the cotton plants. The experiment was conducted in Maracaju, Mato Grosso do Sul, Brazil, in the 2012/2013 and 2013/2014 growing seasons, in an area of 10,000 m², planted with the cotton cultivar FM 993. The experimental area was divided into 100 plots of 100 m² (10 × 10 m) each, and five plants per plot were sampled weekly throughout the crop cycle. The number of flower buds with feeding and oviposition punctures and of adult A. grandis was recorded throughout the crop cycle in five plants per plot. After determining the aggregation indices (variance/mean ratio, Morisita’s index, exponent k of the negative binomial distribution, and Green’s coefficient) and adjusting the frequencies observed in the field to the distribution of frequencies (Poisson, negative binomial, and positive binomial) using the chi-squared test, it was observed that flower buds with punctures derived from feeding, oviposition, and feeding + oviposition showed an aggregated distribution in the cultivation area until 85 days after emergence and a random distribution after this stage. The adults of A. grandis presented a random distribution in the cultivation area.     

Promotion time models with time-changing exposure and heterogeneity: application to infectious diseases

Promotion time models have been recently adapted to the context of infectious diseases to take into account discrete and multiple exposures. However, Poisson distribution of the number of pathogens transmitted at each exposure was a very strong assumption and did not allow for inter-individual heterogeneity. Bernoulli, the negative binomial, and the compound Poisson distributions were proposed as alternatives to Poisson distribution for the promotion time model with time-changing exposure. All were derived within the frailty model framework. All these distributions have a point mass at zero to take into account non-infected people. Bernoulli distribution, the two-component cure rate model, was extended to multiple exposures. Contrary to the negative binomial and the compound Poisson distributions, Bernoulli distribution did not enable to connect the number of pathogens transmitted to the delay between transmission and infection detection. Moreover, the two former distributions enable to account for inter-individual heterogeneity. The delay to surgical site infection was an example of single exposure. The probability of infection was very low; thus, estimation of the effect of selected risk factors on that probability obtained with Bernoulli and Poisson distributions were very close. The delay to nosocomial urinary tract infection was a multiple exposure example. The probabilities of pathogen transmission during catheter placement and catheter presence were estimated. Inter-individual heterogeneity was very high, and the fit was better with the compound Poisson and the negative binomial distributions. The proposed models proved to be also mechanistic. The negative binomial and the compound Poisson distributions were useful alternatives to account for inter-individual heterogeneity.     

Efficient Simulation of Multivariate Binomial and Poisson Distributions

Power investigations, for example, in statistical procedures for the assessment of agreement among multiple raters often require the simultaneous simulation of several dependent binomial or Poisson distributions to appropriately model the stochastical dependencies between the raters' results. Regarding the rather large dimensions of the random vectors to be generated and the even larger number of interactions to be introduced into the simulation scenarios to determine all necessary information on their distributions' dependence stucture, one needs efficient and fast algorithms for the simulation of multivariate Poisson and binomial distributions. Therefore two equivalent models for the multivariate Poisson distribution are combined to obtain an algorithm for the quick implementation of its multivariate dependence structure. Simulation of the multivariate Poisson distribution then becomes feasible by first generating and then convoluting independent univariate Poisson variates with appropriate expectations. The latter can be computed via linear recursion formulae. Similar means for simulation are also considered for the binomial setting. In this scenario it turns out, however, that exact computation of the probability function is even easier to perform; therefore corresponding linear recursion formulae for the point probabilities of multivariate binomial distributions are presented, which only require information about the index parameter and the (simultaneous) success probabilities, that is the multivariate dependence structure among the binomial marginals.     

负二项分布与昆虫种群空间格局分析的研究现状

对农业有害生物及其天敌种群密度的正确估计是实施IPM(有害生物综合治理)方案的先决条件,因此,抽样方法一直被列为昆虫学,生态学和植物保护科学中最重要的基本     

The spatial distribution of the wheat-bulb fly,Leptohylemyia coarctata (fall.) (Diptera: Anthomyiidae)

The spatial distribution of the eggs, larvae, pupae and adults of the wheat-bulb fly was investigated by fitting 42 sets of data comprising 1334 samples to the Poisson and negative binomial distributions, and by using the power law (S²=am^b). In general, the tests indicated that all stages were aggregated and fitted the negative binomial model.     

Effect of arbuscular mycorrhizal fungi (Glomus intraradices) on the oviposition of rice water weevil (Lissorhoptrus oryzophilus)

Root-feeding insects are important drivers in ecosystems, and links between aboveground oviposition preference and belowground larval performance have been suggested. The root-colonizing arbuscular mycorrhizal fungi (AMF) play a central role in plant nutrition and are known to change host quality for root-feeding insects. However, it is not known if and how AMF affect the aboveground oviposition of insects whose offspring feed on roots. According to the preference–performance hypothesis, insect herbivores oviposit on plants that will maximize offspring performance. In a greenhouse experiment with rice (Oryza sativa), we investigated the effects of AMF (Glomus intraradices) on aboveground oviposition of rice water weevil (Lissorhoptrus oryzophilus), the larvae of which feed belowground on the roots. Oviposition (i.e., the numbers of eggs laid by weevil females in leaf sheaths) was enhanced when the plants were colonized by AMF. However, the leaf area consumed by adult weevils was not affected. Although AMF reduced plant biomass, it increased nitrogen (N) and phosphorus concentrations in leaves and N in roots. The results suggest that rice water weevil females are able to discriminate plants for oviposition depending on their mycorrhizal status. The discrimination is probably related to AMF-mediated changes in plant quality, i.e., the females choose to oviposit more on plants with higher nutrient concentrations to potentially optimize offspring performance. AMF-mediated change in plant host choice for chewing insect oviposition is a novel aspect of below- and aboveground interactions.