Responses of invertebrate trophic level, feeding guild and body size to the management of improved grassland field margins

P>1. Management of lowland mesotrophic grasslands in north-west Europe often makes use of inorganic fertilizers, high stocking densities and silage-based forage systems to maximize productivity. The impact of these practices has resulted in a simplification of the plant community combined with wide-scale declines in the species richness of grassland invertebrates. We aim to identify how field margin management can be used to promote invertebrate diversity across a suite of functionally diverse taxa (beetles, planthoppers, true bugs, butterflies, bumblebees and spiders). 2. Using an information theoretic approach we identify the impacts of management (cattle grazing, cutting and inorganic fertilizer) and plant community composition (forb species richness, grass species richness and sward architecture) on invertebrate species richness and body size. As many of these management practices are common to grassland systems throughout the world, understanding invertebrate responses to them is important for the maintenance of biodiversity. 3. Sward architecture was identified as the primary factor promoting increased species richness of both predatory and phytophagous trophic levels, as well as being positively correlated with mean body size. In all cases phytophagous invertebrate species richness was positively correlated with measures of plant species richness. 4. The direct effects of management practices appear to be comparatively weak, suggesting that their impacts are indirect and mediated though the continuous measures of plant community structure, such as sward architecture or plant species richness. 5. Synthesis and applications. By partitioning field margins from the remainder of the field, economically viable intensive grassland management can be combined with extensive management aimed at promoting native biodiversity. The absence of inorganic fertilizer, combined with a reduction in the intensity of both cutting and grazing regimes, promotes floral species richness and sward architectural complexity. By increasing sward architecture the total biomass of invertebrates also increased (by c. 60% across the range of sward architectural measures seen in this study), increasing food available for higher trophic levels, such as birds and mammals.

Choosing the number of doses and the cohort size for phase I dose-escalation studies

This paper reviews Bayesian procedures for phase 1 dose-escalation studies and compares different dose schedules and cohort sizes. The methodology described is motivated by the situation of phase 1 dose-escalation studiesin oncology, that is, a single dose administered to each patient, with a single binary response ("toxicity"' or "no toxicity") observed. It is likely that a wider range of applications of the methodology is possible. In this paper, results from 10000-fold simulation runs conducted using the software package Bayesian ADEPT are presented. Four designs were compared under six scenarios. The simulation results indicate that there are slight advantages of having more dose levels and smaller cohort sizes.

Comparison of sample size formulae for 2x2 cross-over designs applied to bioequivalence studies

We consider the comparison of two formulations in terms of average bioequivalence using the 2 × 2 cross-over design. In a bioequivalence study, the primary outcome is a pharmacokinetic measure, such as the area under the plasma concentration by time curve, which is usually assumed to have a lognormal distribution. The criterion typically used for claiming bioequivalence is that the 90% confidence interval for the ratio of the means should lie within the interval (0.80, 1.25), or equivalently the 90% confidence interval for the differences in the means on the natural log scale should be within the interval (-0.2231, 0.2231). We compare the gold standard method for calculation of the sample size based on the non-central t distribution with those based on the central t and normal distributions. In practice, the differences between the various approaches are likely to be small. Further approximations to the power function are sometimes used to simplify the calculations. These approximations should be used with caution, because the sample size required for a desirable level of power might be under- or overestimated compared to the gold standard method. However, in some situations the approximate methods produce very similar sample sizes to the gold standard method. Copyright © 2005 John Wiley & Sons, Ltd.

Microbe-associated molecular pattern (MAMP) signatures, synergy, size and charge: influences on perception or mobility and host defence responses

Triggering of defences by microbes has mainly been investigated using single elicitors or microbe-associated molecular patterns (MAMPs), but MAMPs are released in planta as complex mixtures together with endogenous oligogalacturonan (OGA) elicitor. We investigated the early responses in Arabidopsis of calcium influx and oxidative burst induced by non-saturating concentrations of bacterial MAMPs, used singly and in combination: flagellin peptide (flg22), elongation factor peptide (elf18), peptidoglycan (PGN) and component muropeptides, lipo-oligosaccharide (LOS) and core oligosaccharides. This revealed that some MAMPs have additive (e.g. flg22 with elf18) and even synergistic (flg22 and LOS) effects, whereas others mutually interfere (flg22 with OGA). OGA suppression of flg22-induced defences was not a result of the interference with the binding of flg22 to its receptor flagellin-sensitive 2 (FLS2). MAMPs induce different calcium influx signatures, but these are concentration dependent and unlikely to explain the differential induction of defence genes [pathogenesis-related gene 1 (PR1), plant defensin gene 1.2 (PDF1.2) and phenylalanine ammonia lyase gene 1 (PAL1)] by flg22, elf18 and OGA. The peptide MAMPs are potent elicitors at subnanomolar levels, whereas PGN and LOS at high concentrations induce low and late host responses. This difference might be a result of the restricted access by plant cell walls of MAMPs to their putative cellular receptors. flg22 is restricted by ionic effects, yet rapidly permeates a cell wall matrix, whereas LOS, which forms supramolecular aggregates, is severely constrained, presumably by molecular sieving. Thus, MAMPs can interact with each other, whether directly or indirectly, and with the host wall matrix. These phenomena, which have not been considered in detail previously, are likely to influence the speed, magnitude, versatility and composition of plant defences.

On the question of proportionality of the count of observed Scrapie cases and the size of holding

Background: The present paper investigates the question of a suitable basic model for the number of scrapie cases in a holding and applications of this knowledge to the estimation of scrapie-ffected holding population sizes and adequacy of control measures within holding. Is the number of scrapie cases proportional to the size of the holding in which case it should be incorporated into the parameter of the error distribution for the scrapie counts? Or, is there a different - potentially more complex - relationship between case count and holding size in which case the information about the size of the holding should be better incorporated as a covariate in the modeling? Methods: We show that this question can be appropriately addressed via a simple zero-truncated Poisson model in which the hypothesis of proportionality enters as a special offset-model. Model comparisons can be achieved by means of likelihood ratio testing. The procedure is illustrated by means of surveillance data on classical scrapie in Great Britain. Furthermore, the model with the best fit is used to estimate the size of the scrapie-affected holding population in Great Britain by means of two capture-recapture estimators: the Poisson estimator and the generalized Zelterman estimator. Results: No evidence could be found for the hypothesis of proportionality. In fact, there is some evidence that this relationship follows a curved line which increases for small holdings up to a maximum after which it declines again. Furthermore, it is pointed out how crucial the correct model choice is when applied to capture-recapture estimation on the basis of zero-truncated Poisson models as well as on the basis of the generalized Zelterman estimator. Estimators based on the proportionality model return very different and unreasonable estimates for the population sizes. Conclusion: Our results stress the importance of an adequate modelling approach to the association between holding size and the number of cases of classical scrapie within holding. Reporting artefacts and speculative biological effects are hypothesized as the underlying causes of the observed curved relationship. The lack of adjustment for these artefacts might well render ineffective the current strategies for the control of the disease.

Some general comparative points on Chao's and Zelterman's estimators of the population size

Two simple and frequently used capture–recapture estimates of the population size are compared: Chao's lower-bound estimate and Zelterman's estimate allowing for contaminated distributions. In the Poisson case it is shown that if there are only counts of ones and twos, the estimator of Zelterman is always bounded above by Chao's estimator. If counts larger than two exist, the estimator of Zelterman is becoming larger than that of Chao's, if only the ratio of the frequencies of counts of twos and ones is small enough. A similar analysis is provided for the binomial case. For a two-component mixture of Poisson distributions the asymptotic bias of both estimators is derived and it is shown that the Zelterman estimator can experience large overestimation bias. A modified Zelterman estimator is suggested and also the bias-corrected version of Chao's estimator is considered. All four estimators are compared in a simulation study.

A simple variance formula for population size estimators by conditioning

This note considers the variance estimation for population size estimators based on capture–recapture experiments. Whereas a diversity of estimators of the population size has been suggested, the question of estimating the associated variances is less frequently addressed. This note points out that the technique of conditioning can be applied here successfully which also allows us to identify sources of variation: the variance due to estimation of the model parameters and the binomial variance due to sampling n units from a population of size N. It is applied to estimators typically used in capture–recapture experiments in continuous time including the estimators of Zelterman and Chao and improves upon previously used variance estimators. In addition, knowledge of the variances associated with the estimators by Zelterman and Chao allows the suggestion of a new estimator as the weighted sum of the two. The decomposition of the variance into the two sources allows also a new understanding of how resampling techniques like the Bootstrap could be used appropriately. Finally, the sample size question for capture–recapture experiments is addressed. Since the variance of population size estimators increases with the sample size, it is suggested to use relative measures such as the observed-to-hidden ratio or the completeness of identification proportion for approaching the question of sample size choice.

Longevity, early emergence and body size in a pollinating fig wasp - implications for stability in a fig-pollinator mutualism

1. Fig trees (Ficus) are pollinated only by agaonid wasps, whose larvae also gall fig ovules. Each ovule develops into either a seed (when pollinated) or a wasp (when an egg is also laid inside) but not both. 2. Ovipositing wasps (foundresses) favour ovules near the centre of the enclosed inflorescence (syconium or 'fig'), leaving ovules near the outer wall to develop into seeds. This spatial stratification of wasps and seeds ensures reproduction in both partners, and thereby enables mutualism persistence. However, the mechanism(s) responsible remain(s) unknown. 3. Theory shows that foundresses will search for increasingly rare inner ovules and ignore outer ovules, as long as ovipositing in outer ovules is sufficiently slow and/or if inner ovules confer greater fitness to wasps. The fig-pollinator mutualism can therefore be stabilized by strong time constraints on foundresses and by offspring fitness gradients over variation in ovule position. 4. Female fig wasps cannot leave their galls without male assistance. We found that females in outer ovules were unlikely to be released. Inner ovules thus have added value to foundresses, because their female offspring are more likely to mate and disperse. 5. For those offspring that did emerge, gall position (inner/outer) and body size did not influence the order in which female pollinators exited syconia, nor did early emerging wasps enjoy increased life spans. 6. We also found that the life spans of female wasps nearly doubled when given access to moisture. We suggest that conflict resolution in the fig-pollinator mutualism may thus be influenced by tropical seasonality, because wasps may be less able to over-exploit ovules in dry periods due to time constraints.

Sperm competition and the evolution of testes size in terrestrial mammalian carnivores

Summary Understanding the factors influencing variation in the degree of sperm competition is a key question underlying the mechanisms driving sexual conflict. Previous behavioural and comparative studies have indicated that carnivores appear to have evolved under sperm competition but an analysis of the predictors of the level of sperm competition is missing. In this study, we use phylogenetic comparative methods to investigate life-history parameters predicted to affect the degree of sperm competition in terrestrial carnivores using variation in relative testes size (RTS, after controlling for body size allometry) as a measure of the level of sperm competition. Due to a paucity of consistent data across taxa, we used three measures of RTS: testes mass (n = 40 species), testes and epididymes mass combined (n = 38), and testes volume (n = 48). We also created a derived data set (n = 79) with testes mass estimated from regression analyses on the other measures of testes size. Carnivores with shorter mating seasons had relatively larger testes, consistent with the hypothesis that sperm competition is greater when the degree of female oestrous synchrony is high. This relationship was stronger in spontaneous versus induced ovulators, suggesting higher sperm competition levels in spontaneous ovulators. This is the first comparative study to show this within mammalian taxa. Neither social mating system nor reproductive lifespan were significantly associated with variation in RTS and hence are poor predictors of sperm competition levels. None of the above relationships were found to be significant for the testes and epididymes mass combined data set, but our understanding of the role of the epididymis in sperm competition is too limited to draw any conclusions. Finally, we consistently found a significant phylogenetic signal in all analyses, indicating that phylogeny has played a significant role in the evolution of carnivore testes size and, therefore, in shaping levels of sperm competition. Our results shed new light into the factors affecting levels of sperm competition in terrestrial carnivores by showing that the degree of oestrous synchrony and ovulation type interact to predict variation in RTS.

Extending Zelterman’s approach for robust estimation of population size to zero-truncated clustered data

Estimation of population size with missing zero-class is an important problem that is encountered in epidemiological assessment studies. Fitting a Poisson model to the observed data by the method of maximum likelihood and estimation of the population size based on this fit is an approach that has been widely used for this purpose. In practice, however, the Poisson assumption is seldom satisfied. Zelterman (1988) has proposed a robust estimator for unclustered data that works well in a wide class of distributions applicable for count data. In the work presented here, we extend this estimator to clustered data. The estimator requires fitting a zero-truncated homogeneous Poisson model by maximum likelihood and thereby using a Horvitz-Thompson estimator of population size. This was found to work well, when the data follow the hypothesized homogeneous Poisson model. However, when the true distribution deviates from the hypothesized model, the population size was found to be underestimated. In the search of a more robust estimator, we focused on three models that use all clusters with exactly one case, those clusters with exactly two cases and those with exactly three cases to estimate the probability of the zero-class and thereby use data collected on all the clusters in the Horvitz-Thompson estimator of population size. Loss in efficiency associated with gain in robustness was examined based on a simulation study. As a trade-off between gain in robustness and loss in efficiency, the model that uses data collected on clusters with at most three cases to estimate the probability of the zero-class was found to be preferred in general. In applications, we recommend obtaining estimates from all three models and making a choice considering the estimates from the three models, robustness and the loss in efficiency. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

ONeSAMP: a program to estimate effective population size using approximate Bayesian computation

The estimation of effective population size from one sample of genotypes has been problematic because most estimators have been proven imprecise or biased. We developed a web-based program, ONeSAMP that uses approximate Bayesian computation to estimate effective population size from a sample of microsatellite genotypes. ONeSAMP requires an input file of sampled individuals' microsatellite genotypes along with information about several sampling and biological parameters. ONeSAMP provides an estimate of effective population size, along with 95% credible limits. We illustrate the use of ONeSAMP with an example data set from a re-introduced population of ibex Capra ibex.

Bayesian sample size for exploratory clinical trials incorporating historical data

This paper presents a simple Bayesian approach to sample size determination in clinical trials. It is required that the trial should be large enough to ensure that the data collected will provide convincing evidence either that an experimental treatment is better than a control or that it fails to improve upon control by some clinically relevant difference. The method resembles standard frequentist formulations of the problem, and indeed in certain circumstances involving 'non-informative' prior information it leads to identical answers. In particular, unlike many Bayesian approaches to sample size determination, use is made of an alternative hypothesis that an experimental treatment is better than a control treatment by some specified magnitude. The approach is introduced in the context of testing whether a single stream of binary observations are consistent with a given success rate p(0). Next the case of comparing two independent streams of normally distributed responses is considered, first under the assumption that their common variance is known and then for unknown variance. Finally, the more general situation in which a large sample is to be collected and analysed according to the asymptotic properties of the score statistic is explored. Copyright (C) 2007 John Wiley & Sons, Ltd.

Origin of avian genome size and structure in non-avian dinosaurs

Avian genomes are small and streamlined compared with those of other amniotes by virtue of having fewer repetitive elements and less non-coding DNA(1,2). This condition has been suggested to represent a key adaptation for flight in birds, by reducing the metabolic costs associated with having large genome and cell sizes(3,4). However, the evolution of genome architecture in birds, or any other lineage, is difficult to study because genomic information is often absent for long-extinct relatives. Here we use a novel bayesian comparative method to show that bone-cell size correlates well with genome size in extant vertebrates, and hence use this relationship to estimate the genome sizes of 31 species of extinct dinosaur, including several species of extinct birds. Our results indicate that the small genomes typically associated with avian flight evolved in the saurischian dinosaur lineage between 230 and 250 million years ago, long before this lineage gave rise to the first birds. By comparison, ornithischian dinosaurs are inferred to have had much larger genomes, which were probably typical for ancestral Dinosauria. Using comparative genomic data, we estimate that genome-wide interspersed mobile elements, a class of repetitive DNA, comprised 5 - 12% of the total genome size in the saurischian dinosaur lineage, but was 7 - 19% of total genome size in ornithischian dinosaurs, suggesting that repetitive elements became less active in the saurischian lineage. These genomic characteristics should be added to the list of attributes previously considered avian but now thought to have arisen in non-avian dinosaurs, such as feathers(5), pulmonary innovations 6, and parental care and nesting