Likelihood-free estimation of model evidence

Statistical methods of inference typically require the likelihood function to be computable in a reasonable amount of time. The class of “likelihood-free” methods termed Approximate Bayesian Computation (ABC) is able to eliminate this requirement, replacing the evaluation of the likelihood with simulation from it. Likelihood-free methods have gained in efficiency and popularity in the past few years, following their integration with Markov Chain Monte Carlo (MCMC) and Sequential Monte Carlo (SMC) in order to better explore the parameter space. They have been applied primarily to estimating the parameters of a given model, but can also be used to compare models. Here we present novel likelihood-free approaches to model comparison, based upon the independent estimation of the evidence of each model under study. Key advantages of these approaches over previous techniques are that they allow the exploitation of MCMC or SMC algorithms for exploring the parameter space, and that they do not require a sampler able to mix between models. We validate the proposed methods using a simple exponential family problem before providing a realistic problem from human population genetics: the comparison of different demographic models based upon genetic data from the Y chromosome.

Aerosol contribution to the rapid warming of near-term climate under RCP 2.6

The importance of aerosol emissions for near term climate projections is investigated by analysing simulations with the HadGEM2-ES model under two different emissions scenarios: RCP2.6 and RCP4.5. It is shown that the near term warming projected under RCP2.6 is greater than under RCP4.5, even though the greenhouse gas forcing is lower. Rapid and substantial reductions in sulphate aerosol emissions due to a reduction of coal burning in RCP2.6 lead to a reduction in the negative shortwave forcing due to aerosol direct and indirect effects. Indirect effects play an important role over the northern hemisphere oceans, especially the subtropical northeastern Pacific where an anomaly of 5-10\,Wm$^{-2}$ develops. The pattern of surface temperature change is consistent with the expected response to this surface radiation anomaly, whilst also exhibiting features that reflect redistribution of energy, and feedbacks, within the climate system. These results demonstrate the importance of aerosol emissions as a key source of uncertainty in near term projections of global and regional climate.

The structure of the optimal income tax in the quasi-linear model

Existing numerical characterizations of the optimal income tax have been based on a limited number of model specifications. As a result, they do not reveal which properties are general. We determine the optimal tax in the quasi-linear model under weaker assumptions than have previously been used; in particular, we remove the assumption of a lower bound on the utility of zero consumption and the need to permit negative labor incomes. A Monte Carlo analysis is then conducted in which economies are selected at random and the optimal tax function constructed. The results show that in a significant proportion of economies the marginal tax rate rises at low skills and falls at high. The average tax rate is equally likely to rise or fall with skill at low skill levels, rises in the majority of cases in the centre of the skill range, and falls at high skills. These results are consistent across all the specifications we test. We then extend the analysis to show that these results also hold for Cobb-Douglas utility.

Meta-analysis of relationships between enteric methane yield and milk fatty acid profile in dairy cattle

Various studies have indicated a relationship between enteric methane (CH4) production and milk fatty acid (FA) profiles of dairy cattle. However, the number of studies investigating such a relationship is limited and the direct relationships reported are mainly obtained by variation in CH4 production and milk FA concentration induced by dietary lipid supplements. The aim of this study was to perform a meta-analysis to quantify relationships between CH4 yield (per unit of feed and unit of milk) and milk FA profile in dairy cattle and to develop equations to predict CH4 yield based on milk FA profile of cows fed a wide variety of diets. Data from 8 experiments encompassing 30 different dietary treatments and 146 observations were included. Yield of CH4 measured in these experiments was 21.5 ± 2.46 g/kg of dry matter intake (DMI) and 13.9 ± 2.30 g/ kg of fat- and protein-corrected milk (FPCM). Correlation coefficients were chosen as effect size of the relationship between CH4 yield and individual milk FA concentration (g/100 g of FA). Average true correlation coefficients were estimated by a random-effects model. Milk FA concentrations of C6:0, C8:0, C10:0, C16:0, and C16:0-iso were significantly or tended to be positively related to CH4 yield per unit of feed. Concentrations of trans-6+7+8+9 C18:1, trans-10+11 C18:1, cis- 11 C18:1, cis-12 C18:1, cis-13 C18:1, trans-16+cis-14 C18:1, and cis-9,12 C18:2 in milk fat were significantly or tended to be negatively related to CH4 yield per unit of feed. Milk FA concentrations of C10:0, C12:0, C14:0-iso, C14:0, cis-9 C14:1, C15:0, and C16:0 were significantly or tended to be positively related to CH4 yield per unit of milk. Concentrations of C4:0, C18:0, trans-10+11 C18:1, cis-9 C18:1, cis-11 C18:1, and cis- 9,12 C18:2 in milk fat were significantly or tended to be negatively related to CH4 yield per unit of milk. Mixed model multiple regression and a stepwise selection procedure of milk FA based on the Bayesian information criterion to predict CH4 yield with milk FA as input (g/100 g of FA) resulted in the following prediction equations: CH4 (g/kg of DMI) = 23.39 + 9.74 × C16:0- iso – 1.06 × trans-10+11 C18:1 – 1.75 × cis-9,12 C18:2 (R2 = 0.54), and CH4 (g/kg of FPCM) = 21.13 – 1.38 × C4:0 + 8.53 × C16:0-iso – 0.22 × cis-9 C18:1 – 0.59 × trans-10+11 C18:1 (R2 = 0.47). This indicated that milk FA profile has a moderate potential for predicting CH4 yield per unit of feed and a slightly lower potential for predicting CH4 yield per unit of milk. Key words: methane , milk fatty acid profile , metaanalysis , dairy cattle

The role of CO2 and dynamic vegetation on the impact of temperate land use change in the HadCM3 coupled climate model

Human induced land-use change (LUC) alters the biogeophysical characteristics of the land surface influencing the surface energy balance. The level of atmospheric CO2 is expected to increase in the coming century and beyond, modifying temperature and precipitation patterns and altering the distribution and physiology of natural vegetation. It is important to constrain how CO2-induced climate and vegetation change may influence the regional extent to which LUC alters climate. This sensitivity study uses the HadCM3 coupled climate model under a range of equilibrium forcings to show that the impact of LUC declines under increasing atmospheric CO2, specifically in temperate and boreal regions. A surface energy balance analysis is used to diagnose how these changes occur. In Northern Hemisphere winter this pattern is attributed in part to the decline in winter snow cover and in the summer due to a reduction in latent cooling with higher levels of CO2. The CO2-induced change in natural vegetation distribution is also shown to play a significant role. Simulations run at elevated CO2 yet present day vegetation show a significantly increased sensitivity to LUC, driven in part by an increase in latent cooling. This study shows that modelling the impact of LUC needs to accurately simulate CO2 driven changes in precipitation and snowfall, and incorporate accurate, dynamic vegetation distribution.

Ecological and life-history traits predict bee species responses to environmental disturbances

The ability to predict the responses of ecological communities and individual species to human-induced environmental change remains a key issue for ecologists and conservation managers alike. Responses are often variable among species within groups making general predictions difficult. One option is to include ecological trait information that might help to disentangle patterns of response and also provide greater understanding of how particular traits link whole clades to their environment. Although this ‘‘trait-guild” approach has been used for single disturbances, the importance of particular traits on general responses to multiple disturbances has not been explored. We used a mixed model analysis of 19 data sets from throughout the world to test the effect of ecological and life-history traits on the responses of bee species to different types of anthropogenic environmental change. These changes included habitat loss, fragmentation, agricultural intensification, pesticides and fire. Individual traits significantly affected bee species responses to different disturbances and several traits were broadly predictive among multiple disturbances. The location of nests – above vs. below ground – significantly affected response to habitat loss, agricultural intensification, tillage regime (within agriculture) and fire. Species that nested above ground were on average more negatively affected by isolation from natural habitat and intensive agricultural land use than were species nesting below ground. In contrast below-ground-nesting species were more negatively affected by tilling than were above-ground nesters. The response of different nesting guilds to fire depended on the time since the burn. Social bee species were more strongly affected by isolation from natural habitat and pesticides than were solitary bee species. Surprisingly, body size did not consistently affect species responses, despite its importance in determining many aspects of individuals’ interaction with their environment. Although synergistic interactions among traits remain to be explored, individual traits can be useful in predicting and understanding responses of related species to global change.

Goal sketching with activity diagrams

Goal orientation is acknowledged as an important paradigm in requirements engineering. The structure of a goal-responsibility model provides opportunities for appraising the intention of a development. Creating a suitable model under agile constraints (time, incompleteness and catching up after an initial burst of creativity) can be challenging. Here we propose a marriage of UML activity diagrams with goal sketching in order to facilitate the production of goal responsibility models under these constraints.

Meta-analysis: a unifying meta-likelihood approach framing unobserved heterogeneity, study covariates, publication bias, and study quality

OBJECTIVES: This contribution provides a unifying concept for meta-analysis integrating the handling of unobserved heterogeneity, study covariates, publication bias and study quality. It is important to consider these issues simultaneously to avoid the occurrence of artifacts, and a method for doing so is suggested here. METHODS: The approach is based upon the meta-likelihood in combination with a general linear nonparametric mixed model, which lays the ground for all inferential conclusions suggested here. RESULTS: The concept is illustrated at hand of a meta-analysis investigating the relationship of hormone replacement therapy and breast cancer. The phenomenon of interest has been investigated in many studies for a considerable time and different results were reported. In 1992 a meta-analysis by Sillero-Arenas et al. concluded a small, but significant overall effect of 1.06 on the relative risk scale. Using the meta-likelihood approach it is demonstrated here that this meta-analysis is due to considerable unobserved heterogeneity. Furthermore, it is shown that new methods are available to model this heterogeneity successfully. It is argued further to include available study covariates to explain this heterogeneity in the meta-analysis at hand. CONCLUSIONS: The topic of HRT and breast cancer has again very recently become an issue of public debate, when results of a large trial investigating the health effects of hormone replacement therapy were published indicating an increased risk for breast cancer (risk ratio of 1.26). Using an adequate regression model in the previously published meta-analysis an adjusted estimate of effect of 1.14 can be given which is considerably higher than the one published in the meta-analysis of Sillero-Arenas et al. In summary, it is hoped that the method suggested here contributes further to a good meta-analytic practice in public health and clinical disciplines.

Adaptation and speciation: what can F-st tell us?

A useful way of summarizing genetic variability among different populations is through estimates of the inbreeding coefficient, F-st. Several recent studies have tried to use the distribution of estimates of F-st from individual genetic loci to detect the effects of natural selection. However, the promise of this approach has yet to be fully realized owing to the pervasive dogma that this distribution is highly dependent on demographic history. Here, I review recent theoretical results that indicate that the distribution of estimates of F-st is generally expected to be robust to the vagaries of demographic history. I suggest that analyses based on it provide a useful first step for identifying candidate genes that might be under selection, and explore the ways in which this information can be used in ecological and evolutionary studies.

Evaluation of milk urea nitrogen as a diagnostic of protein feeding

An evaluation of milk urea nitrogen (MUN) as a diagnostic of protein feeding in dairy cows was performed using mean treatment data (n = 306) from 50 production trials conducted in Finland (n = 48) and Sweden (n = 2). Data were used to assess the effects of diet composition and certain animal characteristics on MUN and to derive relationships between MUN and the efficiency of N utilization for milk production and urinary N excretion. Relationships were developed using regression analysis based on either models of fixed factors or using mixed models that account for between-experiment variations. Dietary crude protein (CP) content was the best single predictor of MUN and accounted for proportionately 0.778 of total variance [ MUN (mg/dL) = -14.2 + 0.17 x dietary CP content (g/kg dry matter)]. The proportion of variation explained by this relationship increased to 0.952 when a mixed model including the random effects of study was used, but both the intercept and slope remained unchanged. Use of rumen degradable CP concentration in excess of predicted requirements, or the ratio of dietary CP to metabolizable energy as single predictors, did not explain more of the variation in MUN (R-2 = 0.767 or 0.778, respectively) than dietary CP content. Inclusion of other dietary factors with dietary CP content in bivariate models resulted in only marginally better predictions of MUN (R-2 = 0.785 to 0.804). Closer relationships existed between MUN and dietary factors when nutrients (CP to metabolizable energy) were expressed as concentrations in the diet, rather than absolute intakes. Furthermore, both MUN and MUN secretion (g/d) provided more accurate predictions of urinary N excretion (R-2 = 0.787 and 0.835, respectively) than measurements of the efficiency of N utilization for milk production (R-2 = 0.769). It is concluded that dietary CP content is the most important nutritional factor influencing MUN, and that measurements of MUN can be utilized as a diagnostic of protein feeding in the dairy cow and used to predict urinary N excretion.

Data based constructive identification - overcoming the curse of dimensionality

The modelling of a nonlinear stochastic dynamical processes from data involves solving the problems of data gathering, preprocessing, model architecture selection, learning or adaptation, parametric evaluation and model validation. For a given model architecture such as associative memory networks, a common problem in non-linear modelling is the problem of "the curse of dimensionality". A series of complementary data based constructive identification schemes, mainly based on but not limited to an operating point dependent fuzzy models, are introduced in this paper with the aim to overcome the curse of dimensionality. These include (i) a mixture of experts algorithm based on a forward constrained regression algorithm; (ii) an inherent parsimonious delaunay input space partition based piecewise local lineal modelling concept; (iii) a neurofuzzy model constructive approach based on forward orthogonal least squares and optimal experimental design and finally (iv) the neurofuzzy model construction algorithm based on basis functions that are Bézier Bernstein polynomial functions and the additive decomposition. Illustrative examples demonstrate their applicability, showing that the final major hurdle in data based modelling has almost been removed.

A new approach to reduced-order modelling

An error polynomial is defined, the coefficients of which indicate the difference at any instant between a system and a model of lower order approximating the system. It is shown how Markov parameters and time series proportionals of the model can be matched with those of the system by setting error polynomial coefficients to zero. Also discussed is the way in which the error between system and model can be considered as being a filtered form of an error input function specified by means of model parameter selection.

Plant-symbiotic fungi as chemical engineers: multi-genome analysis of the Clavicipitaceae reveals dynamics of alkaloid Loci

The fungal family Clavicipitaceae includes plant symbionts and parasites that produce several psychoactive and bioprotective alkaloids. The family includes grass symbionts in the epichloae clade (Epichloë and Neotyphodium species), which are extraordinarily diverse both in their host interactions and in their alkaloid profiles. Epichloae produce alkaloids of four distinct classes, all of which deter insects, and some—including the infamous ergot alkaloids—have potent effects on mammals. The exceptional chemotypic diversity of the epichloae may relate to their broad range of host interactions, whereby some are pathogenic and contagious, others are mutualistic and vertically transmitted (seed-borne), and still others vary in pathogenic or mutualistic behavior. We profiled the alkaloids and sequenced the genomes of 10 epichloae, three ergot fungi (Claviceps species), a morning-glory symbiont (Periglandula ipomoeae), and a bamboo pathogen (Aciculosporium take), and compared the gene clusters for four classes of alkaloids. Results indicated a strong tendency for alkaloid loci to have conserved cores that specify the skeleton structures and peripheral genes that determine chemical variations that are known to affect their pharmacological specificities. Generally, gene locations in cluster peripheries positioned them near to transposon-derived, AT-rich repeat blocks, which were probably involved in gene losses, duplications, and neofunctionalizations. The alkaloid loci in the epichloae had unusual structures riddled with large, complex, and dynamic repeat blocks. This feature was not reflective of overall differences in repeat contents in the genomes, nor was it characteristic of most other specialized metabolism loci. The organization and dynamics of alkaloid loci and abundant repeat blocks in the epichloae suggested that these fungi are under selection for alkaloid diversification. We suggest that such selection is related to the variable life histories of the epichloae, their protective roles as symbionts, and their associations with the highly speciose and ecologically diverse cool-season grasses.

Genetic variation at flowering time loci in wild and cultivated barley

The worldwide spread of barley cultivation required adaptation to agricultural environments far distant from those found in its centre of domestication. An important component of this adaptation is the timing of flowering, achieved predominantly in response to day length and temperature. Here, we use a collection of cultivars, landraces and wild barley accessions to investigate the origins and distribution of allelic diversity at four major flowering time loci, mutations at which have been under selection during the spread of barley cultivation into Europe. Our findings suggest that while mutant alleles at the PPD-H1 and PPD-H2 photoperiod loci occurred pre-domestication, the mutant vernalization non-responsive alleles utilized in landraces and cultivars at the VRN-H1 and VRN-H2 loci occurred post-domestication. The transition from wild to cultivated barley is associated with a doubling in the number of observed multi-locus flowering-time haplotypes, suggesting that the resulting phenotypic variation has aided adaptation to cultivation in the diverse ecogeographic locations encountered. Despite the importance of early-flowering alleles during the domestication of barley in Europe, we show that novel VRN alleles associated with early flowering in wild barley have been lost in domesticates, highlighting the potential of wild germplasm as a source of novel allelic variation for agronomic traits.

Property loss potentials for European midlatitude storms in a changing climate

Winter storms of the midlatitudes are an important factor for property losses caused by natural hazards over Europe. The storm series in early 1990 and late 1999 led to enormous economic damages and insured claims. Although significant trends in North Atlantic/European storm activity have not been identified for the last few decades, recent studies provide evidence that under anthropogenic climate change the number of extreme storms could increase, whereas the total number of cyclones may be slightly reduced. In this study, loss potentials derived from an ensemble of climate models using a simple storm damage model under climate change conditions are shown. For the United Kingdom and Germany ensemble-mean storm-related losses are found to increase by up to 37%. Furthermore, the interannual variability of extreme events will increase leading to a higher risk of extreme storm activity and related losses.