Bayesian inference for stochastic epidemic models with time-inhomogeneous removal rates

Stochastic compartmental models of the SEIR type are often used to make inferences on epidemic processes from partially observed data in which only removal times are available. For many epidemics, the assumption of constant removal rates is not plausible. We develop methods for models in which these rates are a time-dependent step function. A reversible jump MCMC algorithm is described that permits Bayesian inferences to be made on model parameters, particularly those associated with the step function. The method is applied to two datasets on outbreaks of smallpox and a respiratory disease. The analyses highlight the importance of allowing for time dependence by contrasting the predictive distributions for the removal times and comparing them with the observed data.      

Architecture of the pruned tree: impact of contrasted pruning procedures over 2 years on shoot demography and spatial distribution of leaf area in apple (Malus domestica)

BACKGROUND AND AIMS: Demography and spatial distribution of shoots are rarely studied on pruned trees. The present 2-year study deals with the effect of pruning strategies on shoot demography and development, and consequences on the spatial distribution of leaf area in three architecturally contrasted - from type II to IV - apple cultivars: 'Scarletspur Delicious', 'Golden Delicious' and 'Granny Smith'. METHODS: All trees were initially subjected during 5 years to Central Leader training with winter heading on all long shoots. For 2 years, half of the trees were further trained with Centrifugal training, where removal of flowering shoots - called extinction pruning - was carried out along the trunk and at the bottom of branches at flowering time. During these 2 years, shoot type (vegetative, inflorescence) and length, and the three-dimensional spatial distribution of all shoots were assessed with an electromagnetic digitizer. KEY RESULTS: Shoot demography, frequency of transitions toward an inflorescence from either an inflorescence (bourse-over-bourse) or a vegetative shoot (trend toward flowering), and the number of bourse-shoots per bourse were strongly affected by cultivar, with little influence of tree manipulation. In contrast, the proportion of vegetative long shoots developing from previous year latent buds was significantly lower in Centrifugal-trained trees for the three cultivars. Canopy volume showed large variations between cultivars, but only that of 'Granny Smith' was affected by tree manipulation in the 2 years. Spatial distribution of shoots varied significantly according to cultivar and manipulation. In 'Scarletspur Delicious' and, to a lesser extent 'Golden Delicious', the distribution of vegetative and flowering shoots in the outer and the inner parts, respectively, was not affected by tree manipulation. In contrast, in 'Granny Smith', vegetative shoots were stimulated in the periphery of Central Leader trees, whereas flowering shoots were stimulated in the periphery of Centrifugal-trained trees. CONCLUSIONS: In apple, the variability of responses to contrasted pruning strategies partly depends on the genetically determined growth and flowering habit of the cultivar.     

Stochastic simulation of daily air temperature and precipitation from monthly normals in North America north of Mexico

A simple, stochastic daily temperature and precipitation generator (TEMPGEN) was developed to generate inputs for the study of the effects of climate change on models driven by daily weather information when climate data are available as monthly summaries. The model uses as input only 11 sets of monthly normal statistics from individual weather stations. It needs no calibration, and was parameterized and validated for use in Canada and the continental United States. Monthly normals needed are: mean and standard deviation of daily minimum and maximum temperature, first and second order autoregressive terms for daily deviations of minimum and maximum temperatures from their daily means, correlation of deviations of daily minimum and maximum temperatures, total precipitation, and the interannual variance of total precipitation. The statistical properties and distributions of daily temperature and precipitation data produced by this generator compared quite favorably with observations from 708 stations throughout North America (north of Mexico). The algorithm generates realistic seasonal patterns, variability and extremes of temperature, precipitation, frost-free periods and hot spells. However, it predicts less accurately the daily probability of precipitation, extreme precipitation events and the duration of extreme droughts.     

Phylogeographic patterns in Drosophila montana

The Drosophila virilis species group offers valuable opportunities for studying the roles of chromosomal re-arrangements and mating signals in speciation. The 13 species are divided into two subgroups, the montana and virilis 'phylads'. There is greater differentiation among species within the montana phylad in both karyotype and acoustic signals than exists among members of the virilis phylad. Drosophila montana is a divergent species which is included in the montana phylad. Here, we analyse the phylogeography of D. montana to provide a framework for understanding divergence of acoustic signals among populations. We analysed mitochondrial sequences corresponding to the cytochrome oxidase I and cytochrome oxidase II genes, as well as 16 microsatellite loci, from 108 lines of D. montana covering most of the species' range. The species shows a clear genetic differentiation between North American and Scandinavian populations. Microsatellite allele frequencies and mitochondrial DNA haplotypes gave significant FST values between populations from Canada, USA and Finland. A Bayesian analysis of population structure based on the microsatellite frequencies showed four genetically distinct groups, corresponding to these three populations plus a small sample from Japan. A network based on mitochondrial haplotypes showed two Finnish clades of very different shape and variability, and another clade with all sequences from North America and Japan. All D. montana populations showed evidence of demographic expansion but the patterns inferred by coalescent analysis differed between populations. The divergence times between Scandinavian and North American clades were estimated to range from 450,000 to 900,000 years with populations in Canada and the USA possibly representing descendants of different refugial populations. Long-term separation of D. montana populations could have provided the opportunity for differentiation observed in male signal traits, especially carrier frequency of the song, but relaxation of sexual selection during population expansion may have been necessary.     

Seed bank dynamics govern persistence of Brassica hybrids in crop and natural habitats

Background and Aims Gene flow from crops to their wild relatives has the potential to alter population growth rates and demography of hybrid populations, especially when a new crop has been genetically modified (GM). This study introduces a comprehensive approach to assess this potential for altered population fitness, and uses a combination of demographic data in two habitat types and mathematical (matrix) models that include crop rotations and outcrossing between parental species.Methods Full life-cycle demographic rates, including seed bank survival, of non-GM Brassica rapa × B. napus F₁ hybrids and their parent species were estimated from experiments in both agricultural and semi-natural habitats. Altered fitness potential was modelled using periodic matrices including crop rotations and outcrossing between parent species.Key Results The demographic vital rates (i.e. for major stage transitions) of the hybrid population were intermediate between or lower than both parental species. The population growth rate (λ) of hybrids indicated decreases in both habitat types, and in a semi-natural habitat hybrids became extinct at two sites. Elasticity analyses indicated that seed bank survival was the greatest contributor to λ. In agricultural habitats, hybrid populations were projected to decline, but with persistence times up to 20 years. The seed bank survival rate was the main driver determining persistence. It was found that λ of the hybrids was largely determined by parental seed bank survival and subsequent replenishment of the hybrid population through outcrossing of B. rapa with B. napus.Conclusions Hybrid persistence was found to be highly dependent on the seed bank, suggesting that targeting hybrid seed survival could be an important management option in controlling hybrid persistence. For local risk mitigation, an increased focus on the wild parent is suggested. Management actions, such as control of B. rapa, could indirectly reduce hybrid populations by blocking hybrid replenishment.     

Deciphering death: a commentary on Gompertz (1825) ‘On the nature of the function expressive of the law of human mortality,and on a new mode of determining the value of life contingencies’

In 1825, the actuary Benjamin Gompertz read a paper, ‘On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies’, to the Royal Society in which he showed that over much of the adult human lifespan, age-specific mortality rates increased in an exponential manner. Gompertz''s work played an important role in shaping the emerging statistical science that underpins the pricing of life insurance and annuities. Latterly, as the subject of ageing itself became the focus of scientific study, the Gompertz model provided a powerful stimulus to examine the patterns of death across the life course not only in humans but also in a wide range of other organisms. The idea that the Gompertz model might constitute a fundamental ‘law of mortality’ has given way to the recognition that other patterns exist, not only across the species range but also in advanced old age. Nevertheless, Gompertz''s way of representing the function expressive of the pattern of much of adult mortality retains considerable relevance for studying the factors that influence the intrinsic biology of ageing. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.     

Demographic inferences using short‐read genomic data in an approximate Bayesian computation framework: in silico evaluation of power,biases and proof of concept in Atlantic walrus

Approximate Bayesian computation (ABC) is a powerful tool for model‐based inference of demographic histories from large genetic data sets. For most organisms, its implementation has been hampered by the lack of sufficient genetic data. Genotyping‐by‐sequencing (GBS) provides cheap genome‐scale data to fill this gap, but its potential has not fully been exploited. Here, we explored power, precision and biases of a coalescent‐based ABC approach where GBS data were modelled with either a population mutation parameter (θ) or a fixed site (FS) approach, allowing single or several segregating sites per locus. With simulated data ranging from 500 to 50 000 loci, a variety of demographic models could be reliably inferred across a range of timescales and migration scenarios. Posterior estimates were informative with 1000 loci for migration and split time in simple population divergence models. In more complex models, posterior distributions were wide and almost reverted to the uninformative prior even with 50 000 loci. ABC parameter estimates, however, were generally more accurate than an alternative composite‐likelihood method. Bottleneck scenarios proved particularly difficult, and only recent bottlenecks without recovery could be reliably detected and dated. Notably, minor‐allele‐frequency filters – usual practice for GBS data – negatively affected nearly all estimates. With this in mind, we used a combination of FS and θ approaches on empirical GBS data generated from the Atlantic walrus (Odobenus rosmarus rosmarus), collectively providing support for a population split before the last glacial maximum followed by asymmetrical migration and a high Arctic bottleneck. Overall, this study evaluates the potential and limitations of GBS data in an ABC‐coalescence framework and proposes a best‐practice approach.     

Root turnover in pasture species: chicory,lucerne, perennial ryegrass and white clover

For pastures, root turnover can have an important influence on nutrient and carbon cycling, and plant performance. Turnover was calculated from mini‐rhizotron observations for chicory (Cichorium intybus), lucerne (Medicago sativa), perennial ryegrass (Lolium perenne) and white clover (Trifolium repens) grown in the Manawatu, New Zealand. The species were combined factorially with four earthworm species treatments and a no‐earthworm control. Split plots compared the effects of not cutting and cutting the shoots at intervals. Observations were made c. 18 days apart for 2.5 years. This article concentrates on differences between plant species in root turnover in the whole soil profile to 40 cm depth. At this scale, earthworm effects were generally small and short lived. For ryegrass and white clover, root length and mass were linearly related (R² = 0.82–0.99). For chicory and lucerne, the relationships were poorer (R² = 0.38–0.77), so for those species length turnover may be a poor indicator of mass turnover. Standing root length, total growth and death generally decreased in the sequence ryegrass > lucerne > chicory = white clover. In length terms, scaled turnover (growth divided by average standing root length) generally followed the sequence lucerne > white clover > perennial ryegrass = chicory. Across species the scaled turnover rate averaged 3.4 per year or 0.9% per day. Cutting shoots reduced standing root length, growth and death, but increased scaled turnover. These results indicate fast and prolonged root turnover. For ryegrass and white clover, at least there is need to reappraise how to measure and model shoot : root ratios, dry matter production and carbon cycling.     

Parallel declines in survival of adult Northern Fulmars Fulmarus glacialis at colonies in Scotland and Ireland

Assessing broad‐scale changes in seabird populations across the North Atlantic requires an integration of available datasets to understand the spatial extent of potential drivers and demographic change. Here, we compared survival of Northern Fulmars Fulmarus glacialis from a Scottish and an Irish colony from 1974 to 2009. Despite lower recapture probabilities of monel‐ringed Irish birds compared with colour‐ringed Scottish birds, survival probability decreased at both colonies. The extent to which the decline in survival is related to density‐dependent processes or other external drivers remains uncertain, but our results suggest that these changes in survival are possibly indicative of larger‐scale processes and are not confined to local colony dynamics.     

Age‐ratio bias among hunter‐based surveys of Eurasian Wigeon Anas penelope based on wing vs. field samples

We compared age and sex ratios among Eurasian Wigeon Anas penelope derived from Danish field observations and hunter‐based shot samples throughout an entire winter. Sex ratios did not differ significantly between the two samples. Overall, first‐year males were more than three times more likely to be represented than adult males in the hunter sample compared with field samples and were 7–20 times overrepresented in the hunting sample at the beginning of the season. These results confirm the need to account for such bias and its temporal variation when using the results of hunting surveys to model population parameters. Hunter‐shot age ratios may provide a long‐term measure of reproductive success of dabbling duck flyway populations given an understanding of such bias.