Nut crop yield records show that budbreak-based chilling requirements may not reflect yield decline chill thresholds.

Warming winters due to climate change may critically affect temperate tree species. Insufficiently cold winters are thought to result in fewer viable flower buds and the subsequent development of fewer fruits or nuts, decreasing the yield of an orchard or fecundity of a species. The best existing approximation for a threshold of sufficient cold accumulation, the "chilling requirement" of a species or variety, has been quantified by manipulating or modeling the conditions that result in dormant bud breaking. However, the physiological processes that affect budbreak are not the same as those that determine yield. This study sought to test whether budbreak-based chilling thresholds can reasonably approximate the thresholds that affect yield, particularly regarding the potential impacts of climate change on temperate tree crop yields. County-wide yield records for almond (Prunus dulcis), pistachio (Pistacia vera), and walnut (Juglans regia) in the Central Valley of California were compared with 50 years of weather records. Bayesian nonparametric function estimation was used to model yield potentials at varying amounts of chill accumulation. In almonds, average yields occurred when chill accumulation was close to the budbreak-based chilling requirement. However, in the other two crops, pistachios and walnuts, the best previous estimate of the budbreak-based chilling requirements was 19-32 % higher than the chilling accumulations associated with average or above average yields. This research indicates that physiological processes beyond requirements for budbreak should be considered when estimating chill accumulation thresholds of yield decline and potential impacts of climate change.

Detecting nonlinear response of spring phenology to climate change by Bayesian analysis.

The impact of climate change on the advancement of plant phenological events has been heavily studied in the last decade. Although the majority of spring plant phenological events have been trending earlier, this is not universally true. Recent work has suggested that species that are not advancing in their spring phenological behavior are responding more to lack of winter chill than increased spring heat. One way to test this hypothesis is by evaluating the behavior of a species known to have a moderate to high chilling requirement and examining how it is responding to increased warming. This study used a 60-year data set for timing of leaf-out and male flowering of walnut (Juglans regia) cultivar 'Payne' to examine this issue. The spring phenological behavior of 'Payne' walnut differed depending on bud type. The vegetative buds, which have a higher chilling requirement, trended toward earlier leaf-out until about 1994, when they shifted to later leaf-out. The date of male bud pollen shedding advanced over the course of the whole record. Our findings suggest that many species which have exhibited earlier bud break are responding to warmer spring temperatures, but may shift into responding more to winter temperatures (lack of adequate chilling) as warming continues.

Bayesian analysis of the species-specific lengthening of the growing season in two European countries and the influence of an insect pest.

A recent lengthening of the growing season in mid and higher latitudes of the northern hemisphere is reported as a clear indicator for climate change impacts. Using data from Germany (1951-2003) and Slovenia (1961-2004), we study whether changes in the start, end, and length of the growing season differ among four deciduous broad-leaved tree species and countries, how the changes are related to temperature changes, and what might be the confounding effects of an insect attack. The functional behaviour of the phenological and climatological time series and their trends are not analysed by linear regression, but by a new Bayesian approach taking into account different models for the functional description (one change-point, linear, constant models). We find advanced leaf unfolding in both countries with the same species order (oak > horse chestnut, beech, and birch). However, this advance is non linear over time and more apparent in Germany with clear change-points in the late 1970s, followed by marked advances (on average 3.67 days decade(-1) in the 2000s). In Slovenia, we find a more gradual advance of onset dates (on average 0.8 days decade(-1) in the 2000s). Leaf colouring of birch, beech, and oak has been slightly delayed in the last 3 decades, especially in Germany, however with no clear functional behaviour. Abrupt changes in leaf colouring dates of horse chestnut with recent advancing onset dates can be linked across countries to damage by a newly emerging pest, the horse chestnut leaf-miner (Cameraria ohridella). The lengthening of the growing season, more distinct in Germany than in Slovenia (on average 4.2 and 1.0 days decade(-1) in the 2000s, respectively), exhibits the same species order in both countries (oak > birch > beech). Damage by horse chestnut leaf-miner leads to reduced lengthening (Germany) and drastic shortening (Slovenia) of the horse chestnut growing season (-12 days decade(-1) in the 2000s). Advanced spring leaf unfolding and lengthening of the growing season of oak, beech and birch are highly significantly related to increasing March temperatures in both countries. Only beech and oak leaf unfolding in Germany, which is generally observed later in the year than that of the other two species, is more closely correlated with April temperatures, which comparably exhibit marked change-points at the end of the 1970s.

Invariance priors for Bayesian feed-forward neural networks.

Neural networks (NN) are famous for their advantageous flexibility for problems when there is insufficient knowledge to set up a proper model. On the other hand, this flexibility can cause overfitting and can hamper the generalization of neural networks. Many approaches to regularizing NN have been suggested but most of them are based on ad hoc arguments. Employing the principle of transformation invariance, we derive a general prior in accordance with the Bayesian probability theory for feed-forward networks. An optimal network is determined by Bayesian model comparison, verifying the applicability of this approach. Additionally the prior presented affords cell pruning.

Bayesian neural-networks-based evaluation of binary speckle data.

We present a new method using Bayesian probability theory and neural networks for the evaluation of speckle interference patterns for an automated analysis of deformation and erosion measurements. The method is applied to the fringe pattern reconstruction of speckle measurements with a Twyman-Green interferometer. Given a binary speckle image, the method returns the fringe pattern without noise, thus removing the need for smoothing and allowing a straightforward unwrapping procedure and determination of the surface shape. Because no parameters have to be adjusted, the method is especially suited for continuous and automated monitoring of surface changes.