How much flower-rich habitat is enough for wild pollinators? Answering a key policy question with incomplete knowledge

In 2013, an opportunity arose in England to develop an agri-environment package for wild pollinators, as part of the new Countryside Stewardship scheme launched in 2015. It can be understood as a 'policy window', a rare and time-limited opportunity to change policy, supported by a narrative about pollinator decline and widely supported mitigating actions. An agri-environment package is a bundle of management options that together supply sufficient resources to support a target group of species. This paper documents information that was available at the time to develop such a package for wild pollinators. Four questions needed answering: (1) Which pollinator species should be targeted? (2) Which resources limit these species in farmland? (3) Which management options provide these resources? (4) What area of each option is needed to support populations of the target species? Focussing on wild bees, we provide tentative answers that were used to inform development of the package. There is strong evidence that floral resources can limit wild bee populations, and several sources of evidence identify a set of agri-environment options that provide flowers and other resources for pollinators. The final question could only be answered for floral resources, with a wide range of uncertainty. We show that the areas of some floral resource options in the basic Wild Pollinator and Farmland Wildlife Package (2% flower-rich habitat and 1 km flowering hedgerow), are sufficient to supply a set of six common pollinator species with enough pollen to feed their larvae at lowest estimates, using minimum values for estimated parameters where a range was available. We identify key sources of uncertainty, and stress the importance of keeping the Package flexible, so it can be revised as new evidence emerges about how to achieve the policy aim of supporting pollinators on farmland.

The urban cool island phenomenon in a high-rise high-density city and its mechanisms

The urban heat island (UHI) phenomenon has been studied extensively, but there are relatively fewer reports on the so-called urban cool island (UCI) phenomenon. We reveal here that the UCI phenomenon exists in Hong Kong during the day, and is associated with the UHI at night under all wind and cloud conditions. The possible mechanisms for the UCI phenomenon in such a high-rise compact city have been discovered using a lumped urban air temperature model. A new concept of urban cool island degree hours (UCIdh) to measure the UCI intensity and duration is proposed. Our analyses reveal that when anthropogenic heat is small or absent, a high-rise and high-density city experiences a significant daytime UCI effect. This is explained by an intensified heat storage capacity and the reduced solar radiation gain of urban surfaces. However, if anthropogenic heat in the urban area increases further, the UCI phenomenon still exists, yet UCIdh decrease dramatically in a high-rise compact city. In a low-rise, low-density city, the UCI phenomenon also occurs when there is no anthropogenic heat, but easily disappears when there is little anthropogenic heat, and the UHI phenomenon dominates. This probably explains why the UHI phenomenon is often observed, but the UCI phenomenon is rarely observed. The co-existence of urban heat/cool island phenomena implies reduction of the daily temperature range (DTR) in such cities, and its dependence on urban morphology also implies that urban morphology can be used to control the urban thermal environment.

Sparse density estimator with tunable kernels

A new sparse kernel density estimator with tunable kernels is introduced within a forward constrained regression framework whereby the nonnegative and summing-to-unity constraints of the mixing weights can easily be satisfied. Based on the minimum integrated square error criterion, a recursive algorithm is developed to select significant kernels one at time, and the kernel width of the selected kernel is then tuned using the gradient descent algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing very sparse kernel density estimators with competitive accuracy to existing kernel density estimators.

Sparse density estimation on multinomial manifold combining local component analysis

A new sparse kernel density estimator is introduced based on the minimum integrated square error criterion combining local component analysis for the finite mixture model. We start with a Parzen window estimator which has the Gaussian kernels with a common covariance matrix, the local component analysis is initially applied to find the covariance matrix using expectation maximization algorithm. Since the constraint on the mixing coefficients of a finite mixture model is on the multinomial manifold, we then use the well-known Riemannian trust-region algorithm to find the set of sparse mixing coefficients. The first and second order Riemannian geometry of the multinomial manifold are utilized in the Riemannian trust-region algorithm. Numerical examples are employed to demonstrate that the proposed approach is effective in constructing sparse kernel density estimators with competitive accuracy to existing kernel density estimators.