We introduce a nonparametric approach for estimating drift and diffusion functions in systems of stochastic differential equations from observations of the state vector. Gaussian processes are used as flexible models for these functions, and estimates are calculated directly from dense data sets using Gaussian process regression. We develop an approximate expectation maximization algorithm to deal with the unobserved, latent dynamics between sparse observations. The posterior over states is approximated by a piecewise linearized process of the Ornstein-Uhlenbeck type and the maximum a posteriori estimation of the drift is facilitated by a sparse Gaussian process approximation.

We present a method for the nonparametric estimation of the drift function of certain types of stochastic differential equations from the empirical density. It is based on a variational formulation of the Fokker-Planck equation. The minimization of an empirical estimate of the variational functional using kernel based regularization can be performed in closed form. We demonstrate the performance of the method on second order, Langevin-type equations and show how the method can be generalized to other noise models.

Insect monitoring has gained global public attention in recent years in the context of insect decline and biodiversity loss. Monitoring methods that can collect samples over a long period of time and independently of human influences are of particular importance. While these passive collection methods, e.g. suction traps, provide standardized and comparable data sets, the time required to analyze the large number of samples and trapped specimens is high. Another challenge is the necessary high level of taxonomic expertise required for accurate specimen processing. These factors create a bottleneck in specimen processing. In this context, machine learning, image recognition and artificial intelligence have emerged as promising tools to address the shortcomings of manual identification and quantification in the analysis of such trap catches. Aphids are important agricultural pests that pose a significant risk to several important crops and cause high economic losses through feeding damage and transmission of plant viruses. It has been shown that long-term monitoring of migrating aphids using suction traps can be used to make, adjust and improve predictions of their abundance so that the risk of plant viruses spreading through aphids can be more accurately predicted. With the increasing demand for alternatives to conventional pesticide use in crop protection, the need for predictive models is growing, e.g. as a basis for resistance development and as a measure for resistance management. In this context, advancing climate change has a strong influence on the total abundance of migrating aphids as well as on the peak occurrences of aphids within a year. Using aphids as a model organism, we demonstrate the possibilities of systematic monitoring of insect pests and the potential of future technical developments in the subsequent automated identification of individuals through to the use of case data for intelligent forecasting models. Using aphids as an example, we show the potential for systematic monitoring of insect pests through technical developments in the automated identification of individuals from static images (i.e. advances in image recognition software). We discuss the potential applications with regard to the automatic processing of insect case data and the development of intelligent prediction models.

Machine learning techniques are shifting the boundaries of feasibility in many fields of ethological research. Here we describe an application of machine learning to the detection/measurement of hygienic behaviour, an important breeding trait in the honey bee (Apis mellifera). Hygienic worker bees are able to detect and destroy diseased brood, thereby reducing the reproduction of economically important pathogens and parasites such as the Varroa mite (Varroa destructor). Video observation of this behaviour on infested combs has many advantages over other methods of measurement, but analysing the recorded material is extremely time-consuming. We approached this problem by combining automatic tracking of bees in the video recordings, extracting relevant features, and training a multi-layer discriminator on positive and negative examples of the behaviour of interest. Including expert knowledge into the design of the features lead to an efficient model for identifying the uninteresting parts of the video which can be safely skipped. This algorithm was then used to semiautomatically identify individual worker bees involved in the behaviour. Application of the machine learning method allowed to save 70% of the time required for manual analysis, and substantially increased the number of cell openings correctly identified. It thereby turns video-observation of individual cell opening events into an economically competitive method for selecting potentially resistant bees. This method presents an example of how machine learning can used to boost ethological research, and how it can generate new knowledge by explaining the learned decision rule in form of meaningful parameters.