Guidelines for correlation coefficient threshold settings in metabolite correlation networks exemplified on a potato association panel

Background Correlation network analysis has become an integral tool to study metabolite datasets. Networks are constructed by omitting correlations between metabolites based on two thresholds—namely the r and the associated p-values. While p-value threshold settings follow the rules of multiple hypotheses testing correction, guidelines for r-value threshold settings have not been defined. Results Here, we introduce a method that allows determining the r-value threshold based on an iterative approach, where different networks are constructed and their network topology is monitored. Once the network topology changes significantly, the threshold is set to the corresponding correlation coefficient value. The approach was exemplified on: (i) a metabolite and morphological trait dataset from a potato association panel, which was grown under normal irrigation and water recovery conditions; and validated (ii) on a metabolite dataset of hearts of fed and fasted mice. For the potato normal irrigation correlation network a threshold of Pearson’s |r|≥ 0.23 was suggested, while for the water recovery correlation network a threshold of Pearson’s |r|≥ 0.41 was estimated. For both mice networks the threshold was calculated with Pearson’s |r|≥ 0.84. Conclusions Our analysis corrected the previously stated Pearson’s correlation coefficient threshold from 0.4 to 0.41 in the water recovery network and from 0.4 to 0.23 for the normal irrigation network. Furthermore, the proposed method suggested a correlation threshold of 0.84 for both mice networks rather than a threshold of 0.7 as applied earlier. We demonstrate that the proposed approach is a valuable tool for constructing biological meaningful networks.

Confidence set for connected stocks of stock market

The problem of analysis of pairwise connections between stocks of financial market by observations on stock returns is considered. Such problem arise in stock market network analysis. It is assumed that joint distribution of stock returns belongs to the wide class of elliptical distributions. Classical Pearson correlation, Fechner correlation and Kendall correlation are used as measure of dependence. The construction problems of sets of stocks with strong connections between its returns are investigated. The construction problems of sets of stocks with strong connections between its returns are investigated. To construct such sets the multiple hypotheses testing procedures on values of correlations are used. The properties of these statistical procedures are investigated by simulations. The simulation results show that procedures based on individual Fechner and Kendall tests lead to such sets of stocks with given confidence probability unlike procedure based on Pearson individual tests which do not control the confidence probability. At the same time it is emphasized that for Student distribution the constructed set is nearly the same to the confidence set. The procedure of consistency testing with elliptical model is proposed and exemplified. The peculiarities of the model are discussed.

How to make methodological decisions when inferring social networks

ABSTRACTConstructing and analysing social networks data can be challenging. When designing new studies, researchers are confronted with having to make decisions about how data are collected and networks are constructed, and the answers are not always straightforward. The current lack of guidance on building a social network for a new study system might lead researchers to try several different methods, and risk generating false results arising from multiple hypotheses testing. We suggest an approach for making decisions when developing a network without jeopardising the validity of future hypothesis tests. We argue that choosing the best edge definition for a network can be made using a priori knowledge of the species, and testing hypotheses that are known and independent from those that the network will ultimately be used to evaluate. We illustrate this approach by conducting a pilot study with the aim of identifying how to construct a social network for colonies of cooperatively breeding sociable weavers. We first identified two ways of collecting data using different numbers of feeders and three ways to define associations among birds. We then identified which combination of data collection and association definition maximised (i) the assortment of individuals into ‘breeding groups’ (birds that contribute towards the same nest and maintain cohesion when foraging), and (ii) socially differentiated relationships (more strong and weak relationships than expected by chance). Our approach highlights how existing knowledge about a system can be used to help navigate the myriad of methodological decisions about data collection and network inference.SIGNIFICANCE STATEMENTGeneral guidance on how to analyse social networks has been provided in recent papers. However less attention has been given to system-specific methodological decisions when designing new studies, specifically on how data are collected, and how edge weights are defined from the collected data. This lack of guidance can lead researchers into being less critical about their study design and making arbitrary decisions or trying several different methods driven by a given preferred hypothesis of interest without realising the consequences of such approaches. Here we show that pilot studies combined with a priori knowledge of the study species’ social behaviour can greatly facilitate making methodological decisions. Furthermore, we empirically show that different decisions, even if data are collected under the same context (e.g. foraging), can affect the quality of a network.