We report on the dynamics of collective alignment in groups of the cichlid fish, Etroplus suratensis. Focusing on small-to-intermediate sized groups (10 N 100), we demonstrate that schooling (highly polarised and coherent motion) is noise-induced, arising from the intrinsic stochasticity associated with finite numbers of interacting fish. The fewer the fish, the greater the (multiplicative) noise and therefore the likelihood of alignment. Such empirical evidence is rare, and tightly constrains the possible underlying interactions between fish: computer simulations indicate that E. suratensis align with each other one at a time, which is at odds with the canonical mechanism of collective alignment, local direction-averaging. More broadly, our results confirm that, rather than simply obscuring otherwise deterministic dynamics, noise is fundamental to the characterisation of emergent collective behaviours, suggesting a need to re-appraise aspects of both collective motion and behavioural inference. arXiv:1903.12132v1 [cond-mat.stat-mech]

Animal groups exhibit many emergent properties that are a consequence of local interactions. Linking individual-level behaviour, which is often stochastic and local, to coarse-grained descriptions of animal groups has been a question of fundamental interest from both biological and mathematical perspectives. In this book chapter, we present two complementary approaches to derive coarse-grained descriptions of collective behaviour at so-called mesoscopic scales, which account for the stochasticity arising from the finite sizes of animal groups. We construct stochastic differential equations (SDEs) for a coarse-grained variable that describes the order/consensus within a group. The first method of construction is based on van Kampen's system-size expansion of transition rates. The second method employs Gillespie's chemical Langevin equations. We apply these two methods to two microscopic models from the literature, in which organisms stochastically interact and choose between two directions/choices of foraging. These 'binary-choice' models differ only in the types of interactions between individuals, with one assuming simple pairwise interactions, and the other incorporating ternary effects. In both cases, the derived mesoscopic SDEs have multiplicative/state-dependent noise, i.e., the strength of the noise depends on the current state of the system. However, the different models demonstrate the contrasting effects of noise: increasing the order/consensus in the pairwise interaction model, whilst reducing the order/consensus in the higher-order interaction model. We verify the validity of such mesoscopic behaviour by numerical simulations of the underlying microscopic models. Although both methods yield identical SDEs for binary-choice systems that are effectively one-dimensional, the relative tractability of the chemical Langevin approach is beneficial in generalizations to higher-dimensions. We hope that this book chapter provides a pedagogical review of two complementary methods to construct mesoscopic descriptions from microscopic rules, how the noise in mesoscopic models is often multiplicative/state-dependent, and finally, how such noise can have counter-intuitive effects on shaping collective behaviour.

Leishmania infantum, causative agent of visceral leishmaniasis in humans, illustrates a complex lifecycle pertaining to two extreme environments, namely, the gut of the sandfly vector and human macrophages. Leishmania is capable of dynamically adapting and tactically switching between these critically hostile situations. The possible metabolic routes ventured by the parasite to achieve this exceptional adaptation to its varying environments are still poorly understood. In this study, we present an extensively reconstructed energy metabolism network of Leishmania infantum as an attempt to identify certain strategic metabolic routes preferred by the parasite to optimize its survival in such dynamic environments. The reconstructed network consists of 142 genes encoding for enzymes performing 237 reactions distributed across five distinct model compartments. We annotated the subcellular locations of different enzymes and their reactions on the basis of strong literature evidence and sequence-based detection of cellular localization signal within a protein sequence. To explore the diverse features of parasite metabolism the metabolic network was implemented and analyzed as a constraint-based model. Using a systems-based approach, we also put forth an extensive set of lethal reaction knockouts; some of which were validated using published data on Leishmania species. Performing a robustness analysis, the model was rigorously validated and tested for the secretion of overflow metabolites specific to Leishmania under varying extracellular oxygen uptake rate. Further, the fate of important non-essential amino acids in L. infantum metabolism was investigated. Stage-specific scenarios of L. infantum energy metabolism were incorporated in the model and key metabolic differences were outlined. Analysis of the model revealed the essentiality of glucose uptake, succinate fermentation, glutamate biosynthesis and an active TCA cycle as driving forces for parasite energy metabolism and its optimal growth. Finally, through our in silico knockout analysis, we could identify possible therapeutic targets that provide experimentally testable hypotheses.

In animal groups, individual decisions are best characterized by probabilistic rules. Furthermore, animals of many species live in small groups. Probabilistic interactions among small numbers of individuals lead to a so-called intrinsic noise at the group level. Theory predicts that the strength of intrinsic noise is not a constant but often depends on the collective state of the group; hence, it is also called a state-dependent noise or a multiplicative noise . Surprisingly, such noise may produce collective order. However, only a few empirical studies on collective behaviour have paid attention to such effects owing to the lack of methods that enable us to connect data with theory. Here, we demonstrate a method to characterize the role of stochasticity directly from high-resolution time-series data of collective dynamics. We do this by employing two well-studied individual-based toy models of collective behaviour. We argue that the group-level noise may encode important information about the underlying processes at the individual scale. In summary, we describe a method that enables us to establish connections between empirical data of animal (or cellular) collectives and the phenomenon of noise-induced states, a field that is otherwise largely limited to the theoretical literature. This article is part of the theme issue ‘Multi-scale analysis and modelling of collective migration in biological systems’.

Most real-world ecological dynamics, ranging from ecosystem dynamics to collective animal movement, are inherently stochastic in nature. Stochastic differential equations (SDEs) are a popular modelling framework to model dynamics with intrinsic randomness. Here, we focus on the inverse question: If one has empirically measured time-series data from some system of interest, is it possible to discover the SDE model that best describes the data. Here, we present PyDaddy (Python library for Data Driven Dynamics), a toolbox to construct and analyze interpretable SDE models based on time-series data. We combine traditional approaches for data-driven SDE reconstruction with an equation learning approach, to derive symbolic equations governing the stochastic dynamics. The toolkit is presented as an open-source Python library, and consists of tools to construct and analyze SDEs. Functionality is included for visual examination of the stochastic structure of the data, guided extraction of the functional form of the SDE, and diagnosis and debugging of the underlying assumptions and the extracted model. Using simulated time-series datasets, exhibiting a wide range of dynamics, we show that PyDaddy is able to correctly identify underlying SDE models. We demonstrate the applicability of the toolkit to real-world data using a previously published movement data of a fish school. Starting from the time-series of the observed polarization of the school, pyDaddy readily discovers the SDE model governing the dynamics of group polarization. The model recovered by PyDaddy is consistent with the previous study. In summary, stochastic and noise-induced effects are central to the dynamics of many biological systems. In this context, we present an easy-to-use package to reconstruct SDEs from timeseries data.