From noise to knowledge: how randomness generates novel phenomena and reveals information

Boettiger, Carl

doi:10.1111/ele.13085

Cited by 68 publications

(81 citation statements)

References 104 publications

(161 reference statements)

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“…Although stochasticity is well known to be one of the key sources of variability in ecological communities, it is not considered as a driver of community dynamics as frequently as other forms of variability (Hart et al ). For example, in diverse communities stochasticity is often equated with neutrality (Vellend et al ) or is simply treated as an impediment to our ability to understand dynamics (Boettiger ). In fact, stochasticity arises from the probabilistic nature of core biological processes, including births, deaths, species interactions, and movement (May , Cohen , Clark , Black and McKane ), each of which can be described by an underlying distribution of possible events.…”

Section: Introductionmentioning

confidence: 99%

Integrating the underlying structure of stochasticity into community ecology

Shoemaker

Sullivan

Donohue

et al. 2019

Ecology

150

125

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Stochasticity is a core component of ecology, as it underlies key processes that structure and create variability in nature. Despite its fundamental importance in ecological systems, the concept is often treated as synonymous with unpredictability in community ecology, and studies tend to focus on single forms of stochasticity rather than taking a more holistic view. This has led to multiple narratives for how stochasticity mediates community dynamics. Here, we present a framework that describes how different forms of stochasticity (notably demographic and environmental stochasticity) combine to provide underlying and predictable structure in diverse communities. This framework builds on the deep ecological understanding of stochastic processes acting at individual and population levels and in modules of a few interacting species. We support our framework with a mathematical model that we use to synthesize key literature, demonstrating that stochasticity is more than simple uncertainty. Rather, stochasticity has profound and predictable effects on community dynamics that are critical for understanding how diversity is maintained. We propose next steps that ecologists might use to explore the role of stochasticity for structuring communities in theoretical and empirical systems, and thereby enhance our understanding of community dynamics.

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Section: Introductionmentioning

confidence: 99%

Integrating the underlying structure of stochasticity into community ecology

Shoemaker

Sullivan

Donohue

et al. 2019

Ecology

150

125

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“…On the other hand, if g(m) is not constant, the strength of the noise depends on the current state m(t). Such noise is called multiplicative, or state-dependent, and is known to produce unexpected results (Horsthemke, 1984;Altschuler et al, 2008;Lawson et al, 2013;Boettiger, 2018). In the following sections, we will not only describe how to derive equations of the form (3) from given probabilistic rules for individual-level behaviour, but also provide some heuristic insight into the different types of behaviours that can arise.…”

Section: Introductionmentioning

confidence: 99%

Deriving Mesoscopic Models of Collective Behavior for Finite Populations

Jhawar

Morris

Guttal

2019

Handbook of Statistics

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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.

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“…Such 'noise-induced' character [23,24] is particularly relevant when trying to infer individual behaviours from that of the collective. Here, rather than simply obscuring the signature of otherwise deterministic dynamics, collective-level noise actually encodes important information about individual interactions [25]. Therefore, not only should fluctuations be extracted with care, but they are also pertinent to a major challenge of behavioural inference: how to distinguish between multiple mechanisms that ostensibly reproduce the same qualitative features of collective motion.…”

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confidence: 99%

Noise-induced schooling of fish

et al. 2020

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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]

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From noise to knowledge: how randomness generates novel phenomena and reveals information

Cited by 68 publications

References 104 publications

Integrating the underlying structure of stochasticity into community ecology

Integrating the underlying structure of stochasticity into community ecology

Deriving Mesoscopic Models of Collective Behavior for Finite Populations

Noise-induced schooling of fish

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