Predictability and hierarchy in Drosophila behavior

Gordon J. Berman; William Bialek; Joshua W. Shaevitz

Source-linked AI summary

Predictability and hierarchy in Drosophila behavior

Gordon J. Berman, William Bialek, Joshua W. Shaevitz

arXiv:1605.03626v1May 11, 2016physics.bio-phcs.ITq-bio.NCstat.AP

TL;DR

The paper asks whether an animal’s full behavioral repertoire is hierarchically organized across multiple time scales, a question for which prior measurements were limited. It tracks stereotyped behaviors in fruit flies and applies an information-bottleneck approach to find compressed representations that optimally predict future states. The results show persistent multi-scale dynamics and a hierarchical organization in which fine-grained representations predict the near future while coarser ones predict more distant behavior.

Problem
Evidence for behavioral hierarchy has been limited across complete repertoires and multiple time scales, with prior analyses often focusing on single behaviors or imposing hierarchy through clustering.
Method
The study discovers stereotyped fly behaviors without a priori definitions and uses information bottleneck representations to optimize prediction of future behavioral states.
Results
Behavioral transitions show memory lasting thousands of transitions, and optimally predictive information-bottleneck partitions are more tree-like than random partitions, revealing hierarchical organization.
Takeaways & Limitations
Fly behavior is organized into nested representations across time scales, with fine-grained partitions useful for near-future prediction and coarser partitions sufficient for the distant future.

Abstract

from arXiv · show

Even the simplest of animals exhibit behavioral sequences with complex temporal dynamics. Prominent amongst the proposed organizing principles for these dynamics has been the idea of a hierarchy, wherein the movements an animal makes can be understood as a set of nested sub-clusters. Although this type of organization holds potential advantages in terms of motion control and neural circuitry, measurements demonstrating this for an animal's entire behavioral repertoire have been limited in scope and temporal complexity. Here, we use a recently developed unsupervised technique to discover and track the occurrence of all stereotyped behaviors performed by fruit flies moving in a shallow arena. Calculating the optimally predictive representation of the fly's future behaviors, we show that fly behavior exhibits multiple time scales and is organized into a hierarchical structure that is indicative of its underlying behavioral programs and its changing internal states.

I. INTRODUCTION

Behavior is widely theorized to be hierarchically organized, but evidence across an animal’s full repertoire and multiple time scales has remained limited. This study addresses that gap by analyzing fruit-fly movements without predefined behavioral categories and testing representations optimized for future prediction.

Hierarchical theories propose that animal actions are nested into modules spanning motion primitives, complex behaviors, and action sequences.
Evidence for hierarchy has often focused on a single behavioral type rather than relationships among diverse behavioral motifs.
Many analyses impose hierarchy through methods such as hierarchical clustering without establishing that the representation accurately describes behavior.
Previous measurements generally examined behavioral dynamics at only one time scale, often using a Markov model in which the next action depends only on the current state.
The study analyzes an hour of Drosophila behavior using unsupervised discovery of stereotyped actions and information-theoretic representations optimized to predict future behavioral states.

II. EXPERIMENTS AND BEHAVIORAL STATES

The experiments measured ground-based male flies continuously in a featureless arena and converted their movements into an unsupervised behavioral map. Pauses at density peaks were treated as 117 discrete behavioral states, whose transitions were then analyzed for modular structure.

Experiments: 59 male flies were recorded for one hour in a largely featureless circular arena using a 100Hz camera.
Behavioral-state discovery: An unsupervised pipeline aligned fly images, decomposed posture dynamics into a low-dimensional basis, and embedded local spectrograms into a two-dimensional behavioral space.
Behavioral-state discovery: Peaks in the behavioral-space probability distribution represented revisited stereotyped movements, including wing grooming, proboscis extension, and alternating tripod locomotion.
Behavioral states: Pauses at behavioral-space peaks were defined as the lowest-level states, yielding a discrete sequence S(n) with N = 117 possible values.
Transition structure: Figure 1 groups the 117 states into six information-bottleneck clusters and displays their transition probabilities on both a matrix and the behavioral map.

III. TRANSITION MATRICES AND NON-MARKOVIAN TIME SCALES

Transition matrices reveal that fly behavior retains structure across long horizons and therefore cannot be described by a purely Markovian model. Eigenvalue decay further shows multiple behavioral time scales, including memory lasting roughly 20 minutes.

Single-step transition structure: The single-step transition matrix is modular and spatially localized, with transitions mainly linking similar behaviors such as nearby grooming actions or locomotion states.The transition structure forms contiguous behavioral categories including locomotion and anterior-body movements.
Markovian benchmark: For Markovian dynamics, the one-step transition matrix fully determines longer-horizon transitions through matrix iteration.The resulting non-leading eigenmode contributions decay exponentially with the transition horizon.
Markovian benchmark: ⟨λ2(1)⟩ = 0.953 ± 0.004 corresponds to a characteristic decay time ⟨t2⟩ = 29 ± 2 transitions for the Markov model.Memory extending beyond approximately 30 transitions would therefore indicate hidden states carrying longer-term memory.
Long-horizon structure: After 100 transitions, the Markov model retains essentially no information, whereas T(100) and T(1000) retain substantial non-random structure.This contrast provides direct evidence for long-time structure in the observed behavioral dynamics.
Long-horizon structure: The leading mode’s apparent decay rate falls by nearly two orders of magnitude before its eigenvalue reaches the noise floor, with similar patterns in higher modes.A Markovian system would instead have a constant apparent decay rate across time scales.
Long-horizon structure: Decay rates near 10^-3 imply internal states retaining memory across at least approximately 10^3 behavioral transitions, or roughly 20 minutes.These time scales are much longer than those apparent in the Markov model, despite the absence of external stimuli.

IV. PREDICTABILITY AND HIERARCHY

The information bottleneck finds compressed behavioral representations that preserve predictability across time lags, revealing spatially contiguous and hierarchically subdividing clusters. These partitions are more tree-like than random across measured future time scales.

Predictive representations: The information bottleneck groups behavioral states to maximize predictive information about future states while constraining retained information about the current state.Increasing β compresses the 117 behavioral states, trading descriptive complexity for predictive power.
Predictability across time: Predictive information decreases with longer time lags, but increasingly close optimal curves at large lags indicate long behavioral time scales.The curves span lags from τ = 1 to τ = 5000.
Spatial organization: For τ = 67, information bottleneck clusters remain spatially contiguous in the behavioral map, indicating that transitions predominantly connect similar behaviors.The 25-cluster partition remains contiguous and is marked with dashed boundaries.
Hierarchical organization: As the number of clusters increases, new clusters largely subdivide existing clusters rather than mix behaviors from different clusters.At τ = 100, probability flow between independently optimized partitions forms a tree-like pattern.
Quantifying hierarchy: The treeness metric quantifies hierarchy by comparing backward and forward path entropy, with 0 ≤ T ≤ 1 and T = 1 denoting a perfect hierarchy.Figure 6 evaluates treeness across future transitions and fine-grained cluster counts.
Quantifying hierarchy: Information bottleneck partitions are much more tree-like than random partitions, even when predicting behavioral states thousands of transitions into the future.The hierarchy emerges from independently solved bottleneck problems rather than being imposed by hierarchical clustering.

V. CONCLUSIONS

Across the measured fruit-fly repertoire, behavioral transitions show multiple time scales and memory extending thousands of transitions into the future. Information bottleneck representations organize these behaviors hierarchically, unlike prior analyses limited in repertoire, time scale, or imposed hierarchy.

Conclusions: Behavioral transitions exhibit multiple time scales and memory that persists thousands of transitions into the future.The authors interpret this persistence as indicative of internal states carrying memory across many observable transitions.
Conclusions: Fine-grained representations predict short-time structure, whereas coarser representations suffice for actions farther removed in time.This organization was obtained from compressed representations that optimally predict the observed dynamics.
Conclusions: The measured hierarchy differs from previous work that used narrower behavioral repertoires, fewer time scales, or analyses that guaranteed hierarchical outputs.The comparison includes hierarchical clustering and related methods.
Conclusions: The observed organization resembles functional clustering and distance-dependent temporal correlations reported in mouse and primate motor cortex.The paper suggests that analogous neuronal patterns may exist in Drosophila, although they have not been specifically found there.

A. Experiments

The experiments recorded individual male Drosophila melanogaster in a controlled arena for one hour to measure their behavioral repertoire.

Experiments: 59 individual male Drosophila melanogaster of the Oregon-R strain were imaged for one hour each.All flies were within their first two weeks post-eclosion during filming.

B. Generating Markovian Models

The Markovian datasets were generated by repeatedly sampling observed behavioral instances and their immediate successors to create first-order sequences matching the original dataset size.

Markovian model generation: Each synthetic sequence starts from a randomly selected state and samples another measured instance performing that behavior.The behavior immediately following the sampled instance is then selected, and the process is iterated.
Markovian model generation: The generated sequences are iterated until they match the size of the original dataset.This procedure is analogous to first-order alphabets used in Shannon’s original information-theory work.

C. Predictive Information Bottleneck

The predictive information bottleneck compresses behavioral states while trading predictive power against description complexity. Solutions are explored across cluster counts, annealed inverse temperatures, time lags, and repeated random initializations, then reduced to a Pareto front.

Optimization: For fixed cluster count K and inverse temperature β, randomly initialized self-consistent equations are iterated until ((Ft − Ft+1)/Ft < 10^-6).The iterations are equivalent to the Blahut-Arimoto algorithm in rate–distortion theory.
Optimization: The optimization anneals β from 0.1 to 500 across 40 exponentially spaced values, using each converged solution to initialize the next.This procedure targets hard clusterings while retaining intermediate solutions for possible inclusion in the Pareto front.
Experimental design: The study performs 24 replicates for K = 2, . . . , 25 across 81 time-lag values between n = 1 and n = 5,000.Intermediate solutions are stored before deterministic limits and information measures are recalculated.
Pareto selection: The Pareto front contains solutions for which no alternative at the same lag has both lower I(Z; S(n)) and higher predictive information.Each clustering is first converted to the deterministic limit before the information values are recalculated.

D. Treeness Index

The treeness index quantifies how consistently behavioral clusters retain lineage as partitions become finer. It compares forward and backward path entropies on graphs linking partitions with successive cluster counts.

Treeness Index: The treeness index compares entropy over forward and backward paths through graphs linking partitions as cluster counts increase.The forward graph uses P(ℓ) transitions, while the backward graph uses Q(ℓ) transitions between adjacent partitionings.
Forward and backward graphs: P(ℓ) gives the probability that a state in cluster i of an ℓ-cluster partition belongs to cluster j in the ℓ+1-cluster partition.These probabilities define the directed, acyclic forward graph.
Forward and backward graphs: Q(ℓ) gives the probability that a state in cluster i of the ℓ+1-cluster partition belongs to cluster j in the ℓ-cluster partition.These probabilities define the corresponding backward graph.
Treeness Index: The index T is the relative reduction in entropy when traversing backward rather than forward through the partition tree.Forward and backward entropies average path probabilities over possible paths and, for backward paths, over ending states.