Signatures of a globally optimal searching strategy in the three-dimensional foraging flights of bumblebees

Bumblebees attend to both the properties of the string and the target in string-pulling tasks, but prioritize the features of the string

Previous studies have demonstrated that associative learning and experience play important roles in the string-pulling of bumblebees (Bombus terrestris). However, the features of the target (artificial flower with sugar reward) and the string that bees learn in such tasks remain unknown. This study aimed to explore the specific aspects of the string-flower arrangement that bumblebees learn and how they prioritize these features. We show that bumblebees trained with string-pulling are sensitive to the flower stimuli; they exhibit a preference for pulling strings connected to flowers over strings that are not attached to a target. Additionally, they chose to pull strings attached to flowers of the same color and shape as experienced during training. The string feature also plays a crucial role for bumblebees when the flower features are identical. Furthermore, bees prioritized the features of the strings rather than the flowers when both cues were in conflict. Our results show that bumblebees solve string-pulling tasks by acquiring knowledge about the characteristics of both targets and strings, and contribute to a deeper understanding of the cognitive processes employed by bees when tackling non-natural skills.

Intermittent Search, Not Strict Lévy Flight, Evolves under Relaxed Foraging Distribution Constraints

AbstractThe survival of an animal depends on its success as a forager, and understanding the adaptations that result in successful foraging strategies is an enduring endeavour of behavioral ecology. Random walks are one of the primary mathematical descriptions of foraging behavior. Power law distributions are often used to model random walks, as they can characterize a wide range of behaviors, including Lévy walks. Empirical evidence indicates the prevalence and efficiency of Lévy walks as a foraging strategy, and theoretical work suggests an evolutionary origin. However, previous evolutionary models have assumed a priori that move lengths are drawn from a power law or other families of distributions. Here, we remove this restriction with a model that allows for the evolution of any distribution. Instead of Lévy walks, our model unfailingly results in the evolution of intermittent search, a random walk composed of two disjoint modes-frequent localized walks and infrequent extensive moves-that consistently outcompeted Lévy walks. We also demonstrate that foraging using intermittent search may resemble a Lévy walk because of interactions with the resources within an environment. These extrinsically generated Lévy-like walks belie an underlying behavior and may explain the prevalence of Lévy walks reported in the literature.

Tracking the flight and landing behaviour of western flower thrips in response to single and two-colour cues

Real-time 3D tracking and high-speed videography was used to examine the behaviour of a worldwide greenhouse pest, the western flower thrips (WFT), in response to different colours in the context of improving trap design. Measurements were taken of the number of landings on, and flight activity near, a lamp containing two LEDs of either the same colour or a combination of two colours presented side by side. Main findings show that landing patterns of WFT are different between colours, with landings on UV(+ red) as highly attractive stimulus being mostly distributed at the bottom half of the lamp, while for yellow also as very attractive and green as a 'neutral' stimulus, landings were clearly on the upper rim of the lamp. Additionally, a positive interaction with the UV-A(+ red) and yellow combination elicited the highest number of landings and flight time in front of the LED lamp. Conversely, a negative interaction was observed with decreased landings and flight time found for yellow when blue was present as the adjacent colour. Overall, differences between treatments were less obvious for flight times compared to number of landings, with tracking data suggesting that WFT might use different colours to orientate at different distances as they approach a visual stimulus.

Front Propagation of Exponentially Truncated Fractional-Order Epidemics

The existence of landscape constraints in the home range of living organisms that adopt Lévy-flight movement patterns, prevents them from making arbitrarily large displacements. Their random movements indeed occur in a finite space with an upper bound. In order to make realistic models, by introducing exponentially truncated Lévy flights, such an upper bound can thus be taken into account in the reaction-diffusion models. In this work, we have investigated the influence of the λ-truncated fractional-order diffusion operator on the spatial propagation of the epidemics caused by infectious diseases, where λ is the truncation parameter. Analytical and numerical simulations show that depending on the value of λ, different asymptotic behaviours of the travelling-wave solutions can be identified. For small values of λ (λ≳0), the tails of the infective waves can decay algebraically leading to an exponential growth of the epidemic speed. In that case, the truncation has no impact on the superdiffusive epidemics. By increasing the value of λ, the algebraic decaying tails can be tamed leading to either an upper bound on the epidemic speed representing the maximum speed value or the generation of the infective waves of a constant shape propagating at a minimum constant speed as observed in the classical models (second-order diffusion epidemic models). Our findings suggest that the truncated fractional-order diffusion equations have the potential to model the epidemics of animals performing Lévy flights, as the animal diseases can spread more smoothly than the exponential acceleration of the human disease epidemics.

Optimal escape-and-feeding dynamics of random walkers: Rethinking the convenience of ballistic strategies

Excited random walks represent a convenient model to study food intake in a media which is progressively depleted by the walker. Trajectories in the model alternate between (i) feeding and (ii) escape (when food is missed and so it must be found again) periods, each governed by different movement rules. Here, we explore the case where the escape dynamics is adaptive, so at short times an area-restricted search is carried out, and a switch to extensive or ballistic motion occurs later if necessary. We derive for this case explicit analytical expressions of the mean escape time and the asymptotic growth of the depleted region in one dimension. These, together with numerical results in two dimensions, provide surprising evidence that ballistic searches are detrimental in such scenarios, a result which could explain why ballistic movement is barely observed in animal searches at microscopic and millimetric scales, therefore providing significant implications for biological foraging.

Foraging behavior in visual search: A review of theoretical and mathematical models in humans and animals

Visual search (VS) is a fundamental task in daily life widely studied for over half a century. A variant of the classic paradigm-searching one target among distractors-requires the observer to look for several (undetermined) instances of a target (so-called foraging) or several targets that may appear an undefined number of times (recently named as hybrid foraging). In these searches, besides looking for targets, the observer must decide how much time is needed to exploit the area, and when to quit the search to eventually explore new search options. In fact, visual foraging is a very common search task in the real world, probably involving additional cognitive functions than typical VS. It has been widely studied in natural animal environments, for which several mathematical models have been proposed, and just recently applied to humans: Lévy processes, composite and area-restricted search models, marginal value theorem, and Bayesian learning (among others). We conducted a systematic search in the literature to understand those mathematical models and study its applicability in human visual foraging. The review suggests that these models might be the first step, but they seem to be limited to fully comprehend foraging in visual search. There are essential variables involving human visual foraging still to be established and understood. Indeed, a jointly theoretical interpretation based on the different models reviewed could better account for its understanding. In addition, some other relevant variables, such as certain individual differences or time perception might be crucial to understanding visual foraging in humans.

Characterizing long-range search behavior in Diptera using complex 3D virtual environments

The exemplary search capabilities of flying insects have established them as one of the most diverse taxa on Earth. However, we still lack the fundamental ability to quantify, represent, and predict trajectories under natural contexts to understand search and its applications. For example, flying insects have evolved in complex multimodal three-dimensional (3D) environments, but we do not yet understand which features of the natural world are used to locate distant objects. Here, we independently and dynamically manipulate 3D objects, airflow fields, and odor plumes in virtual reality over large spatial and temporal scales. We demonstrate that flies make use of features such as foreground segmentation, perspective, motion parallax, and integration of multiple modalities to navigate to objects in a complex 3D landscape while in flight. We first show that tethered flying insects of multiple species navigate to virtual 3D objects. Using the apple fly Rhagoletis pomonella, we then measure their reactive distance to objects and show that these flies use perspective and local parallax cues to distinguish and navigate to virtual objects of different sizes and distances. We also show that apple flies can orient in the absence of optic flow by using only directional airflow cues, and require simultaneous odor and directional airflow input for plume following to a host volatile blend. The elucidation of these features unlocks the opportunity to quantify parameters underlying insect behavior such as reactive space, optimal foraging, and dispersal, as well as develop strategies for pest management, pollination, robotics, and search algorithms.

The Role of Landscapes and Landmarks in Bee Navigation: A Review

The ability of animals to explore landmarks in their environment is essential to their fitness. Landmarks are widely recognized to play a key role in navigation by providing information in multiple sensory modalities. However, what is a landmark? We propose that animals use a hierarchy of information based upon its utility and salience when an animal is in a given motivational state. Focusing on honeybees, we suggest that foragers choose landmarks based upon their relative uniqueness, conspicuousness, stability, and context. We also propose that it is useful to distinguish between landmarks that provide sensory input that changes (“near”) or does not change (“far”) as the receiver uses these landmarks to navigate. However, we recognize that this distinction occurs on a continuum and is not a clear-cut dichotomy. We review the rich literature on landmarks, focusing on recent studies that have illuminated our understanding of the kinds of information that bees use, how they use it, potential mechanisms, and future research directions.

Bumblebees learn foraging routes through exploitation-exploration cycles

How animals explore and acquire knowledge from the environment is a key question in movement ecology. For pollinators that feed on multiple small replenishing nectar resources, the challenge is to learn efficient foraging routes while dynamically acquiring spatial information about new resource locations. Here, we use the behavioural mapping t-Stochastic Neighbouring Embedding algorithm and Shannon entropy to statistically analyse previously published sampling patterns of bumblebees feeding on artificial flowers in the field. We show that bumblebees modulate foraging excursions into distinctive behavioural strategies, characterizing the trade-off dynamics between (i) visiting and exploiting flowers close to the nest, (ii) searching for new routes and resources, and (iii) exploiting learned flower visitation sequences. Experienced bees combine these behavioural strategies even after they find an optimal route minimizing travel distances between flowers. This behavioural variability may help balancing energy costs-benefits and facilitate rapid adaptation to changing environments and the integration of more profitable resources in their routes.

Parallel Multimodal Circuits Control an Innate Foraging Behavior

Foraging strategies emerge from genetically encoded programs that are similar across animal species. Here, we examine circuits that control a conserved foraging state, local search behavior after food removal, in Caenorhabditis elegans. We show that local search is triggered by two parallel groups of chemosensory and mechanosensory glutamatergic neurons that detect food-related cues. Each group of sensory neurons suppresses distinct integrating neurons through a G protein-coupled metabotropic glutamate receptor, MGL-1, to release local search. The chemosensory and mechanosensory modules are separate and redundant; glutamate release from either module can drive the full behavior. A transition from local search to global search over several minutes after food removal is associated with two changes in circuit function. First, the spontaneous activity of sensory neurons falls. Second, the motor pattern generator for local search becomes less responsive to sensory input. This multimodal, distributed short-term food memory provides robust control of an innate behavior.

Revisiting GUD: An empirical test of the size-dependency of patch departure behaviour

Behaviour related to patch resource exploitation is a major determinant of individual fitness. Assuming the size-dependency of patch departure behaviour, model-based approaches have shown size-mediated coexistence in systems of competing species. However, experimental evidence for the influence of body size on patch use behaviour is scarce. In this study, we explore whether allometric principles provide an underlying framework for interspecific patterns of resource use. To this end, we propose a meso-cosm approach using three species of gastropods differing in size as a model system and 32P radio-isotopic techniques as a measure of resource use. Foragers of different size were placed in an artificial patch, provided with a limited amount of labelled resource and let them free to move as resources decrease and scarcity is sensed. We investigated the extent to which individual body size affects the exploitation of resources by examining Giving Up Density (GUD), Giving Up Time (GUT), resource absorption rate and exploitation efficiency as components of individual exploitation behaviour. To compare positive, constant and negative individual size scaling of population energy requirements, experimental trials with an equal numbers and equal biomass of differently sized foragers were carried out, and an experimental trial with equal metabolic requirements was simulated. We observed clear size dependency in the patch departure behaviour of the experimental organisms. Even under conditions of equivalent overall population energy requirements, larger foragers decided to leave the resource patch earlier and at a higher density of resources than smaller ones. Smaller foragers were able to prolong their presence and make more use of the resources, resulting in an inverse body-size scaling of resource exploitation efficiency.

Target tracking and 3D trajectory acquisition of cabbage butterfly (P. rapae) based on the KCF-BS algorithm

Insect behaviour is an important research topic in plant protection. To study insect behaviour accurately, it is necessary to observe and record their flight trajectory quantitatively and precisely in three dimensions (3D). The goal of this research was to analyse frames extracted from videos using Kernelized Correlation Filters (KCF) and Background Subtraction (BS) (KCF-BS) to plot the 3D trajectory of cabbage butterfly (P. rapae). Considering the experimental environment with a wind tunnel, a quadrature binocular vision insect video capture system was designed and applied in this study. The KCF-BS algorithm was used to track the butterfly in video frames and obtain coordinates of the target centroid in two videos. Finally the 3D trajectory was calculated according to the matching relationship in the corresponding frames of two angles in the video. To verify the validity of the KCF-BS algorithm, Compressive Tracking (CT) and Spatio-Temporal Context Learning (STC) algorithms were performed. The results revealed that the KCF-BS tracking algorithm performed more favourably than CT and STC in terms of accuracy and robustness.

Obstacle traversal and route choice in flying honeybees: Evidence for individual handedness

Flying insects constantly face the challenge of choosing efficient, safe and collision-free routes while navigating through dense foliage. We examined the route-choice behavior of foraging honeybees when they encountered a barrier which could be traversed by flying through one of two apertures, positioned side by side. When the bees' choice behavior was averaged over the entire tested population, the two apertures were chosen with equal frequency when they were equally wide. When the apertures were of different width, the bees, on average, showed a preference for the wider aperture, which increased sharply with the difference between the aperture widths. Thus, bees are able to discriminate the widths of oncoming gaps and choose the passage which is presumably safer and quicker to transit. Examination of the behavior of individual bees revealed that, when the two apertures were equally wide, ca. 55% of the bees displayed no side bias in their choices. However, the remaining 45% showed varying degrees of bias, with one half of them preferring the left-hand aperture, and the other half the right-hand aperture. The existence of distinct individual biases was confirmed by measuring the times required by biased bees to transit various aperture configurations: The transit time was longer if a bee's intrinsic bias forced it to engage with the narrower aperture. Our results show that, at the population level, bees do not exhibit 'handedness' in choosing routes; however, individual bees display an idiosyncratic bias that can range from a strong left bias, through zero bias, to a strong right bias. In honeybees, previous studies of olfactory and visual learning have demonstrated clear biases at the population level. To our knowledge, our study is the first to uncover the existence of individually distinct biases in honeybees. We also show how a distribution of biases among individual honeybees can be advantageous in facilitating rapid transit of a group of bees through a cluttered environment, without any centralized decision-making or control.

A Lévy-flight diffusion model to predict transgenic pollen dispersal

The containment of genetically modified (GM) pollen is an issue of significant concern for many countries. For crops that are bee-pollinated, model predictions of outcrossing rates depend on the movement hypothesis used for the pollinators. Previous work studying pollen spread by honeybees, the most important pollinator worldwide, was based on the assumption that honeybee movement can be well approximated by Brownian motion. A number of recent studies, however, suggest that pollinating insects such as bees perform Lévy flights in their search for food. Such flight patterns yield much larger rates of spread, and so the Brownian motion assumption might significantly underestimate the risk associated with GM pollen outcrossing in conventional crops. In this work, we propose a mechanistic model for pollen dispersal in which the bees perform truncated Lévy flights. This assumption leads to a fractional-order diffusion model for pollen that can be tuned to model motion ranging from pure Brownian to pure Lévy. We parametrize our new model by taking the same pollen dispersal dataset used in Brownian motion modelling studies. By numerically solving the model equations, we show that the isolation distances required to keep outcrossing levels below a certain threshold are substantially increased by comparison with the original predictions, suggesting that isolation distances may need to be much larger than originally thought.

The evolutionary origins of Lévy walk foraging

We study through a reaction-diffusion algorithm the influence of landscape diversity on the efficiency of search dynamics. Remarkably, the identical optimal search strategy arises in a wide variety of environments, provided the target density is sparse and the searcher’s information is restricted to its close vicinity. Our results strongly impact the current debate on the emergentist vs. evolutionary origins of animal foraging. The inherent character of the optimal solution (i.e., independent on the landscape for the broad scenarios assumed here) suggests an interpretation favoring the evolutionary view, as originally implied by the Lévy flight foraging hypothesis. The latter states that, under conditions of scarcity of information and sparse resources, some organisms must have evolved to exploit optimal strategies characterized by heavy-tailed truncated power-law distributions of move lengths. These results strongly suggest that Lévy strategies—and hence the selection pressure for the relevant adaptations—are robust with respect to large changes in habitat. In contrast, the usual emergentist explanation seems not able to explain how very similar Lévy walks can emerge from all the distinct non-Lévy foraging strategies that are needed for the observed large variety of specific environments. We also report that deviations from Lévy can take place in plentiful ecosystems, where locomotion truncation is very frequent due to high encounter rates. So, in this case normal diffusion strategies—performing as effectively as the optimal one—can naturally emerge from Lévy. Our results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

How organisms improve the search for food, mates, etc., is a key factor to their survival. Mathematically, the best strategy to look for randomly distributed re-visitable resources—under scarce information and sparse conditions—results from Lévy distributions of move lengths (the probability of taking a step ℓ is proportional to 1/ℓ²). Today it is well established that many animal species in different habitats do perform Lévy foraging. This fact has raised a heated debate, viz., the emergent versus evolutionary hypotheses. For the former, a Lévy foraging is an emergent property, a consequence of searcher-environment interactions: certain landscapes induce Lévy patterns, but others not. In this view, the optimal strategy depends on the particular habitat. The evolutionary explanation, in contrast, is that Lévy foraging strategies are adaptations that evolved via natural selection. In this article, through simulations we exhaustively analyze the influence of distinct environments on the foraging efficiency. We find that the optimal procedure is the same in all situations, provided density is low and landscape information is scarce. So, the best search strategy is remarkably independent of details. These results constitute the strongest theoretical evidence to date supporting the evolutionary origins of experimentally observed Lévy walks.

The Weierstrassian movement patterns of snails

Weierstrassian Lévy walks are the archetypical form of random walk that do not satisfy the central limit theorem and are instead characterized by scale invariance. They were originally regarded as a mathematical abstraction but subsequent theoretical studies showed that they can, in principle, at least, be generated by chaos. Recently, Weierstrassian Lévy walks have been found to provide accurate representations of the movement patterns of mussels (Mytilus edulis) and mud snails (Hydrobia ulvae) recorded in the laboratory under controlled conditions. Here, we tested whether Weierstrassian Lévy walks and chaos are present under natural conditions in intertidal limpets Patella vulgata and P. rustica, and found that both characteristics are pervasive. We thereby show that Weierstrassian Lévy walks may be fundamental to how molluscs experience and interact with the world across a wide range of ecological contexts. We also show in an easily accessible way how chaos can produce a wide variety of Weierstrassian Lévy walk movement patterns. Our findings support the Lévy flight foraging hypothesis that posits that because Lévy walks can optimize search efficiencies, natural selection should have led to adaptations for Lévy walks.