Flock Dynamics Research Articles

Flock Dynamics, Production Challenges and Opportunities of Indigenous Goat and Sheep Populations in North Western and Western Zones of Tigray Region, Ethiopia

Flock Dynamics, Production Challenges and Opportunities of Indigenous Goat and Sheep Populations in North Western and Western Zones of Tigray Region, Ethiopia

Learning interpretable dynamics of stochastic complex systems from experimental data

Complex systems with many interacting nodes are inherently stochastic and best described by stochastic differential equations. Despite increasing observation data, inferring these equations from empirical data remains challenging. Here, we propose the Langevin graph network approach to learn the hidden stochastic differential equations of complex networked systems, outperforming five state-of-the-art methods. We apply our approach to two real systems: bird flock movement and tau pathology diffusion in brains. The inferred equation for bird flocks closely resembles the second-order Vicsek model, providing unprecedented evidence that the Vicsek model captures genuine flocking dynamics. Moreover, our approach uncovers the governing equation for the spread of abnormal tau proteins in mouse brains, enabling early prediction of tau occupation in each brain region and revealing distinct pathology dynamics in mutant mice. By learning interpretable stochastic dynamics of complex systems, our findings open new avenues for downstream applications such as control.

Flocking dynamics of agents moving with a constant speed and a randomly switching topology

Abstract In this paper, we present a sufficient framework to exhibit the sample path-wise asymptotic flocking dynamics of the Cucker–Smale model with unit-speed constraint and the randomly switching network topology. We employ a matrix formulation of the given equation, which allows us to evaluate the diameter of velocities with respect to the adjacency matrix of the network. Unlike the previous result on the randomly switching Cucker–Smale model, the unit-speed constraint disallows the system to be considered as a nonautonomous linear ordinary differential equation on velocity vector, which forces us to get a weaker form of the flocking estimate than the result for the original Cucker–Smale model.

Production Systems and Management Practices of Chicken Populations in Zambia

The study was carried out to describe the population, population dynamics, production systems and management practices of chicken types reared in Zambia, using the 2017/2018 livestock and aquaculture census data provided by the Zambia Statistics Agency and the Ministry of Fisheries and Livestock. Data on the chicken types - Indigenous, Broiler and Layer, was analyzed for both quantitative and qualitative parameters. The population estimates for the chickens were 15,313,780, 6,078,694 and 742,981 for indigenous, broiler and layer, respectively. Flock dynamics could not be ascertained conclusively due to inadequate information. Chicken ownership was significantly skewed towards the male gender for broilers (67%) and layers (79%) while almost equal for the indigenous chickens. Indigenous chickens were more prominent in provinces with high agricultural production (Southern, Central, and Eastern at 51%). Broilers and Layers were more prominent in provinces with commercial centres (Copperbelt and Lusaka at 68% and 75% respectively). The main purpose of rearing indigenous chickens was mainly sales for income (66.1%) and home consumption (32.3%). The main production systems were found to be traditional for indigenous chickens (87%) and intensive for broiler and layer chickens (70.3% and 44%, respectively). The main feeding practices were free-range feeding (80.6%) and free-range with supplementation (17.4%) for indigenous chickens). Diseases notably, Newcastle was found to be debilitating and a great hindrance to livestock production and productivity. The data collection instrument will require fine-tuning to obtain more technical details on production and productivity and better estimate the population dynamics.

The Multifaceted Contributions of Community‐Based Breeding Program of Bonga Sheep to Flock Dynamics, Animal Performance, and Socio‐economic Benefits of Beneficiaries in Kafa Zone, Ethiopia

The Multifaceted Contributions of Community‐Based Breeding Program of Bonga Sheep to Flock Dynamics, Animal Performance, and Socio‐economic Benefits of Beneficiaries in Kafa Zone, Ethiopia

Higher-order dialectic variation and syntactic convergence in the complex warble song of budgerigars.

Dialectic signatures in animal acoustic signals are key in the identification of and association with group members. Complex vocal sequences may also convey information about behavioral state, and may thus vary according to social environment. Some bird species, such as psittaciforms, learn and modify their complex acoustic signals throughout their lives. However, the structure and function of vocal sequences in open-ended vocal learners remains understudied. Here, we examined vocal sequence variation in the warble song of budgerigars, and how these change upon contact between social groups. Budgerigars are open-ended vocal learners which exhibit fission-fusion flock dynamics in the wild. We found that two captive colonies of budgerigars exhibited colony-specific differences in the syntactic structure of their vocal sequences. Individuals from the two colonies differed in the propensity to repeat certain note types, forming repetitive motifs which served as higher-order signatures of colony identity. When the two groups were brought into contact, their vocal sequences converged, and these colony-specific repetitive patterns disappeared, with males from both erstwhile colonies now producing similar sequences with similar syntactic structure. We present data suggesting that the higher-order temporal arrangement of notes/vocal units is modified throughout life by social learning as groups of birds continually associate and dissociate. Our study sheds light on the importance of examining signal structure at multiple levels of organization, and the potential for psittaciform birds as model systems to examine the influence of learning and social environment on acoustic signals.

Influence of behavioural and morphological group composition on pigeon flocking dynamics.

Animals rely on movement to explore and exploit resources in their environment. While movement can provide energetic benefits, it also comes with energetic costs. This study examines how group phenotypic composition individual speed and energy expenditure during group travel in homing pigeons. We manipulated the composition of pigeon groups based on body mass and leadership rank. Our findings indicate that groups of leader phenotypes show faster speeds and greater cohesion than follower phenotype groups. Additionally, we show that groups of homogenous mass composition, whether all heavy or all light, were faster and expended less energy over the course of a whole flight than flocks composed of a mixture of heavy and light individuals. We highlight the importance of considering individual-level variation in social-level studies, and the interaction between individual and group-level traits in governing speed and the cost of travel.

Stochastic flocking dynamics of the inertial spin model with state‐dependent noises

AbstractWe study stochastic flocking dynamics of the inertial spin (IS) model with state‐dependent noises. The IS model was considered to describe the collective behaviors of starling flocks moving with constant speed. Unlike mechanical flocking models extensively studied in the literature, this model incorporates an internal dynamic observable, namely spin (internal angular momentum) in addition to mechanical observables (position and velocity), and it describes how spin interacts with mechanical observables. In previous works, emergent dynamics of the deterministic counterparts for the IS model and its mean‐field limit have been investigated under some specific setting in which network topology is multiplicatively separable. In this work, we present sufficient frameworks for stochastic flocking dynamics of the IS model, which state‐dependent noises vanish at the equilibria of the deterministic IS model. The proposed frameworks are in terms of coupling strength, friction, and inertial coefficients, and our asymptotic convergence results for sample paths are given in both an almost sure and an expectation sense. We have also conducted several numerical experiments to verify our analytical results and to explore what can be studied further in future work

Characterization of bird formations using fuzzy modelling.

The investigation of the emergent collective behaviour in flying birds is a challenging task, yet it has always fascinated scientists from different disciplines. In the attempt of studying and modelling line formation, we collected high-precision position data of 29 free-flying northern bald ibises (Geronticus eremita) using Global Navigation Satellite System loggers, to investigate whether the spatial relationships within a flock can be explained by birds maintaining energetically advantageous positions. Specifically, we exploited domain knowledge and available literature information to model by means of fuzzy logic where the air vortices lie behind a flying bird. This allowed us to determine when a leading bird provides the upwash to a following bird, reducing its overall effort. Our results show that the fuzzy model allows to easily distinguish which bird is flying in the wake of another individual, provides a clear indication about flying flock dynamics and also gives a hint about birds' social relationships.

Leveraging on Flock Dynamics and Farmers’ Production Constraints in Designing Flock Health Program for Accelerated Goat Production

Leveraging on Flock Dynamics and Farmers’ Production Constraints in Designing Flock Health Program for Accelerated Goat Production

Evaluating Flock Dynamics, Offtake-rate, and Farmers’ Perception on Benefits of Community Based Breeding Program in Doyogena District, Central Ethiopia

Evaluating Flock Dynamics, Offtake-rate, and Farmers’ Perception on Benefits of Community Based Breeding Program in Doyogena District, Central Ethiopia

Energy Cost for Flocking of Active Spins: The Cusped Dissipation Maximum at the Flocking Transition.

We study the energy cost of flocking in the active Ising model (AIM) and show that, besides the energy cost for self-propelled motion, an additional energy dissipation is required to power the alignment of spins. We find that this additional alignment dissipation reaches its maximum at the flocking transition point in the form of a cusp with a discontinuous first derivative with respect to the control parameter. To understand this singular behavior, we analytically solve the two- and three-site AIM models and obtain the exact dependence of the alignment dissipation on the flocking order parameter and control parameter, which explains the cusped dissipation maximum at the flocking transition. Our results reveal a trade-off between the energy cost of the system and its performance measured by the flocking speed and sensitivity to external perturbations. This trade-off relationship provides a new perspective for understanding the dynamics of natural flocks and designing optimal artificial flocking systems.

Sensor-based detection of a Haemonchus contortus (Barber's pole worm) infection in sheep

Haemonchus contortus, or Barber's Pole worm, is considered one of the most pathogenic parasites of sheep due to the production, profitability and animal welfare implications associated with infections. However, detection of H. contortus infections by routine observation of sheep flocks is difficult, and producers are usually unaware of a problem until animals are severely infected. The aim of the current study was to explore the potential for accelerometer-based activity monitoring to detect H. contortus infections in sheep.A three-month clinical study was conducted in Central Queensland, Australia, whereby 45, 12-month-old merino wethers were randomly allocated to one of three treatment groups: control (n = 9), low H. contortus infection (n = 18) or high H. contortus infection (n = 18). Infection occurred on Day 0, and accelerometer sensors were attached to a halter and deployed on all animals from Day 21 to Day 70. Animals were sampled weekly (faecal and blood) and treated with an anthelmintic on Day 56. Following the clinical period, five study animals were observed for a total of five hours to compare direct behavioral observations against accelerometer data. This was then used to develop a machine learning (ML) model to classify the accelerometer data into active or inactive behavior, which was further summarized to determine the proportion of time spent active per day. The most valuable features in the selected ML model were movement variation (MV), maximum X-axis value (MaxX), standard deviation of the X-axis (SDX), maximum Y-axis value (MaxY) and standard deviation of the Z-axis (SDZ).Linear mixed-effects models identified a significant difference in all sheep activity pre- and post-anthelmintic drench on Day 56 (P < 0.001). Conversely, there was no significant difference between activity levels of infected animals compared to controls (P = 0.14). To further explore how the activity of sheep changed with clinical presentations of H. contortus infections, weekly faecal egg count (FEC) and blood packed cell volume (PCV) were compared to sheep activity using a Spearman's rank correlation test. There was a weak but significant negative correlation between FEC and sheep activity (P < 0.001) and a weak but significant positive correlation between PCV and sheep activity (P < 0.001).In conclusion, this study has shown that accelerometer-based activity monitoring may be able to identify changes in sheep activity associated with clinical presentations of H. contortus infections and between periods prior to and following anthelmintic treatment. However, the ability to detect activity differences between infected and control animals was less clear. Further research is needed to determine the impact of individual behavior variability and flock dynamics when using on-animal sensors for the detection of behavioral changes associated with disease.

Composition and dynamics of mixed flocks of birds in a remnant of Submontane Atlantic Rain Forest in southern Brazil

Mixed flocks are associations of two or more species that are formed and maintained through mutual behavioral responses, with advantages such as maximizing foraging and protecting against predation. This study aimed to evaluate the composition, temporal dynamics, and presence of core species in mixed flocks of birds in a remnant of the Submontane Atlantic Rain Forest in the Parque Nacional Aparados da Serra, southern Santa Catarina state, Brazil. Data collection took place from October 2016 to September 2017 through monthly campaigns, consisting of three consecutive observation days, with sampling sessions of six hours per day, resulting in a total effort of 216 h of observations. For each contact with the flocks, we recorded the species and number of individuals, stratum of occurrence, substrates of search, and agonistic interactions. We recorded 152 mixed flocks, with a total of 76 species belonging to 24 families, and five orders, with Thraupidae, Tyrannidae, Furnariidae, and Rhynchocyclidae being the richest. The flocks had an average of 4.5 ± 2.7 species and 8.7 ± 5.8 individuals, with richness and the number of individuals being positively correlated (R² = 0.8). Mixed flocks occurred throughout the year. There was a great variation in the number of contacts from October to February (from 5 to 20 contacts). Meanwhile from March to September, the coldest period of the year in the region, the number of contacts did not vary (from 9 to 14 contacts). However, there was no difference in the number of contacts between these months (z = 0.37; p = 0.691). Basileuterus culicivorus and Habia rubica were the core species because, in addition to their high participation (46.7 and 32.9%, respectively), they showed frequent and conspicuous movement and vocalization. Thus, a high capacity to enlist a greater number of individuals from different species for the flocks was demonstrated.

Effects of adaptive acceleration response of birds on collective behaviors

Collective dynamics of many interacting particles have been widely studied because of a wealth of their behavioral patterns quite different from the individual traits. A selective way of birds that reacts to their neighbors is one of the main factors characterizing the collective behaviors. Individual birds can react differently depending on their local environment during the collective decision-making process, and these variable reactions can be a source of complex spatiotemporal flocking dynamics. Here, we extend the deterministic Cucker–Smale model by including the individual’s reaction to neighbors’ acceleration where the reaction time depends on the local state of polarity. Simulation results show that the adaptive reaction of individuals induces the collective response of the flock. Birds are not frozen in a complete synchronization but remain sensitive to perturbations coming from environments. We confirm that the adaptivity of the reaction also generates natural fluctuations of orientation and speed, both of which are indeed scale-free as experimentally reported. This work may provide essential insight in designing resilient systems of many active agents working in complex, unpredictable environments.

Flock Dynamics and Approaches for Reducing Mortality Rate among Mubende Goats at BuZARDI Semi-Intensive Farm, Hoima, Uganda

Goats are globally very important domestic small ruminants being kept for meat, milk, skin, byproducts and several socio-cultural purposes. Goat farmers in the Lake Albert Crescent Zone (LACZ) of Uganda identified dry-season feed scarcity, poor breeds, diseases, informal marketing and theft as major constraints which underscore the scarcity of information on improved management technologies and the need for targeted decisions. At BuZARDI goat farm, a semi-intensive farm that is also experiencing similar challenges, we documented management practices and collected production related data for 2 years. We computed flock dynamics and mortality rates purposely to influence decisions aimed at increasing the farm’s productivity. Data were collected using pens and books, validated and analyzed using MS office 2013 and SPSS version 22. The flock size increased from 37 goats in July 2020 to 175 goats in June 2022. One hundred twenty-five goats were introduced into the farm as breeding stock, 89 kids were born on the farm and 61 goats died due to various causes. The average number of goats in the farm per month was 109.2 (SEM = 13.7), female 79.8 (SEM = 10.8) and male 29.4, (SEM = 9.9). Average population of goats at risk of death was 95 and the Mortality rate was 27 goats per 1000 goat months. The disaggregated mortality rate of 5 goats per 1000 goat months and 39 goats per 1000 goat months were obtained for the period FY 2020-2021 and FY2021-2022 respectively. The main contributors to the mortality of goats were worm infestation (33%), fracture and injuries arising from stampedes (18%), Ticks and tick borne diseases (18%), respiratory tract infections (11%) and malnutrition (10%). We recommend strict adherence to the flock health program; improved parasite management, separation & improved care for kids, vaccinations, safer feeding, and evidence based disease management, adoption of digital data collection tools and development of an appropriate app for more accurate determination of mortality rates.

Asymptotic flocking dynamics of a relativistic Cucker–Smale flock under singular communications

We study collision avoidance and flocking dynamics for the relativistic Cucker–Smale (RCS) model with a singular communication weight. For a bounded and regular communication weight, RCS particles can exhibit collisions in finite time depending on the geometry of the initial configuration. In contrast, for a singular communication weight, when particles collide, the associated Cucker–Smale vector field becomes unbounded and the standard Cauchy–Lipschitz theory cannot be applied so that existence theory after collisions is problematic. Thus, the collision avoidance problem is directly linked to the global solvability of the singular RCS model and asymptotic flocking dynamics. In this paper, we present sufficient frameworks leading to the nonexistence of finite-time collisions and asymptotic flocking in terms of initial configuration and blow-up rate at the singular point of communication weight.

Tight Bounds for Asymptotic and Approximate Consensus

Agreeing on a common value among a set of agents is a fundamental problem in distributed computing, which occurs in several variants: In contrast to exact consensus, approximate variants are studied in systems where exact agreement is not possible or required, e.g., in human-made distributed control systems and in the analysis of natural distributed systems, such as bird flocking and opinion dynamics. We study the time complexity of two classical agreement problems: non-terminating asymptotic consensus and terminating approximate consensus. Asymptotic consensus, requires agents to repeatedly set their outputs such that the outputs converge to a common value within the convex hull of initial values; approximate consensus requires agents to eventually stop setting their outputs, which must then lie within a predefined distance of each other. We prove tight lower bounds on the contraction ratios of asymptotic consensus algorithms subject to oblivious message adversaries, from which we deduce bounds on the time complexity of approximate consensus algorithms. In particular, the obtained bounds show optimality of asymptotic and approximate consensus algorithms presented by Charron-Bost et al. (ICALP’16) for certain systems, including the strongest oblivious message adversary in which asymptotic and approximate consensus are solvable. As a corollary we also obtain asymptotically tight bounds for asymptotic consensus in the classical asynchronous model with crashes. Central to the lower-bound proofs is an extended notion of valency, the set of reachable limits of an asymptotic consensus algorithm starting from a given configuration. We further relate topological properties of valencies to the solvability of exact consensus, shedding some light on the relation of these three fundamental problems in dynamic networks.

Bioeconomic Modelling to Assess the Impacts of Using Native Shrubs on the Marginal Portions of the Sheep and Beef Hill Country Farms in New Zealand

New Zealand hill country sheep and beef farms contain land of various slope classes. The steepest slopes have the lowest pasture productivity and livestock carrying capacity and are the most vulnerable to soil mass movements. A potential management option for these areas of a farm is the planting of native shrubs which are browsable and provide erosion control, biodiversity, and a source of carbon credits. A bioeconomic whole farm model was developed by adding a native shrub sub-model to an existing hill country sheep and beef enterprise model to assess the impacts on feed supply, flock dynamics, and farm economics of converting 10% (56.4 hectares) of the entire farm, focusing on the steep slope areas, to native shrubs over a 50-year period. Two native shrub planting rates of 10% and 20% per year of the allocated area were compared to the status quo of no (0%) native shrub plantings. Mean annual feed supply dropped by 6.6% and 7.1% causing a reduction in flock size by 10.9% and 11.6% for the 10% and 20% planting rates, respectively, relative to 0% native shrub over the 50 years. Native shrub expenses exceeded carbon income for both planting rates and, together with reduced income from sheep flock, resulted in lower mean annual discounted total sheep enterprise cash operating surplus for the 10% (New Zealand Dollar (NZD) 20,522) and 20% (NZD 19,532) planting scenarios compared to 0% native shrubs (NZD 22,270). All planting scenarios had positive Net Present Value (NPV) and was highest for the 0% native shrubs compared to planting rates. Break-even carbon price was higher than the modelled carbon price (NZD 32/ New Zealand Emission Unit (NZU)) for both planting rates. Combined, this data indicates planting native shrubs on 10% of the farm at the modelled planting rates and carbon price would result in a reduction in farm sheep enterprise income. It can be concluded from the study that a higher carbon price above the break-even can make native shrubs attractive in the farming system.

Minimalistic Control Scheme for the Development of Search Tasks with Flocks of Robots

This paper proposes a minimalist strategy of agent coordination in a multi-robot system with flocking behavior intended for the development of search tasks in dynamic and unknown environments. The minimalist design principle seeks the ability to implement the strategy on small low-cost robots, with hardware limitations, and with small functional variations among them, a real case of most robotic platforms. We also seek a robust decentralized strategy (without central control) where all agents are virtually identical from the functional point of view, and therefore the damage of a fraction of these agents does not prevent the development of the task. In this sense, our scheme is based on local readings, from which the agents identify the region of the environment in which they find themselves, including obstacles and neighboring agents, and from this information autonomously establish their movement strategy to produce the flocking dynamics to the system. The navigation of the environment is guaranteed by relaxed ergodic movement rules, and the convergence of the search process is achieved by grouping a given number of agents in a particular region of the environment. The strategy was successfully evaluated by simulation by replicating the functional characteristics of real robots and scaling them to large populations.