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Cosner C, Rodríguez N. On the Allee effect and directed movement on the whole space. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2023; 20:8010-8030. [PMID: 37161183 DOI: 10.3934/mbe.2023347] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
It is well known that relocation strategies in ecology can make the difference between extinction and persistence. We consider a reaction-advection-diffusion framework to analyze movement strategies in the context of species which are subject to a strong Allee effect. The movement strategies we consider are a combination of random Brownian motion and directed movement through the use of an environmental signal. We prove that a population can overcome the strong Allee effect when the signals are super-harmonic. In other words, an initially small population can survive in the long term if they aggregate sufficiently fast. A sharp result is provided for a specific signal that can be related to the Fokker-Planck equation for the Orstein-Uhlenbeck process. We also explore the case of pure diffusion and pure aggregation and discuss their benefits and drawbacks, making the case for a suitable combination of the two as a better strategy.
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Affiliation(s)
- Chris Cosner
- University of Miami, Department of Mathematics, 1365 Memorial Drive, Ungar 515, Coral Gables, FL 33146, USA
| | - Nancy Rodríguez
- CU Boulder, Department of Applied Mathematics, 11 Engineering Dr, Boulder, CO 80309, USA
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2
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Eliaš J, Izuhara H, Mimura M, Tang BQ. An aggregation model of cockroaches with fast-or-slow motion dichotomy. J Math Biol 2022; 85:28. [PMID: 36098821 DOI: 10.1007/s00285-022-01797-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2021] [Revised: 08/13/2022] [Accepted: 08/25/2022] [Indexed: 10/14/2022]
Abstract
We propose a mathematical model, namely a reaction-diffusion system, to describe social behaviour of cockroaches. An essential new aspect in our model is that the dispersion behaviour due to overcrowding effect is taken into account as a counterpart to commonly studied aggregation. This consideration leads to an intriguing new phenomenon which has not been observed in the literature. Namely, due to the competition between aggregation towards areas of higher concentration of pheromone and dispersion avoiding overcrowded areas, the cockroaches aggregate more at the transition area of pheromone. Moreover, we also consider the fast reaction limit where the switching rate between active and inactive subpopulations tends to infinity. By utilising improved duality and energy methods, together with the regularisation of heat operator, we prove that the weak solution of the reaction-diffusion system converges to that of a reaction-cross-diffusion system.
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Affiliation(s)
- Ján Eliaš
- Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria
| | - Hirofumi Izuhara
- Faculty of Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai Nishi, Miyazaki, 889-2192, Japan.
| | - Masayasu Mimura
- Graduate School of Integrated Sciences for Life, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima City, Hiroshima, 739-8526, Japan
| | - Bao Q Tang
- Institute of Mathematics and Scientific Computing, University of Graz, Heinrichstrasse 36, 8010, Graz, Austria
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3
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Differential Gene Expression Correlates with Behavioural Polymorphism during Collective Behaviour in Cockroaches. Animals (Basel) 2022; 12:ani12182354. [PMID: 36139214 PMCID: PMC9495117 DOI: 10.3390/ani12182354] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/15/2022] [Revised: 09/01/2022] [Accepted: 09/05/2022] [Indexed: 11/16/2022] Open
Abstract
Simple Summary It is currently well accepted that animals differ from one another in their behaviour and tendency to perform actions, a property we refer to as animal personality. In group-living animals, variation in animal personality can be important to determine group survival, as it determines how individuals interact with each other and with their environment. However, we have little knowledge of the proximal mechanisms underlying personality, particularly in group-living organisms. Here, we investigate the relationship between gene expression and two behavioural types (bold and shy) in a gregarious species: the American cockroach. Our results show that bold individuals have upregulated genes with functions associated with sensory activity (phototaxis and odour detection) and aggressive/dominant behaviour, and suggest that social context can modulate gene expression related to bold/shy characteristics. This work could help identify genes important in the earliest stages of group living and social life, and provides a first step toward establishing cockroaches as a focal group for the study of the evolution of sociality. Abstract Consistent inter-individual variation in the propensity to perform different tasks (animal personality) can contribute significantly to the success of group-living organisms. The distribution of different personalities in a group influences collective actions and therefore how these organisms interact with their environment. However, we have little understanding of the proximate mechanisms underlying animal personality in animal groups, and research on this theme has often been biased towards organisms with advanced social systems. The goal of this study is to investigate the mechanistic basis for personality variation during collective behaviour in a species with rudimentary societies: the American cockroach. We thus use an approach which combines experimental classification of individuals into behavioural phenotypes (‘bold’ and ‘shy’ individuals) with comparative gene expression. Our analyses reveal differences in gene expression between behavioural phenotypes and suggest that social context may modulate gene expression related to bold/shy characteristics. We also discuss how cockroaches could be a valuable model for the study of genetic mechanisms underlying the early steps in the evolution of social behaviour and social complexity. This study provides a first step towards a better understanding of the molecular mechanisms associated with differences in boldness and behavioural plasticity in these organisms.
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Planas-Sitjà I. Personality variation improves collective decision-making in cockroaches. Behav Processes 2020; 177:104147. [PMID: 32454182 DOI: 10.1016/j.beproc.2020.104147] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2020] [Revised: 05/21/2020] [Accepted: 05/21/2020] [Indexed: 11/16/2022]
Abstract
Many animals live in groups and engage in collective actions which can enhance their fitness. One common example is collective decision-making, which mainly arises from social interactions that modify the individual behaviour. Despite the widespread interest in animal personalities on the one hand and in social effects (such as social organisation, social learning or anti-predator behaviour) on the other, the question of how the amount of among-individual differences, coupled with social interactions, influence group cohesion has rarely been addressed. For this purpose, I used a modelling approach based on aggregation behaviour of cockroaches to explore the mechanisms underlying such context-dependent behaviour. The results of simulations considering different degrees (none, medium, high) of personality variation in a non-social and social context were compared to experimental patterns of aggregation dynamics in cockroaches. The comparison between the simulated and experimental data show that only a model that considers differences in individuals was able to reproduce the experimental patterns of individuals and groups. In addition, the comparison between models suggest that some individuals may play a keystone role during aggregation dynamics, influencing the behaviour of others and facilitating the collective decision. Finally, I show that personality variation amplifies the effects of social inter-attractions, thus increasing the speed of aggregation, shedding light on the mechanisms underpinning social modification of individual behaviour.
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Affiliation(s)
- Isaac Planas-Sitjà
- Systematic Zoology Laboratory, Tokyo Metropolitan University, 1-1 Minami-Osawa, Hachioji, Tokyo, 192-0397, Japan.
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Planas-Sitjà I, Laurent Salazar MO, Sempo G, Deneubourg JL. Emigration dynamics of cockroaches under different disturbance regimes do not depend on individual personalities. Sci Rep 2017; 7:44528. [PMID: 28300147 PMCID: PMC5353543 DOI: 10.1038/srep44528] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/16/2016] [Accepted: 02/10/2017] [Indexed: 11/09/2022] Open
Abstract
Group-level properties, such as collective movements or decisions, can be considered an outcome of the interplay between individual behavior and social interactions. However, the respective influences of individual preferences and social interactions are not evident. In this research, we study the implications of behavioral variability on the migration dynamics of a group of gregarious insects (Periplaneta americana) subjected to two different disturbance regimes (one without disturbances and another one with high frequency of disturbances). The results indicate that individuals presented consistent behavior during the nighttime (active phase of cockroaches) in both conditions. Moreover, we used a modeling approach to test the role of personality during the migration process. The model considers identical individuals (no personality) without memory and no direct inter-attraction between individuals. The agreement between theoretical and experimental results shows that behavioral variability play a secondary role during migration dynamics. Our results showing individual personality during the nighttime (spontaneous decision to forage) but not during the emigration process (induced by environmental disturbances) highlight the plasticity of personality traits.
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Affiliation(s)
- I Planas-Sitjà
- Unit of Social Ecology - CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO - level 5, B-1050 Bruxelles, Belgium
| | - M O Laurent Salazar
- Unit of Social Ecology - CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO - level 5, B-1050 Bruxelles, Belgium
| | - G Sempo
- Unit of Social Ecology - CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO - level 5, B-1050 Bruxelles, Belgium
| | - J L Deneubourg
- Unit of Social Ecology - CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO - level 5, B-1050 Bruxelles, Belgium
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Broly P, Mullier R, Devigne C, Deneubourg JL. Regulatory mechanisms of group distributions in a gregarious arthropod. ROYAL SOCIETY OPEN SCIENCE 2015; 2:150428. [PMID: 26715999 PMCID: PMC4680614 DOI: 10.1098/rsos.150428] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/24/2015] [Accepted: 10/29/2015] [Indexed: 06/05/2023]
Abstract
In a patchy environment, how social animals manage conspecific and environmental cues in their choice of habitat is a leading issue for understanding their spatial distribution and their exploitation of resources. Here, we experimentally tested the effects of environmental heterogeneities (artificial shelters) and some of their characteristics (size and fragmentation) on the aggregation process of a common species of terrestrial isopod (Crustacea). One hundred individuals were introduced into three different heterogeneous set-ups and in a homogeneous set-up. In the four set-ups, the populations split into two aggregates: one large (approx. 70 individuals) and one smaller (approx. 20 individuals). These aggregates were not randomly distributed in the arena but were formed diametrically opposite from one another. The similarity of the results among the four set-ups shows that under experimental conditions, the environmental heterogeneities have a low impact on the aggregation dynamics and spatial patterns of the isopod, merely serving to increase the probability of nucleation of the larger aggregation at these points. By contrast, the regulation of aggregate sizes and the regular distribution of groups are signatures of local amplification processes, in agreement with the short-range activator and long-range inhibitor model (scale-dependent feedbacks). In other words, we show how small-scale interactions may govern large-scale spatial patterns. This experimental illustration of spatial self-organization is an important step towards comprehension of the complex game of competition among groups in social species.
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Affiliation(s)
- Pierre Broly
- Unité d’Ecologie Sociale, Université Libre de Bruxelles, Campus de la Plaine, Bruxelles, Belgium
| | - Romain Mullier
- Laboratoire Ecologie et Biodiversité, Faculté de Gestion, Economie et Sciences, UCLILLE, Lille, France
| | - Cédric Devigne
- Laboratoire Ecologie et Biodiversité, Faculté de Gestion, Economie et Sciences, UCLILLE, Lille, France
- Forensic Taphonomy Unit, University Lille Nord de France—UDSL, 59000 Lille, France
| | - Jean-Louis Deneubourg
- Unité d’Ecologie Sociale, Université Libre de Bruxelles, Campus de la Plaine, Bruxelles, Belgium
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Behavioural Contagion Explains Group Cohesion in a Social Crustacean. PLoS Comput Biol 2015; 11:e1004290. [PMID: 26067565 PMCID: PMC4465910 DOI: 10.1371/journal.pcbi.1004290] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2014] [Accepted: 04/17/2015] [Indexed: 11/26/2022] Open
Abstract
In gregarious species, social interactions maintain group cohesion and the associated adaptive values of group living. The understanding of mechanisms leading to group cohesion is essential for understanding the collective dynamics of groups and the spatio-temporal distribution of organisms in environment. In this view, social aggregation in terrestrial isopods represents an interesting model due to its recurrence both in the field and in the laboratory. In this study, and under a perturbation context, we experimentally tested the stability of groups of woodlice according to group size and time spent in group. Our results indicate that the response to the disturbance of groups decreases with increases in these two variables. Models neglecting social effects cannot reproduce experimental data, attesting that cohesion of aggregation in terrestrial isopods is partly governed by a social effect. In particular, models involving calmed and excited individuals and a social transition between these two behavioural states more accurately reproduced our experimental data. Therefore, we concluded that group cohesion (and collective response to stimulus) in terrestrial isopods is governed by a transitory resting state under the influence of density of conspecifics and time spent in group. Lastly, we discuss the nature of direct or indirect interactions possibly implicated. Terrestrial isopods, commonly named woodlice or pill bugs, are commonly distributed soil-dwelling arthropods, particularly important in soils as macro-decomposers of leaf litter. Many species of woodlice are synanthropic and, for this reason, are easily observable in gardens, urban parks or composts. Harmless organisms and easy to raise, the woodlice represent an excellent pedagogical model in many schools, so that children may perform on these organisms various behavioral tests such as light escape or introduction to social behaviors. Indeed, woodlice are gregarious species and exhibit long phases of aggregation. Here, we propose a model based on simple rules involving calmed and excited individuals and a social transition between these two behavioural states to explain group cohesion in woodlice. This contagion model well reproduces our experimental results. Our approach provides important clues for the understanding of how social group effects and collective mechanisms may govern the stability and dispersion of aggregates in gregarious arthropods.
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Planas-Sitjà I, Deneubourg JL, Gibon C, Sempo G. Group personality during collective decision-making: a multi-level approach. Proc Biol Sci 2015; 282:20142515. [PMID: 25652834 PMCID: PMC4344149 DOI: 10.1098/rspb.2014.2515] [Citation(s) in RCA: 54] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Accepted: 01/07/2015] [Indexed: 12/27/2022] Open
Abstract
Collective decision-making processes emerge from social feedback networks within a group. Many studies on collective behaviour underestimate the role of individual personality and, as a result, personality is rarely analysed in the context of collective dynamics. Here, we show evidence of sheltering behaviour personality in a gregarious insect (Periplaneta americana), which is characterized by a collective personality at the group level. We also highlight that the individuals within groups exhibited consistent personality traits in their probability of sheltering and total time sheltered during the three trials over one week. Moreover, the group personality, which arises from the synergy between the distribution of behaviour profiles in the group and social amplifications, affected the sheltering dynamics. However, owing to its robustness, personality did not affect the group probability of reaching a consensus. Finally, to prove social interactions, we developed a new statistical method that will be helpful for future research on personality traits and group behaviour. This approach will help to identify the circumstances under which particular group compositions may improve the fitness of individuals in gregarious species.
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Affiliation(s)
- Isaac Planas-Sitjà
- Unit of Social Ecology-CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO-level 5, 1050 Bruxelles, Belgium
| | - Jean-Louis Deneubourg
- Unit of Social Ecology-CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO-level 5, 1050 Bruxelles, Belgium
| | - Céline Gibon
- Unit of Social Ecology-CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO-level 5, 1050 Bruxelles, Belgium
| | - Grégory Sempo
- Unit of Social Ecology-CP 231, Université libre de Bruxelles (ULB), Campus Plaine, Boulevard du Triomphe, Building NO-level 5, 1050 Bruxelles, Belgium
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