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Reinforcement in Biology: Stochastic models of group formation and network construction
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Mathematics, Analysis and Applied Mathematics. (collective behaviour)
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Empirical studies show that similar patterns emerge from a large number of different biological systems. For example, the group size distributions of several fish species and house sparrows all follow power law distributions with an exponential truncation. Networks built by ant colonies, slime mold and those are designed by engineers resemble each other in terms of structure and transportation efficiency. Based on the investigation of experimental data, we propose a variety of simple stochastic models to unravel the underlying mechanisms which lead to the collective phenomena in different systems. All the mechanisms employed in these models are rooted in the concept of selective reinforcement. In some systems the reinforcement can build optimal solutions for biological problem solving. This thesis consists of five papers. In the first three papers, I collaborate with biologists to look into group formation in house sparrows  and the movement decisions of damsel fish.  In the last two articles, I look at how shortest paths and networks are  constructed by slime molds and pheromone laying ants, as well as studying  speed-accuracy tradeoffs in slime molds' decision making. The general goal of the study is to better understand how macro level patterns and behaviors emerges from micro level interactions in both spatial and non-spatial biological systems. With the combination of mathematical modeling and experimentation, we are able to reproduce the macro level patterns in the studied biological systems and predict behaviors of the systems using minimum number of parameters.

Place, publisher, year, edition, pages
Uppsala: Department of Mathematics, 2012. , 31 p.
Series
Uppsala Dissertations in Mathematics, ISSN 1401-2049 ; 80
Keyword [en]
reinforcement in biology, merge and split model, preferential attachment, reinforced random walk, network construction, shortest path problem, transport networks, ant algorithm, slime mould, physarum polycephalum, speed-accuracy tradeoff.
National Category
Other Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
URN: urn:nbn:se:uu:diva-186989ISBN: 978-91-506-2327-7 (print)OAI: oai:DiVA.org:uu-186989DiVA: diva2:574200
Public defence
2013-01-10, Häggsalen, Ångström Laboratory, Lägerhyddsvägen 1, Uppsala, 13:15 (English)
Opponent
Supervisors
Available from: 2012-12-20 Created: 2012-12-01 Last updated: 2012-12-20Bibliographically approved
List of papers
1. Understanding Animal Group-Size Distributions
Open this publication in new window or tab >>Understanding Animal Group-Size Distributions
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2011 (English)In: PLoS ONE, ISSN 1932-6203, E-ISSN 1932-6203, Vol. 6, no 8, e23438- p.Article in journal (Refereed) Published
Abstract [en]

One of the most striking aspects of animal groups is their remarkable variation in size, both within and between species. While a number of mechanistic models have been proposed to explain this variation, there are few comprehensive datasets against which these models have been tested. In particular, we only vaguely understand how environmental factors and behavioral activities affect group-size distributions. Here we use observations of House sparrows (Passer domesticus) to investigate the factors determining group-size distribution. Over a wide range of conditions, we observed that animal group sizes followed a single parameter distribution known as the logarithmic distribution. This single parameter is the mean group size experienced by a randomly chosen individual (including the individual itself). For sparrows, the experienced mean group size, and hence the distribution, was affected by four factors: morning temperature, place, behavior and the degree of food spillage. Our results further indicate that the sparrows regulate the mean group size they experience, either by groups splitting more or merging less when local densities are high. We suggest that the mean experienced group size provides a simple but general tool for assessing the ecology and evolution of grouping.

National Category
Biological Sciences
Identifiers
urn:nbn:se:uu:diva-159483 (URN)10.1371/journal.pone.0023438 (DOI)000294678300004 ()
Available from: 2011-10-03 Created: 2011-10-03 Last updated: 2017-12-08Bibliographically approved
2. A first principles derivation of animal group size distributions
Open this publication in new window or tab >>A first principles derivation of animal group size distributions
2011 (English)In: Journal of Theoretical Biology, ISSN 0022-5193, E-ISSN 1095-8541, Vol. 283, no 1, 35-43 p.Article in journal (Refereed) Published
Abstract [en]

Several empirical studies have shown that the animal group size distribution of many species can be well fit by power laws with exponential truncation. A striking empirical result due to Niwa is that the exponent in these power laws is one and the truncation is determined by the average group size experienced by an individual. This distribution is known as the logarithmic distribution. In this paper we provide first principles derivation of the logarithmic distribution and other truncated power laws using a site-based merge and split framework. In particular, we investigate two such models. Firstly, we look at a model in which groups merge whenever they meet but split with a constant probability per time step. This generates a distribution similar, but not identical to the logarithmic distribution. Secondly, we propose a model, based on preferential attachment, that produces the logarithmic distribution exactly. Our derivation helps explain why logarithmic distributions are so widely observed in nature. The derivation also allows us to link splitting and joining behavior to the exponent and truncation parameters in power laws.

Keyword
Truncated power law, The logarithmic distribution, Merge and split dynamics
National Category
Natural Sciences
Identifiers
urn:nbn:se:uu:diva-167671 (URN)10.1016/j.jtbi.2011.04.031 (DOI)000298526600005 ()
Available from: 2012-02-01 Created: 2012-01-31 Last updated: 2017-12-08Bibliographically approved
3. Initiators, leaders and recruitment mechanisms in the collective movements of damselfish
Open this publication in new window or tab >>Initiators, leaders and recruitment mechanisms in the collective movements of damselfish
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2013 (English)In: American Naturalist, ISSN 0003-0147, E-ISSN 1537-5323, Vol. 181, no 6, 748-760 p.Article in journal (Refereed) Published
Abstract [en]

Explaining how individual behavior and social interactions give rise to group-level outcomes and affect issues such as leadership is fundamental to the understanding of collective behavior. Here we examined individual and collective behavioral dynamics in groups of humbug damselfish both before and during a collective movement. During the predeparture phase, group activity increased until the collective movement occurred. Although such movements were precipitated by one individual, the success or failure of any attempt to instigate a collective movement was not solely dependent on this initiator’s behavior but on the behavior of the group as a whole. Specifically, groups were more active and less cohesive before a successful initiation attempt than before a failed attempt. Individuals who made the most attempts to initiate a collective movement during each trial were ultimately most likely to lead the collective movement. Leadership was not related to dominance but was consistent between trials. The probability of fish recruiting to a group movement initiative was an approximately linear function of the number of fish already recruited. Overall, these results are consistent with nonselective local mimetism, with the decision to leave based on a group’s, rather than any particular individual’s, readiness to leave.

Keyword
Collective Decision-Making, Local Interactions, Shoaling
National Category
Behavioral Sciences Biology
Identifiers
urn:nbn:se:uu:diva-187304 (URN)10.1086/670242 (DOI)000318996500005 ()
Available from: 2012-12-04 Created: 2012-12-04 Last updated: 2017-12-07Bibliographically approved
4. Current-reinforced random walks for constructing transport networks
Open this publication in new window or tab >>Current-reinforced random walks for constructing transport networks
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2013 (English)In: Journal of the Royal Society Interface, ISSN 1742-5689, E-ISSN 1742-5662, Vol. 10, no 80, 20120864- p.Article in journal (Refereed) Published
Abstract [en]

Biological systems that build transport networks, such as trail-laying ants and the slime mould Physarum, can be described in terms of reinforced random walks. In a reinforced random walk, the route taken by 'walking' particles depends on the previous routes of other particles. Here, we present a novel form of random walk in which the flow of particles provides this reinforcement. Starting from an analogy between electrical networks and random walks, we show how to include current reinforcement. We demonstrate that current-reinforcement results in particles converging on the optimal solution of shortest path transport problems, and avoids the self-reinforcing loops seen in standard density-based reinforcement models. We further develop a variant of the model that is biologically realistic, in the sense that the particles can be identified as ants and their measured density corresponds to those observed in maze-solving experiments on Argentine ants. For network formation, we identify the importance of nonlinear current reinforcement in producing networks that optimize both network maintenance and travel times. Other than ant trail formation, these random walks are also closely related to other biological systems, such as blood vessels and neuronal networks, which involve the transport of materials or information. We argue that current reinforcement is likely to be a common mechanism in a range of systems where network construction is observed.

National Category
Other Mathematics
Identifiers
urn:nbn:se:uu:diva-187306 (URN)10.1098/rsif.2012.0864 (DOI)000314285400014 ()
Available from: 2012-12-04 Created: 2012-12-04 Last updated: 2017-12-07Bibliographically approved
5. Speed-accuracy tradeoffs and the construction of transport netowrks
Open this publication in new window or tab >>Speed-accuracy tradeoffs and the construction of transport netowrks
(English)Manuscript (preprint) (Other academic)
Abstract [en]

One of the key challenges in the study of networks is linking structure to function. For example, how do design requirements about the speed and accuracy with which information is transferred through a network determine its form?  We show that different strains of the slime mould Physarum polycephalum form different network structures, ranging from a diffuse network of thin links to a tree-like branching structure.  Using a current-reinforced random walk model, we explain these different structures in terms of two model parameters: the strength and the degree of non-linearity in the reinforcement. These parameters are further shown to tune the speed and accuracy with which the network can detect resource gradients. We use a battery of experimental tests to show that Physarum strains with diffuse networks make more accurate but slower decisions and those with thick, trunk branches make faster less accurate decisions. Intermediate structures can also be found which are relatively fast and accurate. The current reinforced random walk employed by the slime mould provides a tunable algorithm for decision-making, which may also apply in other systems where transport networks are constructed.

National Category
Behavioral Sciences Biology Other Mathematics
Research subject
Mathematics with specialization in Applied Mathematics
Identifiers
urn:nbn:se:uu:diva-186990 (URN)
Available from: 2012-12-01 Created: 2012-12-01 Last updated: 2012-12-01

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