Strategy Diversity Stabilizes Mutualism through Investment Cycles, Phase Polymorphism, and Spatial Bubbles
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{"title"=>"Strategy Diversity Stabilizes Mutualism through Investment Cycles, Phase Polymorphism, and Spatial Bubbles", "type"=>"journal", "authors"=>[{"first_name"=>"Gergely", "last_name"=>"Boza", "scopus_author_id"=>"8690218100"}, {"first_name"=>"Ádám", "last_name"=>"Kun", "scopus_author_id"=>"7004078992"}, {"first_name"=>"István", "last_name"=>"Scheuring", "scopus_author_id"=>"7003538716"}, {"first_name"=>"Ulf", "last_name"=>"Dieckmann", "scopus_author_id"=>"7003359350"}], "year"=>2012, "source"=>"PLoS Computational Biology", "identifiers"=>{"pui"=>"366216185", "scopus"=>"2-s2.0-84870680718", "pmid"=>"23166478", "sgr"=>"84870680718", "issn"=>"1553734X", "doi"=>"10.1371/journal.pcbi.1002660"}, "id"=>"9c2566f8-81dd-3dc4-a0cd-04c4d62427b3", "abstract"=>"There is continuing interest in understanding factors that facilitate the evolution and stability of cooperation within and between species. Such interactions will often involve plasticity in investment behavior, in response to the interacting partner's investments. Our aim here is to investigate the evolution and stability of reciprocal investment behavior in interspecific interactions, a key phenomenon strongly supported by experimental observations. In particular, we present a comprehensive analysis of a continuous reciprocal investment game between mutualists, both in well-mixed and spatially structured populations, and we demonstrate a series of novel mechanisms for maintaining interspecific mutualism. We demonstrate that mutualistic partners invariably follow investment cycles, during which mutualism first increases, before both partners eventually reduce their investments to zero, so that these cycles always conclude with full defection. We show that the key mechanism for stabilizing mutualism is phase polymorphism along the investment cycle. Although mutualistic partners perpetually change their strategies, the community-level distribution of investment levels becomes stationary. In spatially structured populations, the maintenance of polymorphism is further facilitated by dynamic mosaic structures, in which mutualistic partners form expanding and collapsing spatial bubbles or clusters. Additionally, we reveal strategy-diversity thresholds, both for well-mixed and spatially structured mutualistic communities, and discuss factors for meeting these thresholds, and thus maintaining mutualism. Our results demonstrate that interspecific mutualism, when considered as plastic investment behavior, can be unstable, and, in agreement with empirical observations, may involve a polymorphism of investment levels, varying both in space and in time. Identifying the mechanisms maintaining such polymorphism, and hence mutualism in natural communities, provides a significant step towards understanding the coevolution and population dynamics of mutualistic interactions.", "link"=>"http://www.mendeley.com/research/strategy-diversity-stabilizes-mutualism-through-investment-cycles-phase-polymorphism-spatial-bubbles", "reader_count"=>39, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Researcher"=>6, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>15, "Student > Master"=>4, "Student > Bachelor"=>5, "Professor"=>1}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>3, "Researcher"=>6, "Student > Doctoral Student"=>4, "Student > Ph. D. Student"=>15, "Student > Master"=>4, "Student > Bachelor"=>5, "Professor"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>2, "Environmental Science"=>4, "Mathematics"=>1, "Agricultural and Biological Sciences"=>27, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>3, "Economics, Econometrics and Finance"=>1}, "reader_count_by_subdiscipline"=>{"Physics and Astronomy"=>{"Physics and Astronomy"=>3}, "Economics, Econometrics and Finance"=>{"Economics, Econometrics and Finance"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>27}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Mathematics"=>{"Mathematics"=>1}, "Unspecified"=>{"Unspecified"=>2}, "Environmental Science"=>{"Environmental Science"=>4}}, "reader_count_by_country"=>{"Venezuela"=>1, "United States"=>8, "Japan"=>1, "Brazil"=>3, "Tunisia"=>1}, "group_count"=>3}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/540538"], "description"=>"<p>(A) Best-response dynamics. Arrows indicate the succession of best responses, leading to in just four steps. (B) Evolutionary dynamics in a community with low degrees of polymorphism and “pairwise comparison” updating. Arrows indicate changes of the selection gradient along the investment cycle. In A and B, representative evolutionary trajectories are shown starting above the reciprocation threshold (thick gray lines). (C) Resultant changes of investment traits and payoffs along the investment cycle in B. Results in B and C are averaged over 15 replicate model runs for the same initial condition. Parameters: , , , , , , and .</p>", "links"=>[], "tags"=>["reciprocation", "well-mixed"], "article_id"=>211031, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g001"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_investment_cycle_and_reciprocation_threshold_in_well_mixed_communities_/211031", "title"=>"Illustration of investment cycle and reciprocation threshold in well-mixed communities.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:05:04"}
  • {"files"=>["https://ndownloader.figshare.com/files/540593"], "description"=>"<p>(A) Diversity thresholds revealed by the effect of mutational variability on the average payoff in the community. For lower mutational standard deviations , there is no mutualism (left-hand side), while stable community-level mutualism evolves abruptly once mutational variability is high enough (right-hand side). Results are averaged over the two mutualists and 15 replicate model runs. Payoffs can range between 0 and the maximal potential payoff . (B, C, D) Polymorphic spread of strategies in well-mixed communities, and their evolution along the investment cycle, with low, medium, or high mutational standard deviations: in B, in C, and in D. As the averages of the traits and move along the investment cycle, they trace out the shown circular lines, corresponding to cyclic oscillations whose amplitudes decrease as increases. Other parameters: in A and in B, C, and D; lower benefit-to-cost ratio of in A: , , ; higher benefit-to-cost ratio of in A, B, C, and D: , , ; , .</p>", "links"=>[], "tags"=>["mutualistic", "investments", "communities", "higher", "degrees"], "article_id"=>211086, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g002"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Evolution_and_stability_of_mutualistic_investments_in_communities_with_higher_degrees_of_polymorphism_/211086", "title"=>"Evolution and stability of mutualistic investments in communities with higher degrees of polymorphism.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:05:24"}
  • {"files"=>["https://ndownloader.figshare.com/files/540651"], "description"=>"<p>(A) Arrows indicate the selection gradients on a random subsample of individuals of Mutualist A as that mutualist's trait distribution (gray dots) moves along the investment cycle (gray circular lines). Average long-term polymorphic distribution of (B) phases along the investment cycle and (C) corresponding phase asymmetries during the evolution of mutualistic investments, averaged over three replicate model runs and shown on logarithmic scales. The phase asymmetry in pairs of interacting individuals of Mutualist A and B is measured as the difference of their phases, . The peaks at and in B correspond, respectively, to the vertical and horizontal edges of the investment cycle. Parameters: in A and in B and C; in A and in B and C; , , , , and .</p>", "links"=>[], "tags"=>["gradients", "resultant", "well-mixed", "polymorphic"], "article_id"=>211146, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g003"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Selection_gradients_along_the_investment_cycle_and_resultant_phase_distribution_in_a_well_mixed_polymorphic_community_/211146", "title"=>"Selection gradients along the investment cycle and resultant phase distribution in a well-mixed polymorphic community.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:05:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/540707"], "description"=>"<p>(A) Typical snapshot of the spatial mosaic structure, indicating a high degree of polymorphism and spatial bubbles comprising different strategies. Each pixel represents an individual, rendered according to its payoff between zero (light gray) and the maximal value (black). (B) Enlargement of a bubble with its surrounding insulating boundary layer. Notice that individuals inside and outside the bubble both have higher payoffs than the individuals forming the boundary layer. This panel is obtained as an overlay of Mutualist A and B from the third column in D according to their average payoff values. (C) Shading of background strategies ranges from white to mid-gray, while shading for the focal bubble ranges from dark-gray to black, as the payoffs of individuals increase. (D) Time series of snapshots for a spatial bubble (black to dark-gray shading) that first expands and then vanishes, illustrating a spatial “boom and bust” cycle (snapshots are taken in generations 3013, 3040, 3260, 3399, 3493, 3625, 5165, 5620, 6400, and 6408). Parameters: in A and in D; , , , , , and .</p>", "links"=>[], "tags"=>["insulating"], "article_id"=>211206, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g004"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Spatial_bubble_dynamics_and_appearance_of_the_insulating_boundary_layer_/211206", "title"=>"Spatial bubble dynamics and appearance of the insulating boundary layer.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:06:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/540769"], "description"=>"<p>We presume that strategy pairs meet at the interface (white columns) of bubble 1 (dark-gray columns) and bubble 2 (light-gray columns). Here, the following cases can occur: (A) Unidirectional invasion: both mutualists from bubble 1 invade the other bubble, as both A1 and B1 have a higher payoff than A2 and B2. (B) Partner swapping: A1 has a higher payoff and outcompetes A2, but B2 has a higher payoff and outcompetes B1, hence A1 pairs up with B2. (C) Catalyzed invasion: only A1 is able to outcompete its competitor from bubble 2, but as it spreads, it makes it possible for B1 to follow. This is feasible because B2 fares worse with A1 than with A2, so as A1 spreads, the payoff of B2 decreases with its new partner, and hence B1 can now invade. (D) Insulating boundary layer: at the interface of two spatial bubbles, the originally competitively superior strategies A1 and B2 enter the interface, but as both then have a lower payoff than with their original partners, neither can spread further. Column heights depict the payoffs of strategies. For the described dynamics, the payoffs of a strategy with its two possible partners (i.e., from either bubble 1 or 2) at the interface must lie within the interval indicated by the two whiskers in the middle column. (E) Invasion dynamics depend on the strategy compositions of the mutualist pairs. Formation of an insulating boundary layer is the result of the encounter of two strategy pairs (A1&B1, A2&B2) that are mutually unable to invade each other (gray area). Otherwise, one bubble invades and replaces the other (in the white area, the strategy pair of bubble 1 wins, whereas in the black area, the strategy pair of bubble 2 wins). We evaluate these outcomes in the absence of evolution (no mutations) and for one strategy pair (A1&B1) initially occupying one half of the lattice and the other strategy pair (A2&B2) occupying the other half. Parameters: A1 and B1, and ; A2, and ; B2, and ; , , , , and .</p>", "links"=>[], "tags"=>["interface", "spatial"], "article_id"=>211267, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g005"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Possible_replacement_dynamics_at_the_interface_between_two_spatial_bubbles_/211267", "title"=>"Possible replacement dynamics at the interface between two spatial bubbles.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:06:20"}
  • {"files"=>["https://ndownloader.figshare.com/files/540823"], "description"=>"<p>Each individual panel shows the average payoff of Mutualist A and Mutualist B, calculated as the arithmetic mean of their payoffs over the last generations, out of the total of generations, and averaged over five replicate model runs. The three parameters of the benefit and cost functions are varied as follows: and along the axes and between the upper () and lower () eight panels. The black line on white background indicates the threshold, below which no investments can evolve. Results for well-mixed populations are shown in the eight panels on the left, while results for spatially structured populations are shown in the eight panels on the right. Odd and even columns correspond to synchronous and asynchronous updating, respectively. Rows show results for a constant mutational standard deviation (first and third rows) and a constant mutational coefficient of variation (second and fourth rows). Other parameters: , , and .</p>", "links"=>[], "tags"=>["payoff", "parameters", "spatial"], "article_id"=>211319, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g006"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_payoff_as_a_function_of_the_parameters_of_the_cost_and_benefit_functions_spatial_structure_and_update_rules_/211319", "title"=>"Average payoff as a function of the parameters of the cost and benefit functions, spatial structure, and update rules.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:06:37"}
  • {"files"=>["https://ndownloader.figshare.com/files/540889"], "description"=>"<p>Spheres depict strategies, and the links between spheres represent the interactions between interacting strategies from the two mutualist guilds. (B) According to its own and its partner's strategy, an individual receives a payoff (schematically illustrated by two triangles that become darker and wider as the received payoff increases). The comparison of payoffs between partners shows whether their interaction is more mutualistic (middle) or more exploitative (bottom and top). (D) Average distribution of interaction types in our model, showing that small relative differences between the payoffs of interacting individuals are more common or longer-lasting than extreme exploitations. (E) Average distribution of the payoff sums and relative payoff differences for interacting individuals of Mutualist A and Mutualist B, demonstrating that, on average, payoffs in asymmetric, or exploitative, interactions are lower than in symmetric, or more mutualistic, interactions. The distributions in D and E are based on sampling all individuals in every generation for generations and for five replicate model runs. The relative difference between the payoffs and of individuals and is given by , and is given by . Parameters: , , , , , , and .</p>", "links"=>[], "tags"=>["mutualistic", "interactions", "monomorphic", "polymorphic", "mutualist"], "article_id"=>211388, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Evolutionary Biology"], "users"=>["Gergely Boza", "Ádám Kun", "István Scheuring", "Ulf Dieckmann"], "doi"=>["https://dx.doi.org/10.1371/journal.pcbi.1002660.g007"], "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Schematic_representation_of_mutualistic_interactions_in_A_monomorphic_and_C_polymorphic_mutualist_communities_/211388", "title"=>"Schematic representation of mutualistic interactions in (A) monomorphic and (C) polymorphic mutualist communities.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 20:07:01"}

PMC Usage Stats | Further Information

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Relative Metric

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