Consensus time in a voter model with concealed and publicly expressed opinions

The voter model is a simple agent-based model to mimic opinion dynamics in social networks: a randomly chosen agent adopts the opinion of a randomly chosen neighbour. This process is repeated until a consensus emerges. Although the basic voter model is theoretically intriguing, it misses an important feature of real opinion dynamics: it does not distinguish between an agent's publicly expressed opinion and her inner conviction. A person may not feel comfortable declaring her conviction if her social circle appears to hold an opposing view. Here we introduce the Concealed Voter Model where we add a second, concealed layer of opinions to the public layer. If an agent's public and concealed opinions disagree, she can reconcile them by either publicly disclosing her previously secret point of view or by accepting her public opinion as inner conviction. We study a complete graph of agents who can choose from two opinions. We define a martingale $M$ that determines the probability of all agents eventually agreeing on a particular opinion. By analyzing the evolution of $M$ in the limit of a large number of agents, we derive the leading-order terms for the mean and standard deviation of the consensus time (i.e. the time needed until all opinions are identical). We thereby give a precise prediction by how much concealed opinions slow down a consensus.Comment: 21 pages, 6 figures, to appear in J. Stat. Mech. Theory Ex

Intermediate landscape disturbance maximizes metapopulation density

The viability of metapopulations in fragmented landscapes has become a central theme in conservation biology. Landscape fragmentation is increasingly recognized as a dynamical process: in many situations, the quality of local habitats must be expected to undergo continual changes. Here we assess the implications of such recurrent local disturbances for the equilibrium density of metapopulations. Using a spatially explicit lattice model in which the considered metapopulation as well as the underlying landscape pattern change dynamically, we show that equilibrium metapopulation density is maximized at intermediate frequencies of local landscape disturbance. On both sides around this maximum, the metapopulation may go extinct. We show how the position and shape of the intermediate viability maximum is responding to changes in the landscape’s overall habitat quality and the population’s propensity for local extinction. We interpret our findings in terms of a dual effect of intensified landscape disturbances, which on the one hand exterminate local populations and on the other hand enhance a metapopulation’s capacity for spreading between habitat clusters

Élőhelyek térbeli szerkezete, populációk fennmaradása - dinamikai modellek = Habitat structure and population survival - dynamic models

Számítógépes szimulációk segítségével vizsgáltuk különböző környezeti mintázatokon élő populációk dinamikáját. A vizsgálatok térbeli és időbeli léptéke tág tartományt ölelt fel: térben a társulásbeli foltmintázatoktól a táji mintázatokig, időben különböző ökológiai folyamatok léptékétől az evolúciós időskáláig. Közös volt, hogy a külső környezeti tényező és az élőlénypopuláció dinamikáját egységes modellrendszer keretein belül vizsgáltuk. Ehhez az ökológia két nagy területéről merítettük az ismereteket: a tájökológiából és a térbeli populációdinamikából, összekötve a két terület modellezési technikáit. Eredményeink új lehetőségeket nyitottak a természetes populációk védelmében, valamint a klímaváltozások hatásainak előrejelzésében és monitorozásában. | We investigated the dynamics of populations in various habitat patterns. The spatial and temporal scale of the study spanned across a broad range: in space, it ranged from the fine scale of microhabitat patches up to the broad scale of landscape patterns; over time, it ranged from ecological to evolutionary processes. All our studies shared a common feature: population dynamics and habitat dynamics were considered in a unified modeling framework. We connected modeling techniques from landscape ecology and spatial population ecology. Our results opened new avenues of research in the protection of natural populations, and in predicting and monitoring the ecological effects of climate change

Five main phases of landscape degradation revealed by a dynamic mesoscale model analysing the splitting, shrinking, and disappearing of habitat patches

The ecological consequences of habitat loss and fragmentation have been intensively studied on a broad, landscape-wide scale, but have less been investigated on the finer scale of individual habitat patches, especially when considering dynamic turnovers in the habitability of sites. We study changes to individual patches from the perspective of the inhabitant organisms requiring a minimum area for survival. With patches given by contiguous assemblages of discrete habitat sites, the removal of a single site necessarily causes one of the following three elementary local events in the affected patch: splitting into two or more pieces, shrinkage without splitting, or complete disappearance. We investigate the probabilities of these events and the effective size of the habitat removed by them from the population's living area as the habitat landscape gradually transitions from pristine to totally destroyed. On this basis, we report the following findings. First, we distinguish four transitions delimiting five main phases of landscape degradation: (1) when there is only a little habitat loss, the most frequent event is the shrinkage of the spanning patch; (2) with more habitat loss, splitting becomes significant; (3) splitting peaks; (4) the remaining patches shrink; and (5) finally, they gradually disappear. Second, organisms that require large patches are especially sensitive to phase 3. This phase emerges at a value of habitat loss that is well above the percolation threshold. Third, the effective habitat loss caused by the removal of a single habitat site can be several times higher than the actual habitat loss. For organisms requiring only small patches, this amplification of losses is highest during phase 4 of the landscape degradation, whereas for organisms requiring large patches, it peaks during phase 3

Adaptív ökológia változó környezetben = Adaptive ecology in variable environment

A pályázat alapkérdése a versengés és együttélés, szelekció és sokféleség viszonya úgy ökológiai, mint evolúciós szempontból: ökológiában niche elmélet; evolúcióelméletben fajkeletkezés. Ökológiai eredményeink legfontosabbika a korlátozott hasonlóság modell-független elmélete, amely az együttélés robusztusságát összeköti az együttélő fajok közötti - pontos matematikai értelemben vett - niche szegregációval. Az általános összefüggés konkrét megnyilvánulásait specifikus esetekben vizsgáltuk, a klasszikus Lotka-Volterra versengési modelltől a térben strukturált, illetve időben fluktuáló esetekig. Evolúciós kutatásaink a divergens evolúció lehetőségéről szólnak. Az adaptív dinamika elméletének egy új megalapozását adtuk meg, amely azt a populációdinamikából vezeti le a kis evolúciós lépések feltételezésével. Biológiailag ez a populációreguláció és az adaptív tájkép fogalma összekapcsolásának felel meg és megalapozza a szétágazó evolúció niche-szétválásként való értelmezését. A fajkeletkezési probléma másik oldalát, a reproduktív izoláció létrejöttét egy analitikusan kezelhető minimál-modellben vizsgáltuk. A pályázat eredményeiből 13 nemzetközi publikáció született, amelyek együttes impakt faktora 38. | The basic issue of the work, reported here, is the relationship between competition and coexistence; selection and diversity from ecological as well as from evolutionary point of view. In ecology it corresponds to niche theory; in evolutionary theory it is speciation. Our most important ecological result is a model-independent theory of limiting similarity. It connects robustness of coexistence to niche differentiation in a precise mathematical way. We studied the implementations of this general framework in several specific cases from the classical Lotka-Voltarra model to spatially explicit and temporally fluctuating situations. Our evolutionary investigations are concerned about divergent evolution. A new underpinning of adaptive dynamics was introduced: it was derived from the explicitly considered underlying population dynamics with the single assumption of evolution via small steps. From biological point of view it corresponds to establishing a connection between the notions of adaptive landscape and population regulation. The other side of the speciation problem, the emergence of reproductive isolation was studied in an analytically tractable minimal model. We published 13 papers with cumulative impact factor 38

Intermediate landscape disturbance maximizes metapopulation density

Abstract The viability of metapopulations in fragmented landscapes has become a central theme in conservation biology. Landscape fragmentation is increasingly recognized as a dynamical process: in many situations, the quality of local habitats must be expected to undergo continual changes. Here we assess the implications of such recurrent local disturbances for the equilibrium density of metapopulations. Using a spatially explicit lattice model in which the considered metapopulation as well as the underlying landscape pattern change dynamically, we show that equilibrium metapopulation density is maximized at intermediate frequencies of local landscape disturbance. On both sides around this maximum, the metapopulation may go extinct. We show how the position and shape of the intermediate viability maximum is responding to changes in the landscape's overall habitat quality and the population's propensity for local extinction. We interpret our findings in terms of a dual effect of intensified landscape disturbances, which on the one hand exterminate local populations and on the other hand enhance a metapopulation's capacity for spreading between habitat clusters

The impact of hypocrisy on opinion formation: A dynamic model

Humans have a demonstrated tendency to copy or imitate the behavior and attitude of others and actively influence each others opinions. In plenty of empirical contexts, publicly revealed opinions are not necessarily in line with internal opinions, causing complex social influence dynamics. We study to what extent hypocrisy is sustained during opinion formation and how hidden opinions change the convergence to consensus in a group. We build and analyze a modified version of the voter model with hypocrisy in a complete graph with a neutral competition between two alternatives. We compare the process from various initial conditions, varying the proportions between the two opinions in the external (revealed) and internal (hidden) layer. According to our results, hypocrisy always prolongs the time needed for reaching a consensus. In a complete graph, this time span increases linearly with group size. We find that the group-level opinion emerges in two steps: (1) a fast and directional process, during which the number of the two kinds of hypocrites equalizes; and (2) a slower, random drift of opinions. During stage (2), the ratio of opinions in the external layer is approximately equal to the ratio in the internal layer; that is, the hidden opinions do not differ significantly from the revealed ones at the group level. We furthermore find that the initial abundances of opinions, but not the initial prevalence of hypocrisy, predicts the mean consensus time and determines the opinions probabilities of winning. These insights highlight the unimportance of hypocrisy in consensus formation under neutral conditions. Our results have important societal implications in relation to hidden voter preferences in polls and improve our understanding of opinion formation in a more realistic setting than that of conventional voter models.Funding Agencies|European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme [648693]; NKFIH-OTKA [K109215, K124438, K112929]; Szechenyi 2020 program [GINOP-2.3.2-15-2016-00019]</p