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According to the criticality hypothesis , collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the “criticality hypothesis”, appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the “criticality hypothesis”, but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces the complex spreading patterns of a pandemic to a wave-like propagation from the outbreak country, establishing a linear relationship to the arrival time of the unmitigated spread of a disease. However, in the early stages of an outbreak, what concerns decision-makers in countries is understanding the relative risk of active cases arriving in their country—essentially, the likelihood that an active case boarding an airplane at the outbreak location will reach them. While there are data-fitted models available to estimate these risks, accurate mechanistic, parameter-free models are still lacking. Therefore, we introduce the ‘import risk’ model in this study, which defines import probabilities using the effective-distance framework. The model assumes that airline passengers are distributed along the shortest path tree that starts at the outbreak’s origin. In combination with a random walk, we account for all possible paths, thus inferring predominant connecting flights. Our model outperforms other mobility models, such as the radiation and gravity model with varying distance types, and it improves further if additional geographic information is included. The import risk model’s precision increases for countries with stronger connections within the WAN, and it reveals a geographic distance dependence that implies a pull- rather than a push-dynamic in the distribution process.

Groups of animals can perform highly coordinated collective behaviours that confer benefits to the participating individuals by facilitating social information exchange and protection from predators1. Some of these characteristics could arise when groups operate at critical points between two structurally and functionally different states, leading to maximal responsiveness to external stimuli and effective propagation of information2,3. It has been proposed that animal groups constitute examples of self-organized systems at criticality2,3; however, direct empirical evidence of this hypothesis—in particular in the wild—is mostly absent. Here we show that highly conspicuous, repetitive and rhythmic collective dive cascades produced by many thousands of freshwater fish under high predation risk resemble a stochastic excitable system driven by environmental perturbations. Together with the results of an agent-based model of the system, this suggests that these fish shoals might operate at a critical point between a state of high individual diving activity and low overall diving activity. We show that the best fitting model, which is located at a critical point, allows information about external perturbations—such as predator attacks—to propagate most effectively through the shoal. Our results suggest that criticality might be a plausible principle of distributed information processing in large animal collectives.Certain fish shoals ward off bird attacks by touching the water surface in a manner resembling waves observed in stadiums. This behaviour exhibits characteristics that suggest the fish might operate close to criticality.

Background While the majority of the German population was fully vaccinated at the time (about 65%), COVID-19 incidence started growing exponentially in October 2021 with about 41% of recorded new symptomatic cases aged twelve or above being symptomatic breakthrough infections, presumably also contributing to the dynamics. So far, it remained elusive how significant this contribution was and whether targeted non-pharmaceutical interventions (NPIs) may have stopped the amplification of the crisis. Methods We develop and introduce a contribution matrix approach based on the next-generation matrix of a population-structured compartmental infectious disease model to derive contributions of respective inter- and intragroup infection pathways of unvaccinated and vaccinated subpopulations to the effective reproduction number and new infections, considering empirical data of vaccine efficacies against infection and transmission. Results Here we show that about 61%–76% of all new infections were caused by unvaccinated individuals and only 24%–39% were caused by the vaccinated. Furthermore, 32%–51% of new infections were likely caused by unvaccinated infecting other unvaccinated. Decreasing the transmissibility of the unvaccinated by, e. g. targeted NPIs, causes a steeper decrease in the effective reproduction number R than decreasing the transmissibility of vaccinated individuals, potentially leading to temporary epidemic control. Reducing contacts between vaccinated and unvaccinated individuals serves to decrease R in a similar manner as increasing vaccine uptake. Conclusions A minority of the German population—the unvaccinated—is assumed to have caused the majority of new infections in the fall of 2021 in Germany. Our results highlight the importance of combined measures, such as vaccination campaigns and targeted contact reductions to achieve temporary epidemic control. Plain language summary With about 65% of its citizens vaccinated at the time, Germany experienced a large wave of COVID-19 in the fall of 2021, regionally overburdening the healthcare system. We are interested in how much this crisis was driven by infections in vaccinated versus unvaccinated people. We use a mathematical model to show that transmission of the disease during this period was largely driven by the unvaccinated population, despite representing a smaller proportion of the overall population. Our results suggest that higher vaccine uptake, reduced mixing between vaccinated and unvaccinated people, and targeted contact-reduction measures would have been effective measures to control spread at the time. These findings may have implications for how we manage future waves of COVID-19 or other diseases. Maier et al. develop a mathematical model to examine the contributions of vaccinated vs. unvaccinated populations to the wave of SARS-CoV-2 infections in Germany in autumn 2021. They report that the unvaccinated population were the main drivers of transmission and that targeted non-pharmaceutical interventions would likely have mitigated this.

Abstract As the coronavirus disease 2019 spread globally, emerging variants such as B.1.1.529 quickly became dominant worldwide. Sustained community transmission favors the proliferation of mutated sub-lineages with pandemic potential, due to cross-national mobility flows, which are responsible for consecutive cases surge worldwide. We show that, in the early stages of an emerging variant, integrating data from national genomic surveillance and global human mobility with large-scale epidemic modeling allows to quantify its pandemic potential, providing quantifiable indicators for pro-active policy interventions. We validate our framework on worldwide spreading variants and gain insights about the pandemic potential of BA.5, BA.2.75, and other sub- and lineages. We combine the different sources of information in a simple estimate of the pandemic delay and show that only in combination, the pandemic potentials of the lineages are correctly assessed relative to each other. Compared to a country-level epidemic intelligence, our scalable integrated approach, that is pandemic intelligence, permits to enhance global preparedness to contrast the pandemic of respiratory pathogens such as SARS-CoV-2.

While the majority of the German population was fully vaccinated at the time (about 65%), COVID-19 incidence started growing exponentially in October 2021 with about 41% of recorded new symptomatic cases aged twelve or above being symptomatic breakthrough infections, presumably also contributing to the dynamics. So far, it remained elusive how significant this contribution was and whether targeted non-pharmaceutical interventions (NPIs) may have stopped the amplification of the crisis. We develop and introduce a contribution matrix approach based on the next-generation matrix of a population-structured compartmental infectious disease model to derive contributions of respective inter- and intragroup infection pathways of unvaccinated and vaccinated subpopulations to the effective reproduction number and new infections, considering empirical data of vaccine efficacies against infection and transmission. Here we show that about 61%-76% of all new infections were caused by unvaccinated individuals and only 24%-39% were caused by the vaccinated. Furthermore, 32%-51% of new infections were likely caused by unvaccinated infecting other unvaccinated. Decreasing the transmissibility of the unvaccinated by, e. g. targeted NPIs, causes a steeper decrease in the effective reproduction number [Formula: see text] than decreasing the transmissibility of vaccinated individuals, potentially leading to temporary epidemic control. Reducing contacts between vaccinated and unvaccinated individuals serves to decrease [Formula: see text] in a similar manner as increasing vaccine uptake. A minority of the German population-the unvaccinated-is assumed to have caused the majority of new infections in the fall of 2021 in Germany. Our results highlight the importance of combined measures, such as vaccination campaigns and targeted contact reductions to achieve temporary epidemic control.

Intensive and size-selective harvesting is an evolutionary driver of life-history as well as individual behavioral traits. Yet, whether and to what degree harvesting modifies the collective behavior of exploited species is largely unknown. We present a multi-generation harvest selection experiment with zebrafish (Danio rerio) as a model species to understand the effects of size-selective harvesting on shoaling behavior. The experimental system is based on a large-harvested (typical of most wild capture fisheries targeting larger size classes) and small-harvested (typical of specialized fisheries and gape-limited predators targeting smaller size classes) selection lines. By combining high resolution tracking of fish behavior with computational agent-based modeling we show that shoal cohesion changed in the direction expected by a trade-off between vigilance and the use of social cues. In particular, we document a decrease of vigilance in the small-harvested line, which was linked to an increase in the attention to social cues, favoring more cohesive shoals. Opposing outcomes were found for the large-harvested line, which formed less cohesive shoals. Using the agent-based model we outline possible consequences of changes is shoaling behavior for both fishing and natural mortality. The changes in shoaling induced by large size-selective harvesting may decrease fishing mortality, but increase mortality by natural predators. Our work suggests an insofar overlooked evolutionary mechanism by which size-selective harvesting can affect mortality and in turn population dynamics of exploited fish. Competing Interest Statement The authors have declared no competing interest. Footnotes * The text has been updated

According to the criticality hypothesis, collective biological systems should operate in a special parameter region, close to so-called critical points, where the collective behavior undergoes a qualitative change between different dynamical regimes. Critical systems exhibit unique properties, which may benefit collective information processing such as maximal responsiveness to external stimuli. Besides neuronal and gene-regulatory networks, recent empirical data suggests that also animal collectives may be examples of self-organized critical systems. However, open questions about self-organization mechanisms in animal groups remain: Evolutionary adaptation towards a group-level optimum (group-level selection), implicitly assumed in the \"criticality hypothesis\", appears in general not reasonable for fission-fusion groups composed of non-related individuals. Furthermore, previous theoretical work relies on non-spatial models, which ignore potentially important self-organization and spatial sorting effects. Using a generic, spatially-explicit model of schooling prey being attacked by a predator, we show first that schools operating at criticality perform best. However, this is not due to optimal response of the prey to the predator, as suggested by the \"criticality hypothesis\", but rather due to the spatial structure of the prey school at criticality. Secondly, by investigating individual-level evolution, we show that strong spatial self-sorting effects at the critical point lead to strong selection gradients, and make it an evolutionary unstable state. Our results demonstrate the decisive role of spatio-temporal phenomena in collective behavior, and that individual-level selection is in general not a viable mechanism for self-tuning of unrelated animal groups towards criticality.

Disease propagation between countries strongly depends on their effective distance, a measure derived from the world air transportation network (WAN). It reduces the complex spreading patterns of a pandemic to a wave-like propagation from the outbreak country, i.e. a linear relationship to the arrival time of the unmitigated spread of a disease. However, in the early stage of an outbreak, what matters to countries' decision makers is knowledge about the relative risk of arrival of active cases, i.e. how likely it is that an active case that boarded at the outbreak location will arrive in their country. As accurate mechanistic models to estimate such risks are still lacking, we propose here the ``import risk'' model that defines an import probability by means of the effective-distance framework. The model assumes that airline passengers are distributed along the shortest path tree that starts at the outbreak's origin. In combination with a random walk, we account for all possible paths, thus inferring predominant connecting flights. Our model outperforms other mobility models, such as the radiation and gravity model with varying distance types, and it improves further if additional geographic information is included. The import risk model's precision increases for countries that are more connected within the WAN, and recovers a geographic distance-dependence that suggests a pull- rather than a push- dynamic of the distribution process.