Threshold extinction in food webs

Synthesising the Relationships Between Food Web Structure and Robustness

For many decades, ecologists have sought to understand the extent to which species losses lead to secondary extinctions-that is, the additional loss of species that occurs when resources or key interactions are lost (i.e. robustness). In particular, ecologists aim to identify generalisable rules that explain which types of food webs are more or less robust to secondary extinctions. Food web structure, or the patterns formed by species and their interactions, has been extensively studied as a potential factor that influences robustness to species loss. We systematically reviewed 28 studies to identify the relationships between food web structure and robustness to species loss and how the conclusions depend on methodological differences. Contrary to popular belief and theory, we found relatively consistent, positive relationships between connectance and robustness, among other generalities. Yet, we also found that conflicting conclusions about structure-robustness relationships can be, in part, attributed to differences in the type of data that studies use, particularly studies that use empirical data versus those generated from theoretical models. This review points towards a need to standardise methodology to answer the open question of whether robustness and its relationship with food web structure and to provide applicable insights for managing complex systems.

Efficient keystone species identification strategy based on tabu search

As species extinction accelerates globally and biodiversity declines dramatically, identifying keystone species becomes an effective way to conserve biodiversity. In traditional approaches, it is considered that the extinction of species with high centrality poses the greatest threat to secondary extinction. However, the indirect effect, which is equally important as the local and direct effects, is not included. Here, we propose an optimized disintegration strategy model for quantitative food webs and introduced tabu search, a metaheuristic optimization algorithm, to identify keystone species. Topological simulations are used to record secondary extinctions during species removal and secondary extinction areas, as well as to evaluate food web robustness. The effectiveness of the proposed strategy is also validated by comparing it with traditional methods. Results of our experiments demonstrate that our strategy can optimize the effect of food web disintegration and identify the species whose extinction is most destructive to the food web through global search. The algorithm provides an innovative and efficient way for further development of keystone species identification in the ecosystem.

On Edge Pruning of Communication Networks under an Age-of-Information Framework

Effective non-repetitive routing among nodes in a network is an essential function in communication networks. To achieve that, pruning the links of the network is helpful with the trade-off of making the network less robust in transmitting messages while reducing redundancy to increase flow with limited network bandwidth, so we enhance the quality of service (QoS). In our paper, we study the case that if a link removal has either no effect or an insignificant effect on the Age of Information (AoI) of the messages delivered in the communication network. The pruning of such links can be applied to the k least significant links in terms of their impact on the AoI of the messages transmitted in the system. The objective of our work is to study the effect of pruning a number of links in a network on the AoI, in order to reduce the redundancy of the messages that may be received at the destination many times while transmitted only once. In our context, the objective of the communication system would be to maintain the information from the source as fresh as possible when it arrives at the destination while reducing the redundancy of messages. In this work, we introduce an efficient reduction method designed for series-parallel networks with links of exponentially distributed wait times. In addition, we consider the deterministic case and present the pruning technique when link removal would not affect the AoI. Lastly, we present a comprehensive simulation to study the effect of pruning the links on the AoI of the network and the redundancy of messages received by the destination.

Modelling photosystem I as a complex interacting network

In this paper, we model the excitation energy transfer (EET) of photosystem I (PSI) of the common pea plant Pisum sativum as a complex interacting network. The magnitude of the link energy transfer between nodes/chromophores is computed by Forster resonant energy transfer (FRET) using the pairwise physical distances between chromophores from the PDB 5L8R (Protein Data Bank). We measure the global PSI network EET efficiency adopting well-known network theory indicators: the network efficiency (Eff) and the largest connected component (LCC). We also account the number of connected nodes/chromophores to P700 (CN), a new ad hoc measure we introduce here to indicate how many nodes in the network can actually transfer energy to the P700 reaction centre. We find that when progressively removing the weak links of lower EET, the Eff decreases, while the EET paths integrity (LCC and CN) is still preserved. This finding would show that the PSI is a resilient system owning a large window of functioning feasibility and it is completely impaired only when removing most of the network links. From the study of different types of chromophore, we propose different primary functions within the PSI system: chlorophyll a (CLA) molecules are the central nodes in the EET process, while other chromophore types have different primary functions. Furthermore, we perform nodes removal simulations to understand how the nodes/chromophores malfunctioning may affect PSI functioning. We discover that the removal of the CLA triggers the fastest decrease in the Eff, confirming that CAL is the main contributors to the high EET efficiency. Our outcomes open new perspectives of research, such comparing the PSI energy transfer efficiency of different natural and agricultural plant species and investigating the light-harvesting mechanisms of artificial photosynthesis both in plant agriculture and in the field of solar energy applications.

A comparative analysis of link removal strategies in real complex weighted networks

In this report we offer the widest comparison of links removal (attack) strategies efficacy in impairing the robustness of six real-world complex weighted networks. We test eleven different link removal strategies by computing their impact on network robustness by means of using three different measures, i.e. the largest connected cluster (LCC), the efficiency (Eff) and the total flow (TF). We find that, in most of cases, the removal strategy based on the binary betweenness centrality of the links is the most efficient to disrupt the LCC. The link removal strategies based on binary-topological network features are less efficient in decreasing the weighted measures of the network robustness (e.g. Eff and TF). Removing highest weight links first is the best strategy to decrease the efficiency (Eff) in most of the networks. Last, we found that the removal of a very small fraction of links connecting higher strength nodes or of highest weight does not affect the LCC but it determines a rapid collapse of the network efficiency Eff and the total flow TF. This last outcome raises the importance of both to adopt weighted measures of network robustness and to focus the analyses on network response to few link removals.

The heterogeneity in link weights may decrease the robustness of real-world complex weighted networks

Here we report a comprehensive analysis of the robustness of seven high-quality real-world complex weighted networks to errors and attacks toward nodes and links. We use measures of the network damage conceived for a binary (e.g. largest connected cluster LCC, and binary efficiency Eff_bin) or a weighted network structure (e.g. the efficiency Eff, and the total flow TF). We find that removing a very small fraction of nodes and links with respectively higher strength and weight triggers an abrupt collapse of the weighted functioning measures while measures that evaluate the binary-topological connectedness are almost unaffected. These findings unveil a problematic response-state where the attack toward a small fraction of nodes-links returns the real-world complex networks in a connected but inefficient state. Our findings unveil how the robustness may be overestimated when focusing on the connectedness of the components only. Last, to understand how the networks robustness is affected by link weights heterogeneity, we randomly assign link weights over the topological structure of the real-world networks and we find that highly heterogeneous networks show a faster efficiency decrease under nodes-links removal: i.e. the robustness of the real-world complex networks against nodes-links removal is negatively correlated with link weights heterogeneity.

Effects of macroalgae loss in an Antarctic marine food web: applying extinction thresholds to food web studies

Antarctica is seriously affected by climate change, particularly at the Western Antarctic Peninsula (WAP) where a rapid regional warming is observed. Potter Cove is a WAP fjord at Shetland Islands that constitutes a biodiversity hotspot where over the last years, Potter Cove annual air temperatures averages increased by 0.66 °C, coastal glaciers declined, and suspended particulate matter increased due to ice melting. Macroalgae are the main energy source for all consumers and detritivores of Potter Cove. Some effects of climate change favor pioneer macroalgae species that exploit new ice-free areas and can also decline rates of photosynthesis and intensify competition between species due to the increase of suspended particulate matter. In this study, we evaluated possible consequences of climate change at Potter Cove food web by simulating the extinction of macroalgae and detritus using a topological approach with thresholds of extinction. Thresholds represent the minimum number of incoming links necessary for species' survival. When we simulated the extinctions of macroalgae species at random, a threshold of extinction beyond 50% was necessary to obtain a significant number of secondary extinctions, while with a 75% threshold a real collapse of the food web occurred. Our results indicate that Potter Cove food web is relative robust to macroalgae extinction. This is dramatically different from what has been found in other food webs, where the reduction of 10% in prey intake caused a disproportionate increase of secondary extinctions. Robustness of the Potter Cove food web was mediated by omnivory and redundancy, which had an important relevance in this food web. When we eliminated larger-biomass species more secondary extinctions occurred, a similar response was observed when more connected species were deleted, yet there was no correlation between species of larger-biomass and high-degree. This similarity could be explained because both criteria involved key species that produced an emerging effect on the food web. In this way, large-biomass and high-degree species could be acting as source for species with few trophic interactions or low redundancy. Based on this work, we expect the Potter Cove food web to be robust to changes in macroalgae species caused by climate change until a high threshold of stress is reached, and then negative effects are expected to spread through the entire food web leading to its collapse.

Weighting and indirect effects identify keystone species in food webs

Species extinctions are accelerating globally, yet the mechanisms that maintain local biodiversity remain poorly understood. The extinction of species that feed on or are fed on by many others (i.e. 'hubs') has traditionally been thought to cause the greatest threat of further biodiversity loss. Very little attention has been paid to the strength of those feeding links (i.e. link weight) and the prevalence of indirect interactions. Here, we used a dynamical model based on empirical energy budget data to assess changes in ecosystem stability after simulating the loss of species according to various extinction scenarios. Link weight and/or indirect effects had stronger effects on food-web stability than the simple removal of 'hubs', demonstrating that both quantitative fluxes and species dissipating their effects across many links should be of great concern in biodiversity conservation, and the potential for 'hubs' to act as keystone species may have been exaggerated to date.

Using food-web theory to conserve ecosystems

Food-web theory can be a powerful guide to the management of complex ecosystems. However, we show that indices of species importance common in food-web and network theory can be a poor guide to ecosystem management, resulting in significantly more extinctions than necessary. We use Bayesian Networks and Constrained Combinatorial Optimization to find optimal management strategies for a wide range of real and hypothetical food webs. This Artificial Intelligence approach provides the ability to test the performance of any index for prioritizing species management in a network. While no single network theory index provides an appropriate guide to management for all food webs, a modified version of the Google PageRank algorithm reliably minimizes the chance and severity of negative outcomes. Our analysis shows that by prioritizing ecosystem management based on the network-wide impact of species protection rather than species loss, we can substantially improve conservation outcomes.

The influence of species conservation on food webs is less well understood than the effects of species loss. Here, the authors test several indices against optimal food web management and find no current metrics are reliably effective at identifying species conservation priorities.

Robustness of empirical food webs with varying consumer's sensitivities to loss of resources

Food web responses to species loss have been mostly studied in binary food webs, thus without accounting for the amount of energy transferred in consumer-resource interactions. We introduce an energetic criterion, called extinction threshold, for which a species goes secondarily extinct when a certain fraction of its incoming energy is lost. We study the robustness to random node loss of 10 food webs based on empirically-derived weightings. We use different extinction scenarios (random removal and from most- to least-connected species), and we simulate 10(5) replicates for each extinction threshold to account for stochasticity of extinction dynamics. We quantified robustness on the basis of how many additional species (i.e. secondary extinctions) were lost after the direct removal of species (i.e. primary extinctions). For all food webs, the expected robustness linearly decreases with extinction threshold, although a large variance in robustness is observed. The sensitivity of robustness to variations in extinction threshold increases with food web species richness and quantitative unweighted link density, while we observed a nonlinear relationship when the predictor is food web connectance and no relationship with the proportion of autotrophs.