Ecology

Our study method includes the following stages: (1) framing the investigation problem, (2) examining the literature, (3) developing and verifying two hypotheses, (4) collecting data, (5) the multiple criteria examination of 173 countries by means of the Degree of Project Utility and Investment Value Assessments (INVAR) method, (6) calculating correlations between 33 indicators and the success of 173 countries, (7) building 12 regression models, (8) compiling eight Maps (of which seven are CSS Maps) visualizing national success and sustainability, (9) spatial perspective analysis, and (10) performing integrated linear regression, multi-variant design and multiple criteria analysis of national policy alternatives, in order to identify rational decisions.This research is a quantitative study to examine the way national success affects 12 indicators of the three dimensions of sustainability in 173 countries, and uses the data from 2020, or the latest available.As investigation methods, our CSS Maps and Models can make it easier to study interdependencies between country success and sustainability. Supplementary Section 1, 4, and 5 presents our literature analysis which is carried out to gain deeper insights into our CSS Maps and Models, and to better understand their components in the worldwide research context.The following two core hypotheses have been proposed and verified for this research:

Hypothesis 1—The increasing success of a country is generally accompanied by increasing values for the three dimensions of sustainability indicators, and declines in these indicators lead to decreases in the country’s success. Improving some sustainability indicators tends to improve other sustainability indicators.

Hypothesis 2—Changes in the number of countries and their traditional key indicators system do not make a very significant difference to the relative national sustainability and success values. Likewise, the boundaries of the seven country clusters discussed in this research do not excessively depend on specific traditional key systems of indicators used in their analysis.

Along with different sets of national 17 success (Supplementary Table S1) and 12 sustainability (Supplementary Table S2) indicators, the INVAR method46 (Supplementary Section 2 and Fig. S1) was used to measure and map the success of the 173 countries selected as the focus for this research. The traditional statistical indicator systems defining country success and the three dimensions of sustainability are based on studies from various countries analyzed and combined. The INVAR method calculates an integrated criterion characterizing the overall success of the countries. This integrated criterion is directly proportional to the relative effect the values and weights of the given criteria make on the country’s success. The multiple-criteria INVAR analysis method has been applied to various countries, including Asian nations47, ex-Soviet states48, and a group of 169 countries49.This research used data from the framework of variables taken from various databases and websites, including Transparency International, Global Data, Eurostat-OECD, the World Bank, Knoema, the World Health Organization, Global Finance, Freedom House, Heritage, the Global Footprint Network, Socioeconomic Data and Applications Center, Our World in Data, Climate Change Knowledge Portal (World Bank Group), and The Institute for Economics and Peace, as well as global and national statistics and publications. All 173 countries analyzed in this article are listed in matrices, along with their 17 detailed success (Supplementary Table S1) and 12 sustainability (Supplementary Table S2) indicators (systems of indicators, their numbering, values, and weights). The INVAR method46 was applied to perform multiple criteria analysis of the 173 countries, and the results are presented in Supplementary Table S1 and Figs. 2, 3, 4 and 5. We use equal and different weights of 17 indicators to calculate the deviation of priorities for the 173 countries, which stands at 5.34% (Supplementary Section 2 and Fig. S2).Along with different sets of 12 national sustainability and 17 success indicators, the INVAR method46 was used to measure and map the success of the 173 countries selected as the focus of this research. The traditional statistical indicator systems defining country success and the three dimensions of sustainability are based on studies from various countries analyzed and combined. The INVAR method calculates an integrated criterion characterizing the overall success of the countries. This integrated criterion is directly proportional to the relative effect the values and weights of the given criteria make on the country’s success.Supplementary Table S3 shows the correlations between all measures determined by analyzing 173 countries. Supplementary Table S4 reveals the correlation coefficient matrix of the 17 success criteria for each of the 173 countries analyzed in this survey.Along the vertical axis y we analyze seven sustainability indicators, and along the horizontal axis x we analyze the success and priority indicators (9 CSS Map dimensions). The median correlation between the survival versus self-expression values and the nine CSS Map dimensions (the x-axis and y-axis) is moderate, whereas the median correlation between the traditional versus secular–rational values and the nine CSS Map dimensions is strong (Fig. 1).Tables S5-S8 show the descriptive statistics of 12 CSS Models (Supplementary Section 3). Supplementary Table S8 shows the extent to which a 1% increase or decrease in success of country’s features can push sustainability indicators up or down, expressed as a percentage. Supplementary Table S8 also shows the degree to which the percentage changes of success or the values of country’s features explain or fail to explain the dispersion of sustainability indicators. These CSS Models (Supplementary Section 3) show that when a country’s success increases by 1%, its 12 indicators related to the three dimensions of sustainability improve by on average 0.85% (Supplementary Table S8). Furthermore, the 17 variables of country success used in the CSS Models explain 80.8% on average of the dispersion of the three dimensions of sustainability and 98.2% of the dispersion of the country success variable (Supplementary Table S8).An increase of 1% in a country’s success is accompanied by a 0.39% average increase in its social and environmental (0.84% on average) sustainability indicators (Supplementary Table S8). On average, the CSS Sustainability Models explain 76.3% of the dispersions among the environmental sustainability indicators, 83.4% of the dispersions among the social sustainability indicators, and 94.5% of the dispersion among economic (i.e. the gross national income per capita) sustainability indicators (Supplementary Table S8).The study produced the eight Maps (of which seven are CSS Maps) of the World based on an analysis of 99–150 countries (the 2020 Inglehart–Welzel Cultural Map of the World focused on 103 analogical CSS Maps countries). The two dimensions of country success on the CSS Maps are represented in a system of 17 variables (Supplementary Table S1). When a country’s success grows, its performance related to the three dimensions of sustainable development increases as well, and the eight Maps (of which seven are CSS Maps) clearly illustrate this relationship (Figs. 2, 3, 4 and 5). The CSS Maps of the World developed as part of this study are described in Supplementary Section 5.Studies from various countries and our research suggest that country success and their features (x-axis) and sustainability indicators (y-axis) are generally strongly interrelated, and move in the same direction over time. This means that successful countries also perform better on sustainability dimensions.Stage 9 involved analysis of the spatial perspective research in place for explaining and predicting globally recognised physical, spatial, and human patterns in multiple ways. We apply 12 CSS Models, alternative design and multi-criteria analysis methods for spatial perspective analysis (Supplementary Section 4).The following additional two research objectives were set: (1) to determine the impact of a country’s success factors on sustainability metrics, and (2) to offer stakeholders recommendations regarding the strategies for improving sustainability indicators. The ways to improve sustainability indicators are determined by analysing 17 dependent variables (the main paper section “Practical applications and implications”, Table S9). As previously mentioned, in stage 10, national policy options have been examined by means of integrated linear regression, multi-variant design and multiple criteria analysis to identify rational decisions. Analysis of multiple alternative options and their detailed indicators, with a consideration of the existing state of the micro, meso, and macro environment, can ensure rational country success and sustainability. Below, a brief analysis of several best global practice examples of ways to identify rational policy, activities, and strategy follows. The examples presented below suggest that multiple possible alternatives must be designed, assessed against a system of micro, meso and macro indicators, and the most effective options selected to make countries more sustainable. In Isham and Jackson’s14 opinion, materialistic lifestyles and values have been associated with adverse effects on human health as well as having detrimental effects on our planet. Therefore, activities and lifestyles should be identified that promote human well-being, yet which at the same time protect ecological security. Isham and Jackson14 identify optimal activities (arts and crafts, reading, sports, meditating) with high levels of human well-being and low environmental costs. It is important to estimate pollution impacts on health in order to come up with the right policies for better health outcomes. Yet, the task is challenging because economic activity can lead to worse pollution, but can also improve health outcomes in its own right37. Humidity, temperature, dispersal by the wind, and other environmental factors contribute to pollution levels. Certain fine particulates can stay in the atmosphere for days, and travel long distances to be inhaled in places far away from the source, even in other continents. Local conditions must be reflected in emissions-control policies, and the global flows of air pollutants must be taken into account6. The explanation for the phenomenon of demographic transition could be improved public health in developed countries which results in a move toward a slower life strategy38. Studies show that children from wealthier backgrounds undergo puberty later than those from poor socio-economic backgrounds. Early puberty can lead to a variety of health problems and a shorter life. By the early adult years, the effects of exposure to trauma, post-traumatic stress disorder, and other conditions can become apparent in the form of diseases related to aging9. Education is a very important factor in economic growth, and is also strongly related to health. In addition to health benefits, substantial increases in education, especially of women, and shrinking gender gaps have an important effect on the roles and status of women in society36.The INVAR method, statistical analysis, and the CSS Maps and Models can help generate multiple policy recommendations for various stakeholders. The possibilities are as follows:

To create alternatives for ways to develop country success and sustainability, by performing countries’ multiple criteria and statistical analysis and identifying decisions that would be rational;

to perform quantitative and qualitative analysis of the existing data and to interpret it. The results obtained this way would prompt automatic recommendations designed for different stakeholders on ways to improve country sustainability. More

Highland lakes in southwestern China supply water to more than 1.4 billion people. Increasingly subject to eutrophication, biodiversity loss, drought and pollution, the lakes urgently need integrated management by government, community stakeholders and scientists to guide development of watershed policy and address these challenges.
Competing Interests
The authors declare no competing interests. More

Conservation biologist Kay Van Damme has spent two decades studying biodiversity on the island of Socotra in Yemen.Credit: Søren Solkær

In 1999, Kay Van Damme joined a United Nations-led multidisciplinary expedition to the Socotra archipelago, a Yemeni island group in the Arabian Sea, to explore freshwater ecosystems. Influenced by the area’s rich and unique biodiversity, Van Damme began to run annual expeditions to underground lakes on the main island, Socotra, as well as to its aquatic and terrestrial ecosystems above ground. In 2010, he earned a PhD on the evolutionary relationships of freshwater crustaceans from Ghent University in Belgium. Over the years, with the island facing the environmental challenges of climate change and a civil war that has been under way since 2014, Van Damme started applying his knowledge to conserving endangered aquatic insects and crabs, as well as the remarkable local trees. Now, alongside undertaking fieldwork on Socotra, where he works directly with local communities, Van Damme is a postdoctoral researcher at Ghent and at Mendel University in Brno, Czech Republic.What’s so special about Socotra?Socotra’s biodiversity treasures are the result of millions of years of secluded evolution. The archipelago separated from southern Arabia during the Miocene epoch (23 million to 5 million years ago). About 37% of its plant species, 90% of its reptiles and 98% of its land snails don’t exist anywhere else. It is the only Yemeni natural site on the UNESCO World Heritage List, to which it was added in 2008.Islands are often called living laboratories of evolution. Studying these habitats is important for natural history and biogeography. In addition, understanding how highly vulnerable endemic birds, plants and invertebrates have survived on these islands could help to save species in other places.How has your fieldwork changed over the years?Continuous exposure to the amazing nature and Socotra’s islanders have had a strong impact on me. The last forest of umbrella-shaped dragon’s blood trees (Dracaena cinnabari) seems out of this world, a relic of Miocene times, when this vegetation type was more widespread around the world. There’s a strange mix of ancient and recent geological features, ranging from granite mountains to coastal sand dunes and enormous limestone caves, harbouring vulnerable and isolated lifeforms.

Socotra hosts the last forest of dragon’s blood trees (Dracaena cinnabari) in the world.Credit: Kay Van Damme

Seeing the uniqueness of Socotra’s biodiversity and its fragility in the face of climate change, I feel my responsibility has grown to include more than exploration and classification. Gradually, my efforts converged on biodiversity conservation, and my fieldwork has become more strategic: doing biodiversity field surveys to assess threats to endemic species. I help Yemen’s environmental protection agency with conservation planning, including establishing and improving protected areas. We do activities in schools and with the Indigenous Soqotri people to ensure that conservation efforts are integrated into the community, while discussing their concerns about their environment and the impacts of climate change.Which species do you focus on, and why?As co-principal investigator of a conservation project funded by the Franklinia Foundation in Geneva, Switzerland, I work with colleagues from Socotra, Mendel University and the Sapienza University of Rome on protecting the dragon’s blood trees and ten endemic species of frankincense tree (Boswellia). Meanwhile, I chair a UK-based charity called the Friends of Soqotra, which runs biodiversity-conservation and environmental-awareness projects. Together with local communities in north Socotra, we have replanted mangrove trees (Avicennia marina) that had disappeared decades before. I also focus on a magnificent damselfly, the Socotra bluet (Azuragrion granti), and a colourful freshwater crab (Socotrapotamon socotrensis), which are included in the International Union for Conservation of Nature’s Red List of Threatened Species.

The Socotra bluet (Azuragrion granti), a type of damselfly, is threatened by drought, pollution and soil erosion.Credit: Kay Van Damme

What are the biggest threats to these ecosystems? Overgrazing by domestic goats, loss of traditional land-management techniques and the effects of climate change. Violent cyclones and droughts in Socotra affect both terrestrial and aquatic ecosystems. For instance, cyclones destroyed considerable proportions of unique woodlands of frankincense and dragon’s blood trees in 2015 and 2018. Likewise, threats to freshwater species include drought; landslides due to vegetation loss; pollution; and invasive species, such as a predatory fish called the Arabian toothcarp (Aphanius dispar).The most effective solution to these threats is for the local communities to get involved in leading the conservation work on the ground. For every tree felled by weather, scientists should work with locals to replant another.How have you gained the trust of the local community?I work with our local team, which continues the fieldwork, and with the Soqotri people, who own the land areas. I have great respect for their immense environmental knowledge. We have long conversations with them during visits, asking what is needed. In Socotra, there is no stronger conservation expertise than that which has been applied for centuries by the Soqotri people. For instance, by understanding the quality of a frankincense tree’s incense and the timing of flowering, they have shown us new hybrid species. Our nursery of young frankincense seedlings is maintained by an older Soqotri woman called Mona, who has traditional knowledge of how to take care of them.How does the ongoing civil war affect your fieldwork?In comparison to the mainland, Socotra has remained relatively safe for fieldwork. However, the political landscape of the island is variable and complex. This requires us to be flexible when discussing conservation issues with local decision makers, who are sometimes replaced more than once during a project.

Van Damme (centre) collaborates with community leaders — Saleh Al-Tamek, chair of a local conservation group (left), and natural-heritage specialist Haifaa Abdulhalim — to protect threatened species of mangrove tree.Credit: Marketa Jakovenko

We constantly assess risks and maintain clear communication between research team members and local communities and their leaders about where we are at which moment, and for what purpose. In such circumstances, scientists should know the local terrain and weather conditions extremely well, avoiding unnecessary risks and checking in frequently by mobile phone with their local teams.Do you have any advice for early-career conservation scientists? Local community leaders have the power to facilitate fieldwork or obstruct it. And because not all leaders prioritize nature conservation, there are some practical tips for building mutual trust with them to help form long-standing partnerships. Focus on constant communication with leaders, respect their culture and environmental knowledge, and cooperate with them in protecting the interests of local people, especially during natural disasters.Have you made any non-scientific discoveries about Socotra?My soul has been touched by Socotra’s people. Their kindness towards others is essential to their culture. They speak an endangered Semitic language that has survived through oral tradition, such as poetry and songs. Soqotri people are excellent orators and communicate using good humour. I brought my parents to Socotra to see what has stolen my heart — they understood.
This interview has been edited for length and clarity. More

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Modelling complex evolved food websOur interest here is to develop a conceptual comparison between the eigenvalue spectrum of a complex, evolved food web and a random matrix analog. We therefore focus on the widely-used generalised Lotka–Volterra equations for consumer-resource interactions. For simplicity, we further restrict to a single basic nutrient source, and require that species feeding on the basic nutrient source are never omnivorous31, e.g., plants do not consume other plants. The original Lotka–Volterra equations32,33 describe spatially and temporally homogeneous, consumer-resource relations. The generalised Lotka–Volterra equations34,35,36 can be used to describe the dynamics of larger, more complex food webs, and encode the dynamics of primary producers as$$begin{aligned} frac{dot{S_i}}{S_i} = k_i left( 1 – sum _{j=1}^{n_1} S_j right) – alpha _i – sum _{k=n_1+1}^{n} eta _{ki} S_k, end{aligned}$$
(1)
where (S_i), (iin {1,dots ,n_1}), denote the population densities of primary producers in units of biomass, normalised to the system carrying capacity and (n_1) denotes the total number of primary producers, (k_i >0) denote the growth rates of the corresponding primary producer (S_i), that is, the maximal reproduction rate at unlimited nutrient availability. We use (k_i=k) for all primary producers. The negative sum on the species (S_j) encodes logistic growth by accounting for nutrient depletion by all primary producers. For all other species, (S_k), (kin {n_1+1,dots ,n}) with n the total number of species in the food web, the equations read$$begin{aligned} frac{dot{S_k}}{S_k} = sum _{m=1}^{n} beta _{km}eta _{km} S_m – alpha _k – sum _{p=n_1+1}^{n} eta _{pk} S_p. end{aligned}$$
(2)
Here, (S_k) is again measured in units of normalised biomass. In Eqs. (1) and (2), (alpha _j >0) is the decay rate of a species (S_j), representing death not caused by consumption through other species. (eta _{ki}ge 0) is the link-specific interaction strength between consumer (S_k) and resource (S_i). On the RHS of either equation, note the final term representing the diminishing effects experienced by each resource species, which is caused by consumption. This term is mirrored by the first term in Eq. (2), which describes the strengthening effect on the consumer side. The coefficients (beta _{ki}le 1) encode link-specific consumption efficiency—that is, potentially incomplete use of energy removed from a resource species by its consumer. (beta _{ki}=1) would describe perfect consumption efficiency whereas in real food webs this value is estimated to lie considerably lower37. In our simulations we use (beta _{ki}=beta) for all interactions present.Equations (1) and (2) describe a simplified food web structure where consumption is modelled by the simple Holling type-I response38, where consumer resource fluxes scale proportional to the product of consumer and resource biomass density and there are no saturation effects. Moreover, Eqs. (1) and (2) assume that the food web is rigid in that species are incapable of adapting their consumption behaviour to changes within the food web, such as a decreasing population of resources or competition from an invasive species39. Yet, these equations allow for a coherent description of the energy fluxes between species and constitute an established framework for complex consumer-resource relations to evolve.To evolve food webs we simulate Eqs. (1) and (2) numerically. New species are added successively to an existing food web. We assume that invasion attempts occur on a slow timescale, such that equilibrium can be reached before the subsequent invasion attempt, though occasionally, the food web does not converge to its equilibrium state. After each invasion attempt the steady state species vector (mathbf {S^*}) is computed. In case of feasibility the eigenvalues of the community matrix are evaluated in order to determine the linear stability of the steady states. If feasibility is not obtained, that is, if (mathbf {S^*}) contain negative populations, Eqs. (1) and (2) are integrated numerically until extinctions occur and feasibility of the remaining species is reached (Details: “Materials and methods”). Examples of several invasion attempts are shown in Fig. 2.Figure 1Evolution of three food webs using different assembly rules. All main panels show decay rates of all species present plotted against invasion attempts, that is, evolutionary steps. The decay rates are plotted as (Delta alpha equiv alpha – alpha _{min}), where (alpha _{min}) denotes the lower limit on decay rates (compare: Table 1). The thin red line highlights the currently lowest producer decay rate. Grey symbols denote producers, yellow and magenta symbols denote consumers of one or two resources, respectively. Cyan symbols denote omnivores. (a) Food webs where only one resource per consumer is allowed, yielding a treelike food web without loops. (b) Consumers can have either one or two resources at the same trophic level. (c) Consumers are allowed one or two resources at any trophic level (lge 1). Note that both axes use logarithmic scaling. Insets: Normalised histograms of species richness, using all data. Note the logarithmic vertical axis scaling.Full size imageFigure 2Time series of a food web during several invasions. The panels (a–f) respectively correspond to invasion attempts 40312–40314, and 40316–40318 in Fig. 1c. Upper row: In each panel, orange circles and red “x”-symbols denote the invasive and extinct species, respectively. The vertical coordinate denotes trophic level, and node areas represent initial biomass densities. The green hexagon represents the basic nutrient source. (a) A species successfully invades the food web, but causes the extinction of two resident species, among these one of its own resources. (b) the invader is successful without causing any extinctions. (c) The invader is a primary producer and causes extinction of the invader from (b). (d) The invader replaces a resident species of same niche as the invader. (e) The invader is unsuccessful in invading the food web as it shares a niche with one of the resident species. (f) The invader is a primary producer and causes the extinction of three resident species, among these the primary producer with lowest decay rate, corresponding to largest intrinsic fitness, which is highlighted by the black arrow. Lower row: Time series corresponding to each of the food webs above, where time is measured in units of the inverse primary producer growth rate, (k^{-1}). Blue and orange lines represent resident and invasive species, respectively, as the new steady state is approached. The black line in the last panel represents the producer with lowest decay rate. Note the double-log axis scaling.Full size imageLoops profoundly impact food web evolutionTo make sure our results do not depend on the details of the invasion process we allow for several qualitatively distinct evolutionary processes: (i) treelike food webs, where each consumer has a single resource; (ii) non-omnivorous food webs with loops; (iii) omnivorous food webs. Loops are known to be relevant for sustained limit cycles and chaotic attractors, thus widening the range of dynamical properties. Indeed, we find treelike food webs to stand out in that fitness, measured by species decay rates, indefinitely increases in the evolutionary process (Fig. 1a, dotted red line), a finding consistent with the recent literature30. This indefinite fitness improvement hinges on the absence of network loops: a given primary producer can only be replaced by an invading primary producer of greater intrinsic fitness, that is, lower decay rate.Allowing for network loops, evolved food web do not show indefinite fitness improvement (Fig. 1b,c) and mean species richness somewhat decreases (Fig. 1, insets). All histograms show a systematic difference in odd and even species richness, with food webs of odd species richness being the most frequent. This tendency is most pronounced for treelike food webs. We interpret this as a manifestation of the requirement of non-overlapping pairing28. Treelike food webs are feasible and stable if every species in the food web can be coincidentally paired with a connected species or nutrient that is not part of another pairing. In food webs of even species richness the nutrient is never included in such a pairing. Food webs consisting of several smaller trees that are connected through the nutrient source are therefore only feasible if every tree satisfies this requirement individually. On the contrary, the nutrient is always included in a pairing in food webs of odd species richness, and therefore odd food webs are more likely to be feasible. To a lesser extent this tendency is also found in the histograms representing food webs with network loops. We interpret this as resulting from the fact that 40-60% of the food webs from simulations allowing network loops are in fact treelike.Why do loops counteract indefinite fitness improvement? This can be seen as a manifestation of relative, rather than absolute, fitness, where a species can consume two resources and thereby can help eliminate even primary producers of high intrinsic fitness (Fig. 1b,c). An example of this is illustrated in Fig. 2f), where the intrinsically fittest producer is a node in a food web loop, and is driven to extinction during the invasion of a producer with lower intrinsic fitness.The evolution of intrinsic fitness in Fig. 1 implies that allowing for interaction loops makes resident species more vulnerable to extinction during invasions, because parameters that characterise high intrinsic fitness before an invasion might characterise low intrinsic fitness during the invasion. This is supported by the cumulative distribution of resident times (Fig. S1a), where residence times in food webs with network loops fall off faster than the residence times in treelike food webs. In Fig. S1b we observe that in accordance with this, the distribution of extinction event size falls off faster for treelike food webs (Fig. S1b), where the extinction event size is measured relative to the total number of species (species richness) in the food web. Fig. S1b therefore implies that interaction loops make food webs less robust to invasions, as invasive species tend to create larger extinction events here than in treelike food webs. Finally, we find invasive species to have higher success rates when invading food webs with interaction loops, and the success rate is found to increase with (beta). In simulations with (beta =0.75) we observe 11.5%, 27.2% and 29.8% for treelike, non-omnivorous, and omnivorous food webs with loops, respectively. The implications of this are twofold. On one hand, it is easier to assemble feasible food webs when multiple resources and omnivory are allowed. On the other hand, these food webs are more susceptible to invasions and their resident species are more vulnerable. If a food web contains two-resource species, removal of one of the two resources of a species (S_i) by an invader can already lead to a cascading extinction of S, as exemplified by Fig. S2.Robustly bi-modal eigenvalue spectraWe now turn to the eigenvalue spectra of the evolved complex food webs, which we present as two-dimensional histograms in the complex plane (Fig. 3). Each simulation conducts (10^5) invasion attempts, yet the number of unique feasible food webs is considerably lower, that is, approximately equal to the aforementioned rates of successful invasions. Furthermore, the number of unique feasibly food webs drastically decreases with species richness. While the data shown represent relatively small networks, we find that key spectral features are very systematic as function of species richness. A generic feature is that spectra typically have many eigenvalues with small negative real parts. Further, the real parts scatter more and more closely at small negative values, as species richness increases beyond two. All spectra contain a considerable fraction of purely real eigenvalues, typically making up 15–30% of a spectrum.Figure 3Complex eigenvalue spectra of evolved food webs. Each panel represents the two-dimensional histogram in the complex plane. Species richness and invasion mechanism are as labelled in panels, that is, rows of panels represent treelike, non-omnivorous, and omnivorous food webs. Note that the colour scale is logarithmic, with green marking the areas with largest likelihood of eigenvalues (Details: “Materials and methods”). Eigenvalue spectra of omnivorous food webs of other species richnesses can be seen in Fig. S3.Full size imageThe origin of purely real eigenvaluesThe first column in Fig. 3 represents food webs with species richness two. These simple food webs only have one feasible configuration, namely that of one primary producer and one consumer. Any differences between spectra in the left column are therefore purely statistical. These food webs can be considered as isolated interactions between a consumer and its resource, hence the analytical eigenvalues of this food web can provide some insight on the dynamics underlying the eigenvalue spectra. From the analytical eigenvalues we obtain that an eigenvalue is purely real if the inequality$$begin{aligned} beta eta le frac{1}{2}left( gamma + sqrt{gamma ^2 + kgamma }right) , ,,,,,,,,text {with},, gamma equiv frac{alpha _2}{1-alpha _1/k}, end{aligned}$$
(3)
is fulfilled (Details: Sec. S3). Here, (alpha _1) and (alpha _2) are the decay rates of the resource and the consumer, respectively, and (beta eta) is short for (beta _{21}eta _{21}), the “consumption rate” of the consumer. (gamma) can be interpreted as the inverse intrinsic fitness of the food web.From feasibility, we have the additional requirement of (gamma < beta eta), hence, the consumer’s “consumption rate” is bounded also from below. As k decreases, the lower and upper boundaries on (beta eta) approach one-another until they are equal for (k=0). A food web with low producer growth rate is therefore likely to have complex eigenvalues. In the opposite limit, when (krightarrow infty), or equivalently (alpha _1 rightarrow 0), we see that (gamma) reduces to (alpha _2). In the first limit Eq. (3) reduces to (beta eta le infty) which will always be satisfied and all eigenvalues are therefore purely real in this limit. This corresponds to a food web where the consumer has infinite access to resources and there is no stress or constraints on the web that could cause oscillations. In the limit where (alpha _1 rightarrow 0), the eigenvalues pick up an imaginary component when (beta eta) is large compared to (alpha _2) and k. This occurs when the consumer population has a large intrinsic growth rate, thus heavily exploiting its resource.Overall, purely real eigenvalues characterise food webs where consumption of the resource is moderate compared to the intrinsic fitness of the resource. This corresponds to an over-damped limit where the consumer does not consume enough to cause any significant displacement of the resource population, hence a perturbation of the consumer population will not spread to its resource. For higher species richness the Jacobian quickly becomes too complicated to be solved analytically. Even so, we expect the dynamics between a consumer and its resources to be conceptually analogous, namely that “sustainable over-consumption” yields oscillating densities and complex eigenvalues.The set of smallest and largest real-valued eigenvalues is obtained when (beta eta) is only slightly larger than (gamma), hence barely satisfying the criterion of feasibility. The eigenvalues then reduce to (lambda _{pm } = -frac{k-alpha _1}{2} pm frac{k-alpha _1}{2}). (lambda _+) is always zero, that is, food webs of species richness two are always stable, and with our choice of parameters (lambda _- ge -0.95). We observe approximately the same range of real values in all numerical spectra of any species richness, thereby implying that the choice of parameters might be more important for the spectrum width than the structure of the food web.The overall shape is qualitatively similar for all food web structures (see: Fig. 3). Importantly, omnivorous spectra are the only ones to contain also eigenvalues with positive real part, that is, unstable eigenvalues. These food webs do therefore not converge to their equilibrium state after an invasion, but are displaying periodic or chaotic dynamics (Details: “Materials and methods”). The unstable eigenvalues are all barely larger than zero, hence hardly visible in Fig. 3. Interestingly, non-omnivorous food webs with network loops exhibit the same species richness and approximate connectivity as the omnivorous food webs, yet they do not yield unstable eigenvalues. The differences between treelike food webs and food webs with network loops discussed earlier must therefore be unrelated to the stability of the food webs, thus emphasising the difference between stability to perturbation of a given food web and its robustness to invasions. For omnivorous food webs the fraction of unstable eigenvalues increases with species richness and decreases with (beta). Intuitively, it seems reasonable that there is a relation between instability and low consumption efficiency. A species with a low consumption efficiency has to compensate by consuming more biomass, thereby putting more stress on its resources. Only for (beta =1) are there no unstable omnivorous eigenvalues.Figure 4Complex eigenvalue spectra of random matrices. Heat maps of eigenvalue spectra of random matrices, corresponding to the respective species richnesses shown in Fig. 3. Off-diagonal entries are drawn from a normal distribution with probability (p(N) = frac{N^2+21N-28}{9N(N-1)}) (Details: Sec. S5), and are otherwise set to zero. Diagonal elements are set to (-1).Full size imageWe now compare the evolved spectra (Fig. 3) to their random counterparts (Fig. 4). The diagonal entries represent self regulation of each species and are set to (d = -1). Off-diagonal entries are drawn from ({mathcal {N}}(0, 1)) with probability p(N), and are otherwise 0.$$begin{aligned} p(N) = frac{N^2+21N-28}{9N(N-1)}, ~~text {for } N >1, end{aligned}$$
(4)
where N is “species richness”, that is, the number of rows (or columns) of the matrix. This corresponds to the implemented connectivity in the simulation allowing network loops and omnivory, that is, the connectivity of omnivorous food webs given no extinctions occur (Details: Sec. S5). As predicted by spectral theory of random matrices, the spectra are centred around d on the real axis and approach a circular geometry as the size of the matrix increases. Already for (N=2) does the spectrum contain unstable eigenvalues. The fraction of unstable eigenvalues increases with N as the circle radius increases. Also for random spectra do we observe a large fraction of purely real eigenvalues. We attribute this to the small size of the matrices, being much smaller than the infinity limit for which the law was derived40.Figure 5Distribution of eigenvalues along the real axis. Normalised frequency distributions of eigenvalues along the real axis for all food web structures and random matrices for species richness (2-9). Eigenvalues representing food webs are taken from simulations using a range of values of (beta) (Table 1), since varying (beta) does not have significant effects on the real-part distributions (Details: Sec. S6). All distributions are scaled to start in (-1). Note the logarithmic vertical axis scaling.Full size imageFinally, we study the real-part frequency distributions of eigenvalues of all four types (treelike, non-omnivorous, omnivorous and random). The frequency distributions for species richness 2–9 can be seen in Fig. 5, where each distribution consists of data from various values of (beta) (see Table 1). In order to facilitate comparison of the functional form of the frequency distributions, rather than the range, the frequency distributions are scaled to be bounded by (-1) on the real axis, that is, we divide each data point by ((|min {x}|)^{-1}) where x is the data points of the distribution. Frequency distributions representing the evolved food webs follow approximately the same curve for a given species richness, and are distinctively different from the random matrices. As also seen in Fig. 3 omnivorous distributions are the only to extended to positive values for species richness greater than two.Once again, we observe quantitative differences between food webs with odd and even species richness: For odd species richness the distribution is bi-modal with a global maximum near (x=0) and a secondary maximum near the lower limit, that is (x=-1). For even species richness, the distribution is initially less strongly peaked. Yet, as species richness increases, a sharp peak emerges around (x = 0). The distribution thus becomes more similar to that of the food webs with an odd number of species.The intermediate part of the spectrum is increasingly depleted of eigenvalues at higher species richness. Comparing Fig. 5 with Fig. 3 we see that the left part of all distributions consists of purely real eigenvalues, whereas it is mostly complex eigenvalues that make up the global maximum near (x=0). This implies that perturbations can be divided into two main groups: perturbations from which the food web quickly returns to the respective steady state, and perturbations that induce oscillations from which the food web takes very long to recover. The peak consisting of purely real eigenvalues near (x=-1) does not change notably with species richness, indicating that, independent of species richness, food webs are robust to certain perturbations. In accordance with this we observe that food webs of all species richness usually return quickly to their steady states after an unsuccessful invasive species goes extinct. The main peak (near (x=0)) becomes both higher and narrower with increasing species richness, that is, the food webs become quasi-stable. In larger food webs there are more species that can be disturbed by a perturbation, which might prolong the effect of the perturbation, that is, push eigenvalues towards zero on the real axis. Overall, we thus find that the histogram of complex food webs becomes strongly bi-modal as food webs consisting of many species are approached in an evolutionary process, whereas random matrix spectra are consistently uni-modal. In Sec. S8–S9 we consider the robustness of the results in Fig. 5 by varying the parameter distributions and implementing Holling type-II response, respectively. More

RESEARCH HIGHLIGHT
29 August 2022

North America’s largest land mammal can double the diversity of native grasses through its grazing.

Home on the range: the American bison’s taste for prairie grasses helps to boost diversity of native flora (pictured, stiff goldenrod, Solidago rigida). Credit: Jill Haukos/Kansas State University

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Grazing animals can shape the grasslands they dine on by preferentially eating certain species, allowing other species to find a foothold. To quantify this effect, Zak Ratajczak at Kansas State University in Manhattan and his colleagues analysed 29 years’ worth of data from plots in an unploughed native tallgrass prairie in eastern Kansas1. Since 1992, the plots have been managed in one of three ways: year-round grazing by bison (Bison bison); seasonal grazing by cattle; or no grazing at all.

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Study sites, experimental design, and field samplingThe Tibetan alpine permafrost region, the largest area of permafrost in the middle and low latitudes of the Northern Hemisphere64, stores substantial soil C (15.3–46.2 Pg C within 3 m depth)65,66,67. With continuous climate warming, permafrost thaw has triggered the formation of widespread thermokarst landscapes across this permafrost area13,68. To explore the impacts of thermokarst formation and development on soil C dynamics, we collected topsoil samples (0–15 cm) from a thaw sequence in 2014 and from five additional sites spread across the region in 2020. The thermokarst landscape was characterized as thermo-erosion gullies (Supplementary Table 2). The elevation of these six sites is between 3515 and 4707 m. The mean annual temperature across this area ranges from −3.1 to 2.6 °C, and the average annual precipitation varies from 353 to 436 mm. The vegetation type across these sites is swamp meadow, with the dominant species being Kobresia tibetica, Kobresia royleana and Carex atrofuscoides. Although the dominant species did not change after permafrost collapse, the forb coverage increased along the thaw sequence and across the five additional thermokarst-impacted sites. The main soil type is Cryosols on the basis of the World Reference Base for Soil Resources69, with soil pH ranging from 5.6 to 7.3 (Supplementary Fig. 1e). The active layer thickness varies between 0.7 and 1.1 m across the six study sites and the underlying soil parent material is either siliciclastic sedimentary or unconsolidated sediments (Supplementary Table 2).To evaluate the dynamics of soil C fractions after permafrost collapse, we collected soil samples across the Tibetan alpine permafrost region based on the following two steps (Supplementary Fig. 5). In the first step, we established six collapsed plots (~15 × 10 m) along a thaw sequence (located in Shaliuhe close to Qinghai Lake, Qinghai Province, China), which had been collapsed for 1, 3, 7, 10, 13, and 16 years before the sampling year of 201413. The collapse time of each plot was estimated by dividing the distance between the collapsed plot and the gully head by the retreat rate (~8.0 m year−1; the rate of the head-wall retreat was determined by Google Earth satellite images and in situ monitoring)13. Then, we set up six paired control (non-collapsed) plots adjacent to these collapsed plots. To limit experimental costs, we selected three paired control and collapsed plots (collapsed for 1, 10, and 16 years, representing the early, middle, and late stages of collapse) to examine the responses of POC, MAOC and OC-Fe to permafrost collapse (Supplementary Fig. 5). Within each collapsed plot, we collected topsoil (0–15 cm) samples from all vegetated patches (Supplementary Fig. 6), and then evenly selected 10 vegetated patches for this study considering the heavy workload and high cost. In each selected vegetated patch, 5–8 soil cores were sampled and completely mixed as one replicate. Within each control plot, topsoil samples were randomly collected from five quadrats at the center and four corners of the plot. In each quadrat, 15–20 soil cores were sampled and mixed as one replicate. Thereby, ten replicates were acquired in each collapsed plot (n = 10), and five replicates were obtained in each control plot (n = 5). In total, we acquired 45 soil samples, including 30 samples from the three collapsed plots and 15 samples from the non-collapsed control for subsequent analysis.In the second step, to further verify the universality of collapse effects on SOC fractions, we collected topsoil (0–15 cm) samples from an additional five similar sites located near the towns of Ebo, Mole, Huashixia, and Huanghe across a 550 km permafrost transect in August 2020 (Fig. 1). Specifically, paired collapsed and control plots (15 × 10 m) were established at the end of a gully and in adjacent non-collapsed areas in each site (Supplementary Fig. 5). In the collapsed plot, we set five 5 × 3 m quadrats at the center and four corners of the plot, and then collected topsoil samples within all the vegetated patches in these quadrats. In each quadrat, all the collected soil cores (15–20 cores) were completely mixed as one replicate, and finally, five replicates were acquired in each collapsed plot (n = 5). Similarly, five replicates were obtained from the five quadrats in each control plot (n = 5). In total, we collected 50 topsoil samples across these five thermokarst-impacted sites. After transportation to the laboratory, all the soil samples were handpicked to remove surface vegetation, roots and gravels, and sieved (2 mm) for subsequent analysis.It should be noted that the space for time approach was only used for the permafrost thaw sequence, not for the other five sites over the regional scale. Across these five sites, we focused on the impact of permafrost collapse on POC, MAOC as well as OC-Fe by comparing soil C fractions inside and outside the gully in each site rather than among the study sites. Given the low coefficient of variation of parameters (i.e., edaphic variables and soil minerals) in the control plot of each site (Supplementary Table 3), the pristine soils in each site could also be regarded as homogeneous70, and the differences in parameters inside and outside the gully could be attributed to the effects of permafrost collapse. Along the permafrost thaw sequence, to verify whether the plots with different collapse times (1, 10, and 16 years) were comparable, we analyzed a series of parameters (i.e., vegetation biomass, edaphic variables, and soil minerals) for the three control plots which were located outside the gully but adjacent to three collapsed plots within the gully (Supplementary Fig. 5). By comparing aboveground biomass, belowground biomass, SOC, soil moisture, pH, bulk density, soil texture, and soil minerals (see below for details of the analytical method), we observed that the above parameters were not significantly different among the three control plots along the thaw sequence (all P  > 0.05; Supplementary Fig. 7). These comparisons demonstrated that the study area was homogeneous before permafrost thaw and thus it was reasonable to adopt the space for time approach along the permafrost thaw sequence.It should also be noted that the collected topsoil samples used in this study were less affected by physical mixing and translocation due to thaw phenomena at the thermokarst-impacted sites. Specifically, to examine changes in soil properties upon permafrost thaw, we chose to collect topsoil within the vegetated patches rather than from the exposed soil areas in the collapsed plots (Supplementary Fig. 6). These vegetated patches (40–60 cm thickness) are formed during the landscape fragmentation after permafrost collapse13. Although permafrost collapse inevitably led to soil translocation, these vegetated patches maintained their original shapes, especially for the topsoil because it is protected by mattic epipedon in this swamp meadow ecosystem on the Tibetan Plateau (which has an intensive root network protecting soils against interference)71,72. Moreover, we collected 0–15 cm of topsoil within the vegetated patches, in which soil cores were at least 10 cm away from the edge of the patch. Due to these two points, topsoil should not be mixed with the subsoil in our case. To test this deduction, we compared the non-collapsed (control) plot with the collapsed plot occurring for 1 year (the early stage of the permafrost thaw sequence), and observed no significant differences in soil properties such as bulk density, SOC, pH, soil texture and soil minerals (all P  > 0.05; Supplementary Fig. 8). These comparisons illustrated that permafrost collapse did not cause soil physical mixing for the topsoil samples involved in this study, and soil layers were comparable between the collapsed and control plots.SOC fractionationWe separated POC and MAOC from bulk soils using a fractionation method based on a combination of density and particle size18 using the following three steps. First, 10 g of soil was put into a 100 mL centrifuge tube, and added with 50 mL of 1.6 g cm−3 NaI. After being completely mixed, the mixture was sonicated and then centrifuged at 1800 × g. The floating particulate organic matter, together with the supernatant, was poured into a GF/C filter membrane for filtration, completely washed with deionized water, and then dried at 60 °C to constant weight. Then, the C content of the particulate organic matter was determined as POC. Second, deionized water were added to the remaining soils in the tube to wash out any residual NaI. The washed soils were then separated with a 53-μm sieve. The residues on the sieve ( >53 μm) were dried and determined as heavy POC. Third, the organic matter that passed through the sieve ( More

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