Ecology

We thank the Bren School of Environment Science and Management of the University of California Santa Barbara for support leading to the initial publication. This work was also supported by a grant overseen by the French ‘Programme Investissement d’Avenir’ as part of the ‘Make Our Planet Great Again’ programme (reference: 17-MPGA-0004) and by a National Science Foundation grant (LTER-1831944). More

Rapeseed crops depend on pollinators such as bees.Credit: fotokostic/iStock/Getty

Farming trends deplete pollinators
Most cultivated crops depend on insect pollinators, such as bees, but global crop trends are leaving pollinators worse off.
Using data from the United Nations’ Food and Agriculture Organization, an international team, led by Marcelo Aizen at the National University of Comahue in Rio Negro, Argentina, assessed changes in the amount of land used for agriculture and the types of crops cultivated between 1961 and 2016. During that time, the area of land used to grow crops increased by around 40%, and pollinator-dependent cropland more than doubled. Soya bean, rapeseed and oil palm — crops associated with deforestation and diversity loss — account for much of the expansion and for the increase in pollinator dependence.

But although the land used has increased, crop diversity has remain largely the same since 2000. Producers have opted for large-scale cultivation of one crop. That’s a problem because monocultures don’t provide pollinators with a stable, year-round supply of food. This ultimately leads to a fall in insect numbers, lower yields and increased deforestation as demand for land surges.
Greater reliance on crops that are dependent on single-species pollinators, coupled with declining pollinator populations, could cause problems for food security. Poorer regions will be the hardest hit by crop failures, but higher-income countries that rely on imported food will also be affected.
Rotating a diverse range of crops on a single piece of land could help to stem the decline in pollinator populations. Planting native flowers and hedgerows on agricultural land and restoring neighbouring natural environments could also preserve pollinator habitats.
Glob. Change Biol. 25, 3516–3527 (2019)
US household food waste calculated
Working out how much food goes uneaten in an individual household is notoriously difficult. Comprehensive data on how much food ends up in the bin does not exist. But Yang Yu and Edward Jaenicke at Pennsylvania State University in University Park used a new method to overcome the lack of data.
Instead of trying to measure food waste directly, Yu and Jaenicke calculated a household’s ability to efficiently convert food brought into the household into the energy required to maintain the body weight of its residents. First, they obtained data on food purchases from around 4,000 households that took part in the 2012 US Department of Agriculture’s National Household Food Acquisition and Purchase Survey. The authors then calculated the metabolic energy requirements of the people living in each household from attributes such as height, weight, age and gender. The amount of food waste was estimated according to the difference between the household’s food inputs and its members’ energy requirements, not accounting for overeating.
The study showed that the average household wasted close to one-third of the food that it bought, which means that the United States wastes an estimated US$240 billion worth of food per year. The most efficient household in the study wasted about 9% of its food. Healthier diets created more waste than unhealthier diets, owing to the greater proportion of fruit and vegetables. Higher-income households wasted about 50% more food than lower-income households, and small households wasted more per person than large households.
Am. J. Agric. Econ. 102, 525–547 (2020)
Hidden hunger a global problem
There is more than enough food to feed the global population. But local patterns of production still leave 10% of the world’s people with insufficient calories, and more than half with inadequate quantities and variety of micronutrients — known as hidden hunger.
These are findings of a detailed analysis of food production by Ozge Geyik and colleagues at Deakin University in Burwood, Australia. The team gathered data on the nutrient content of 174 individual foods produced across 177 countries between 1995 and 2015. The researchers analysed whether individual countries and regions could meet the energy needs of their populations, as well as supply them with protein, iron, zinc, vitamin A, vitamin B12 and folate.
The study is one of the first to take such a detailed look at global patterns of nutrient production using disaggregated food data over time. Previous work has typically grouped foods into broad categories, such as cereals, dairy and vegetable oils, which can lead to under- or overestimates of specific nutrients.
Global food production increased steadily over the two decades, and outpaced increases in food requirements. However, on a regional level, the analysis found that more than half of the countries in Africa and Asia were not producing enough calories for their populations.
In 2015, more than 20% of the global population lived in countries with inadequate iron, vitamin A, vitamin B12 and folate production. Food production often fell short in multiple nutrients. More than 70% of countries with nutrient shortfalls produced inadequate amounts of iron, vitamin A and folate. And more than one-fifth of those not producing enough nutrients, fell short by more than half of what was necessary for their population.
The authors suggest that countries with nutrient deficiencies could prioritize the production of foods that contain the nutrients that their population needs. For example, in places where protein production is adequate, shifting production to protein sources that are higher in vitamin A and iron could alleviate these nutrient shortfalls. Adding micronutrients directly to soils and the leaves of crop plants is another possible solution.
Glob. Food Sec. 24, 100355 (2020)
Nutrient recycling possibilities mapped
The age-old practice of fertilizing crops with livestock manure has been reimagined in a study led by Sheri Spiegal from the US Department of Agriculture in Las Cruces, New Mexico. In the study, the team introduces the concept of a manureshed — land around livestock farms that could benefit from the nutrient-rich manure that those farms produce.
Spiegal and her colleagues mapped a patchwork of more than 3,000 counties across the United States. They classified counties as manure sources if they could supply nutrients in manure from livestock, or sinks if the crops grown could use the nutrients from manure.
The work reveals a surfeit of opportunity to recycle nutrients. The researchers identified counties that could recycle nitrogen and phosphorous nutrients at the local county level, as well as four regional manuresheds — in the northwest, southwest, central and southeast United States — where clusters of source counties could join together to develop sustainable redistribution programmes over longer distances. The work suggests a pathway towards removing manure from areas where it can pollute the local environment and delivering it to nutrient-poor agricultural lands, easing the reliance on commercial fertilizers that pollute the environment and deplete finite natural resources. But the authors note that further research — on how best to recover and transport manure, for instance — will be needed to turn the vision into a reality.
Agric. Syst. 182, 102813 (2020)
Intervention trade-offs assessed
Transforming the way land is managed and food is produced could shore up food supplies and address the challenges of climate change and biodiversity loss. But an assessment of proposed interventions reveals that few are up to the task of protecting both livelihoods and the environment.
Pamela McElwee from Rutgers University in New Brunswick, New Jersey, and her colleagues assessed the benefits and trade-offs of 40 proposed changes to land management, food-production chains and the management of environmental risks. The potential interventions are outlined in the 2019 report from the Intergovernmental Panel on Climate Change, and include improving management of livestock, reforestation, reducing consumer and retail food waste and management of urban sprawl.

The authors assessed each of the actions against the United Nations’ 17 Sustainable Development Goals (SDGs), as well as 18 measures from the Nature’s Contributions to People (NCP) framework, which was drawn up by scientists associated with the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services in 2017. This framework is intended to recognize nature’s social, cultural, spiritual and religious significance, as well as its role in providing food, clean water and healthy air.
The analysis revealed that several interventions carried unintended negative consequences. The production of bioenergy, either with or without carbon capture, planting forests and commercial crop insurance all had potentially negative consequences for both SDGs and NCPs. For example, bioenergy had large negative impacts on maintaining land biodiversity, freshwater quality and food production, despite providing affordable clean energy. About one-third of the interventions proposed had no substantial trade-offs. These included improving water management, increasing soil organic carbon content, reducing pollution, reducing post-harvest losses and fire management.
The analysis could help decision-makers to assess environmental or developmental policies to avoid unintended trade-offs, the authors say.
Glob. Change Biol. 26, 4691–4721 (2020) More

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A farmer inspects her maize crop, grown using a ‘push–pull’ approach.Credit: The ‘Push–Pull’ Farming System: Climate-smart, sustainable agriculture for Africa/ICIPE/Green Ink Ltd UK

On paper, the global agriculture sector has done an admirable job of keeping pace with a growing population. According to the United Nations’ Food and Agriculture Organization, agricultural output per person has increased by 50% since 1960 — impressive, considering the number of mouths to feed has more than doubled.
But the reality is messier. Many people, including those in high-income nations, lack reliable access to nutritious food. And food security is an ongoing struggle for people in poorer regions. Even transient disruptions can have far-reaching consequences. One article1 described the global food supply as being “on a razor’s edge” — weather events or natural disasters in one part of the world can cause the price of grain everywhere to spike by more than 50%. “Globally, we have to increase food production by 60%, and in some areas we have to increase by 100%,” says P. V. Vara Prasad, a crop ecophysiologist at Kansas State University, Manhattan.

Over the past 50 years, producers increased agricultural output in much of the world through the ‘green revolution’. But this revolution has been environmentally harmful, relying heavily on chemical pesticides and fertilizers that have inflicted lasting damage on the soil and water supply. Natural biodiversity has been sacrificed to create vast monoculture fields. And in many low-income nations, survival depends on coaxing greater productivity from existing plots as more and more people scramble for limited resources, says Bernard Vanlauwe, a soil scientist based in Nairobi at the International Institute of Tropical Agriculture.
Many agricultural researchers are now looking to a set of practices known as sustainable intensification. The specifics vary depending on the setting, but a growing number of examples from around the world highlight the possibility of a second green revolution — one that might better live up to its name.
Many roads to sustainability
The concept of sustainable intensification was popularized2 in 1997 by Jules Pretty, an environmental scientist at the University of Essex in Colchester, UK. His goal was to challenge the idea that increasing yield is inherently incompatible with environmental health, with an agricultural philosophy that encompasses parameters such as biodiversity and water quality as well as the social and economic welfare of farmers. Researchers have defined the scope of sustainable intensification in different ways, but the big picture, says Pretty, entails recognizing that agriculture is inexorably connected with the environment and designing cultivation strategies accordingly. “Components of sustainable systems tend to be multifunctional,” he says. “You want a diverse system that provides support to pollinators, fixes nitrogen and provides a break against insects.” Advocates of sustainable intensification recognize that global agriculture can’t be reinvented in one fell swoop and that progress will come from incremental steps that improve efficiency, as well as more-dramatic measures that redesign the farming landscape.
Lucas Garibaldi, an agroecologist at the National University of Río Negro in Bariloche, Argentina, has focused on pollinators as a crucial component of what he calls ecological intensification. “Crop yield depends not only on the count of pollinators, but also on the biodiversity of pollinators,” says Garibaldi. “Millions of honeybees alone will not replace the function of diverse species of wild bees and butterflies and birds.” He notes that different bees pollinate different crops, but also allow more efficient pollination for some plant species. To create a haven for these airborne assistants, Garibaldi advocates minimizing pesticide use and including non-agricultural zones in farmland. These could be wild-plant borders that surround fields or just hedgerow-like strips of flowers that are appealing to the bees that traverse them.
Growing a mix of crops can have many benefits, including attracting pollinators. Conventional monoculture leaves soil exposed for much of the year, Garibaldi says. This creates opportunities for weeds to grow — necessitating herbicides — or leaves soil susceptible to erosion. With multiple crops or rotation throughout the year, more durable root systems that densely and extensively permeate the ground can be established, reinforcing the soil and preventing the nutrient depletion associated with long-term monoculture.

Crops rely on pollinators such as bees. Credit: Chris Gomersall/2020VISION/naturepl.com

Diversity can also eliminate the need for pesticides. Pretty says around 180,000 farmers in Kenya, Uganda and Tanzania now use push–pull cropping practices when growing maize. They plant grasses around the edges of maize plots that produce chemicals that ‘pull’ a common pest, the maize stalk borer (Busseola fusca), away from crops, while the maize itself attracts parasitic wasps that prey on the stalk borer. The farmers also intersperse legumes of the genus Desmodium with the maize that enrich the soil with nitrogen, and produce compounds that ‘push’ away pests and kill off a genus of invasive weed known as Striga.
Sustainable soil management is a thorny issue, particularly in resource-limited settings. Vanlauwe notes that nutrient depletion is one of the greatest threats to yield for African farmers, making a hard-line approach to sustainability unrealistic. “People who say you can trigger agricultural development in Africa without fertilizer do not have on the ground experience,” he says. But there are environmentally friendly ways to feed the soil. Jo Smith, a soil scientist at the University of Aberdeen, UK, has been equipping farmers in Africa and Asia with anaerobic digesters — simple systems that use microbes to convert animal manure into biogas for fuel and leave a nutrient-rich bioslurry. “It’s like giving them a little fertilizer factory — it gives you available ammonium that the crop can take up quickly,” she says. The biogas is also less harmful than conventional fuels, reducing household air pollution and improving quality of life, Smith adds.
Much of the world’s farming takes place on smallholder plots. One study3 estimated that one-third of the global food supply is produced on farms of less than two hectares. This fragmentation can make it challenging to introduce sustainable intensification practices. “Smallholder production systems are absolutely risk-averse,” says Vanlauwe. “Falling from earning US$100 to $50 a month can be the difference between being not-hungry and being hungry.”
Close collaboration with individual farmers is needed, but this is difficult to achieve at scale. Fortunately, smallholders are increasingly participating in collectives that can accelerate information sharing and reduce the risk associated with adopting new cultivation strategies. In August4, Pretty and his colleagues reported that, worldwide, around 8 million such groups have formed over the past two decades. “That’s about 240 million people working in collective-action efforts around areas like irrigation, forest management, pest management and water,” says Pretty. By partnering with these groups, researchers can design programmes that are more likely to be compatible with social, cultural and environmental conditions, and establish local networks of collaborators to facilitate the dissemination of information.
Some governments are also taking a more active role. Ethiopia, for example, has focused on aspects of ecological repair by establishing ‘exclosure’ areas for depleted soils. “Areas are fenced off, and after about ten years the land starts to recover,” Smith says.
In China, Fusuo Zhang, a plant-nutrition specialist at the China Agricultural University in Beijing, and his colleagues are working with government officials to mobilize an effort to help smallholder farmers across the nation transition to more evidence-based, sustainable cultivation. This includes selecting seed varieties that are suited to a given plot, using modelling techniques to guide planting based on levels of sunlight, water and nutrients, and optimizing the timing and density of seed planting. “We sent faculty members and groups of students to live among the farmers in the villages, and work with them to try to change their management,” says Zhengxia Dou, an agricultural scientist at the University of Pennsylvania in Philadelphia, who collaborated with Zhang’s team. By 2015, the effort had grown to include nearly 21 million farmers across China, who, on average, achieved a more than 10% boost in yield while using around 15% less fertilizer and reducing their greenhouse-gas output5.
Many farmers in India are embracing a national programme known as zero-budget natural farming (ZBNF). This cultivation strategy involves using soil microbes and mulch rather than synthetic fertilizers to enrich lands. Farmers in several Indian states are pursuing the approach, including around half a million farmers in Andhra Pradesh. But some scientists are concerned that the approach is untested and unproven. Last year, Panjab Singh, president of the National Academy of Agricultural Sciences in Delhi, told the newspaper The Hindu, “We are worried about the impact on farmers’ income, as well as food security.”

Smith concurs. “It was a political move, not a scientific move,” she says, adding that the natural farming approach has “not been properly trialled”. To assess the technique, she and her colleagues modelled the long-term impact of ZBNF on soil health. They found that the approach could meaningfully and sustainably improve nitrogen levels for low-yield lands, but that it would offer little benefit to farms already achieving high yields6. They concluded that a more targeted implementation of ZBNF is needed to protect overall national food security. Smith remains largely positive about ZBNF, which has been gaining momentum among farmers. “There’s a lot of good things about it, but it needs more science,” she says.
Outside national initiatives, smallholder sustainable intensive farming requires targeted investment and efforts to support social and economic stability. Vanlauwe contends that, in many parts of sub-Saharan Africa, environmental and political conditions mean that many farmers will continue to struggle at the margins for the foreseeable future. Still, he sees a path towards economic mobility. “Give them access to credit they pay back over time, and invest in integration and value-chains so they can get rid of or sell excess produce,” he says. “It’s about creating incentives and access systems.”
But durable change also requires building local expertise in crop and soil research, and in ecosystems. Many specialists in these areas are also involved with international education and training. For example, as director of the Feed the Future Innovation Lab for Collaborative Research on Sustainable Intensification, Prasad has helped to coordinate undergraduate- and graduate-level agriculture programmes in places such as Senegal, Cambodia and Bangladesh. Normally, these programmes take on a few dozen students at a time, but the shift to online training as a result of the coronavirus pandemic could prove to be a long-term gain for capacity building. “We are now talking to about 500 or even 1,000 students,” he says. More

Calculation of solar elevation and azimuth angles versus time
For our numerical calculations, the solar elevation angle θs(t) from the horizon and the solar azimuth angle αs(t) from south (axis y, Fig. 7A) were calculated as a function of time t with an algorithm based on a semi-analytical approximation (analytical Kepler’s orbits modified with astronomical perturbations) and the planetary theory VSOP 87 (Variations Séculaires des Orbites Planètaires) of Bretagnon and Francou30. This method is valid for the 1950–2050 period with an accuracy of 0.01°. Using this algorithm, we calculated the geocentric ecliptical, then the geocentric equatorial, and finally the geocentric horizontal coordinates of the Sun, resulting in the values of θs(t) and αs(t).
Diurnal cloudiness
Total cloud cover (TCC) time series of high temporal resolution (1 h) were evaluated for the period 01.01.2009–31.12.2018 from the ERA5 reanalysis of the European Centre for Medium-Range Weather Forecasts31. The geographic coverage is global with a native spatial resolution of 0.25° × 0.25° ≈ 27 km × 27 km. Climatological mean values of TCC were determined by averaging for each hour of each calendar day of every year in the vegetative period of sunflowers. Since TCC is a dimensionless relative parameter in the range 0–1 (0 is clear sky, 1 is overcast), the hourly climatological means are equivalent to the time-dependent probability 0 ≤ σ(t) ≤ 1 of cloudy situation. We determined the diurnal cloud probability function σ(t) in July, August and September in Boone County (Kentucky, USA, 39° N, − 84.75° E, Fig. 2A), central Italy (41.0° N, 15.0° E, Fig. 2B), central Hungary (47.0° N, 19.0° E, Fig. 2C), and south Sweden (58.0° North, 13.0° East, Fig. 2D). The cloudiness data used in our calculations correspond to the decade between 2009 and 2018. Because similar data are not readily available for the period when sunflowers were domesticated, we assume in this work that the data obtained in the last decade is historically representative. The validity of this assumption can be evaluated when paleo-climatological cloudiness data become available.
Measurement of the elevation angle of mature sunflower heads versus time
In a sunflower plantation at Budaörs (near Budapest), we measured the elevation angle θn of the normal vector of the mature head of the same 100 sunflowers as a function of time t, approximately weakly from 6 July to 11 September 2020. The studied sunflowers were individuals in a given row of the plantation.
Measurement of the absorption spectra of mature sunflower heads
The absorption spectra A(λ) of young (2 weeks after anthesis) and old (4 weeks after anthesis) inflorescence and back of mature sunflower heads were measured in the field with an Ocean Optics STS-VIS spectrometer (Ocean Insight, Largo, USA) in July 2020. Measurements were performed under total overcast conditions to ensure isotropic diffuse skylight illumination. At first, the reflection spectrum of the inflorescence/back was determined as follows: a spectrum was measured by directing the spectrometer’s head on the target at a distance of 5 cm, then another spectrum was registered by pointing the spectrometer to the overcast sky. In the laboratory these two spectra were divided by each other. Finally, assuming that all non-reflected light was absorbed, the absorption spectrum A(λ) = 1 − R(λ) was obtained by subtracting the reflection spectrum R(λ) from 1. Absorption spectra were measured for 3 sunflowers and then averaged.
Calculation of sky irradiance absorbed by a sunflower inflorescence
In the x–y-z reference frame of Fig. 7A, let the normal vector of a mature sunflower inflorescence be

$$underline {text{n}} = , left( {{text{cos}}theta_{{text{n}}} cdot {text{sin}}alpha_{{text{n}}} ,{text{ cos}}theta_{{text{n}}} cdot {text{cos}}alpha_{{text{n}}} ,{text{ sin}}theta_{{text{n}}} } right),$$
(2)

where axes x and y point to west and south, axis z points vertically upward, the elevation angle − 90° ≤ θn ≤  + 90° is measured from the horizontal (θn  > 0°: above the horizon, θn  More

Target species and basic assumptions
We developed and analyzed spatially explicit models that describe range expansion of an invader species’ population that consists of many sub-populations. Invasive species often expand their range by stratified dispersal using human-mediated long-distance dispersal in addition to local expansion of sub-populations20. Extending a model rigorously analyzed by Takahashi et al.31, which explicitly involves (1) short-distance dispersal that expands the area of current sub-populations, and (2) long-distance dispersal that establishes new sub-populations beyond existing sub-populations (Fig. 4), we consider spatially inhomogeneous factors that influence on the long-distance dispersal (e.g., vectors’ distribution). The parameters and functions used in these models are listed in Table 1.
Figure 4

A schematic of short- and long-distance dispersal modes. Human activities may influence the long-distance dispersal by: (1) changing the number of propagules starting the long-distance dispersal ((R cdot varphi (x,y))), and (2) introducing biases in their spatial locations ((psi (x,y))). By compositing these short- and long-distance dispersals, we predict population establishment at the next time step.

Full size image

Table 1 Symbols and their default values.
Full size table

We estimated the population size of the invader species as the area covered by any of these sub-populations in the study area. This simple measure of the population size was based on our assumption that the inside of a sub-population is homogeneous and these sub-populations vary only in their positions, sizes, and shapes. This assumption may oversimplify spatial architectures of the sub-populations, because even clonal colonies of perennial plants often have concentric structures that can influence reproductive output40; but this simplification is applicable when the reproductive rate of the species is high enough to reach a constant carrying capacity quickly.
Short- and long-distance dispersals
We considered stratified dispersals of the invader species. Note that we explicitly considered invader species’ dispersal but their vectors’ movement (e.g., human traffics) was included only implicitly. The short-distance dispersal expands the species’ range only by a constant velocity7. Therefore, we modeled the short-distance dispersal as radial expansion of these sub-populations with a constant speed g. Meanwhile, long-distance dispersal introduces new sub-populations into the population out of its parent sub-population. Empirical observations showed that long-distance dispersal mediated by human activities introduces a new sub-population to an area at a long distance from its source population, e.g., vehicles can move plant seeds for more than hundreds of kilometers41. Long-distance dispersal diminishes the influence of the source location on the destination of a dispersal event, so as a simplifying approximation we assumed that the destination of the long-distance dispersal is independent of the source location of a sub-population.
The assumption of source location independence of the dispersal destination allows us to describe a process of long-distance dispersal by two functions on (S): (1) a function (varphi (x,y)) describing spatial variation in disperser production rates, and (2) a function (psi (x,y)) describing the probability that a coordinate ((x,y)) is selected as a destination of the disperser. Following the notation of Jongejans et al.18, we call (varphi (x,y)) and (psi (x,y)) the source and destination functions, respectively. Note that we define the spatial average of the source function to be one (i.e., ({{int_{S} {varphi (x,y),dxdy} } mathord{left/ {vphantom {{int_{S} {varphi (x,y),dxdy} } {|S|}}} right. kern-nulldelimiterspace} {|S|}} = 1)). We define R as the regional average of the disperser production rate per unit area (a spatially homogeneous component of the disperser production rate). Using this formulation, we calculate an expected disperser production rate of a given area by integrating (Rvarphi (x,y)) over the area. The spatial integration of the destination function over the study area is one because we assume the population of the invader species will reach full carrying capacity.
We have defined a population of the invader species as a spatial union of all sub-populations in the study area because we assume sub-populations are homogeneous. Within the study area, (rho_{t} (x,y)) is 1 if the coordinates ((x,y)) are within at least one of the sub-populations of the invader species at time (t) (and otherwise 0). The integration of (Rvarphi (x,y)) is the expected disperser production rate for a given (rho_{t} (x,y)), and the integration (Rint_{S} {rho_{t} (x,y)varphi (x,y),dxdy}) is the expected total production of dispersers from a population in the t-th time step. Thus, assuming that the total number of dispersers that start long-distance dispersal at time (t) (denoted by (n_{{{text{d,}}t}})) follow a Poisson distribution, we can write a probability that the population produces k dispersers in the t-th time, Eq. (1).

$$ Pr [n_{{{text{d}},t}} = k] = frac{{lambda^{k} e^{ – lambda } }}{k!}{, }lambda = Rint_{S} {rho_{t} (x,y)varphi (x,y),dxdy} . $$
(1)

The destination of the disperser is determined by the destination function (psi (x,y)), which determines probabilities of ending a dispersal event at ((x,y)), which results in a new sub-population being established at that location. In total, the spatial distribution of new sub-populations introduced by long-distance dispersal follows a Poisson point process of which intensities are given as (psi (x,y)Rint_{S} {rho_{t} (x,y)varphi (x,y),dxdy}).
Three model types
We compared three different types of models by varying interactions between the species’ long-distance dispersal and human activities. These included: (1) a source-mediated-dispersal model assuming that the source function (varphi (x,y)) varies spatially by human activity while the destination function (psi (x,y)) is uniform, (2) a destination-mediated-dispersal model assuming that the destination function varies spatially while the source function is uniform, and (3) a full model assuming that both source and destination functions vary spatially.
Let (h(x,y)) be a function representing intensity of human activities at coordinates ((x,y)). Without loss of generality, we can assume that the function (h(x,y)) satisfies (int_{S} {h(x,y),dxdy} = 1), the total intensity over the study area is scaled to one. In the source-mediated-dispersal model, the source function is proportional to the human-activity intensity, i.e., (varphi (x,y) = |S| cdot h(x,y)), and the destination function (psi (x,y)) is uniformly equal to ({1 mathord{left/ {vphantom {1 {|S|}}} right. kern-nulldelimiterspace} {|S|}}). On the contrary, the source function of the destination-mediated-dispersal model is uniform and the destination function is (psi (x,y) = h(x,y)). The full model is a combination of the source- and destination-mediated-dispersal models in which both source and destination functions vary with area. In this study, we assume that a single factor determines both the source and destination functions, i.e., (varphi (x,y) = left| S right| cdot h(x,y)) and (psi (x,y) = h(x,y)) (Table 2).
Table 2 Definitions of model types.
Full size table

Asymptotic growth rate of a population
Spatial dimension introduces complexity, though rigorous mathematical analysis is still viable for a small population with few small sub-populations. This situation may arise with an accidentally transferred population. Here, we consider infinitesimally small populations to be rare for invasive species and derive an asymptotic value of the growth rate to the size of the area inhabited by the population.
Each sub-population includes age, so we incorporated age-structured population dynamics29,31 into the model, described by the differential equation,

$$ frac{partial n(a,t)}{{partial t}} + frac{partial n(a,t)}{{partial a}} = 0, $$
(2)

where (n(a,t)) represents the frequency of sub-populations with age a at time t. Note that Eq. (2) assumes no extinction of sub-populations. The equation has two boundary conditions: (1) (n(a,0)) represents an age distribution of the initial population, and (2) (n(0,t)) represents the number of new sub-populations (i.e., age 0 sub-populations) introduced by the long-distance dispersal at time t.
To determine the number of new sub-populations, we need to determine how many long-distance dispersers will emerge from a given population by including spatial heterogeneities. Recall that a sub-population expands outward by a constant speed g. Therefore, if we ignore overlaps among sub-populations each sub-population keeps a circular shape of radius proportional to age. In addition, if a sub-population is young, i.e., its size is small, we can regard the value of the source function (varphi (x,y)) inside the sub-population as uniform. Let ((x_{i} ,y_{i} )) and (a_{i}) be the position of the center and age of the (i)-th sub-population, respectively. With the above approximations, we can simply derive the expected number of long-distance dispersers that start dispersal from the (i)-th sub-population as (pi R cdot (ga_{i} )^{2} varphi (x_{i} ,y_{i} )).
On the other hand, existing sub-populations also originate from long-distance dispersal. Therefore, a position of the sub-population also follows the destination function (psi (x,y)). Building on the expected number of new sub-populations we described at the last paragraph, we calculate an average over the study area to calculate a mean-field approximation of the number of long-distance dispersers from an age a sub-population as (pi Rint_{S} {psi (x,y)(ga)^{2} varphi (x,y),dxdy}).
We assume that a population consists of a few small sub-populations in this formulation and a disperser will always establish outside existing sub-populations. Therefore, the total number of a new sub-population (i.e., (n(0,t))) is a summation of new sub-populations produced by each of the existing sub-populations,

$$ begin{gathered} n(0,t) = pi Rint_{0}^{t} {n(a,t)left[ {int_{S} {psi (x,y)(ga)^{2} varphi (x,y),dxdy} } right],da} \ = pi Rleft( {int_{S} {psi (x,y)varphi (x,y),dxdy} } right)int_{0}^{t} {(ga)^{2} n(a,t),da} . \ end{gathered} $$
(3)

With Eq. (3), the asymptotic growth rate of the Eq. (2) can be calculated as follows29,31,

$$ left( {2pi Rg^{2} int_{S} {psi (x,y)varphi (x,y),dxdy} } right)^{1/3} . $$
(4)

The asymptotic growth rate indicates that the integration (int_{S} {psi (x,y)varphi (x,y),dxdy}) describes the influence of the source and the destination functions in the early phases of population growth. Therefore, hereafter we call (int_{S} {psi (x,y)varphi (x,y),dxdy}) a spatial factor (F_{{text{h}}}) of the long-distance dispersal. Note that the spatial factor reduces to 1 for both source- and destination-mediated dispersal models. For the full models of which source and destination functions are (varphi (x,y) = left| S right|h(x,y)) and (psi (x,y) = h(x,y)), respectively, we can reduce the spatial factor (F_{{text{h}}}) to (int_{S} {left( {sqrt {left| S right|} h(x,y)} right)^{2} dxdy}), equivalent to Simpsons’ diversity index.
Numerical analysis
We evaluated the effects of the dispersal vector on distribution with an individual-based approach that describes colonies in a population as groups of individuals within a circular shape of various sizes (Fig. 1a,c,e for typical model outputs, see supplemental information SI 1 for detailed settings). To evaluate the effect of spatial heterogeneity on population dynamics, for each model type we generated 100 of (h(x,y)) randomly (see shaded area of Fig. 1a,c,e, and SI 2 for the algorithm used) and ran 100 independent realizations for each (h(x,y)). For each realization, we split the time course into three phases: establishment, expansion, and naturalization. The phases were based on the proportion of area inhabited by the population (Fig. 2a; less than 5%, 5% to 95%, and 95% to complete occupation of the total area, respectively), and measured the length of each phase. We linearly interpolated the time course based on area covered for each phase.
Using the same set of realized time courses, we estimated the asymptotic growth rate as the peak of a distribution of the logarithmic value of the instantaneous growth rate, defined as a difference of logarithmic values of covered area that are adjacent in a time course. We excluded periods that a population covers less than 1% or more than 50% of the total area to avoid strong demographic stochasticity of initial dynamics and a deceleration phase of S-shaped growth, respectively. We gathered these logarithmic values of instantaneous growth rates from 100 realizations with the same (h(x,y)) and dispersal type, then estimated the density distribution using Gaussian kernel estimation. Finally, we determined the maximum point of the estimated density distribution as the estimated asymptotic growth rate. More

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How rapidly can the major functional components of a soil ecosystem appear in volcanic ash?
The overall conclusion from comparing the functional composition of the developing ash-soil with natural forest soils from the same climates, is that the major biological aspects of the system have developed surprisingly quickly. Already by the 24-month and 36-month stage, the ash-soil had a similar diversity of bacterial functional genes to a forest soil (Fig. 8).
This contrasts with the findings of Fujimura et al.3, who found that ash deposited by the Miyakejima volcano still showed a very distinct and low diversity community compared to that expected of normal forest soils. This difference could be attributable to differences in the initial chemical composition of the ash: the pH value of the Miyakejima ash studied by Fujimura et al.3 was much lower than the ash we sampled, due to the persistence of acids from the initial eruption, or acidic rainfall from later outgassing. Our Sakurajima ash samples had only a slightly acidic pH (5.2) at the time of harvesting, which was similar to the average value (5.14) of 251 ash samples from Sakarajima collected from 1955 to 200125, and they remained in the 5–6 pH range at both 24 months and 36 months. Even the ash soil mesocosm samples that were situated on the lower slopes of the Sakurajima volcano, and the nearby natural forest soils at Sakurajima, remained in the pH 5–6 range and had a similar gene composition to other sites, suggesting that the area around the Sakurajima volcano is not subject to frequent highly acidic rain events. The difference between the Sakurajima ash and the Miyakejima ash hints at the importance of details of the chemical environment of the ash for determining its development into a functioning soil ecosystem.
Another factor which may explain the difference between the paths of biota development of the ash from the two volcanoes is the relative availability of propagules. Our ash soils were surrounded by developed ecosystems which could provide a rain of propagules of microorganisms and bryophytes in windblown dust or in rain splash. By contrast the Miyakejima ash field was an area of extensive ecosystem destruction. If bryophytes and lichens had not been able to establish due to unavailability of propagules, an important source of photosynthetically-fixed energy would have been unavailable to the Miyakejima system. This would have impeded the development of a decomposer food chain, of mineral weathering by organic acids and chelates, and of buffering of soil pH and water content and nutrient storage on organic matter and clay surfaces.
Was there a lower taxonomic diversity than is normally found in a developed soil?
At the broadest level, from the metagenomes, the taxonomic composition of the biota of the developing ash-soil resembled that of the developed forest soils—with archaea, fungi, protists and metazoans occurring at similar relative abundances in the ash-soils and forest soils. In this sense, the ash-soil had developed remarkably quickly in terms of the basic taxonomic framework of a functioning soil ecosystem. Bryophytes and lichens were able to establish10,26 with their propagules small enough to enter through the gauze covering, and presumably played an important role in providing carbon and extra niches to the developing ecosystem—even though they are unlikely to be as supportive of a diverse soil biota as the extensive root systems of vascular plants.
There was however—continuing a pattern seen in the 24-month results reported by Kerfahi et al.10—a lower OTU and Shannon diversity of bacteria based on the 16S rRNA amplicon sequencing. The continuing lower OTU-level 16S taxonomic diversity of the ash soils might have had multiple causes.
Firstly, limitations on dispersal and colonization of the ash soil systems might have kept OTU diversity lower. It is assumed that the biota present were mostly derived from the surrounding forest ecosystems—as windblown or rain splashed material. Dispersal limitation of soil biota is likely to play some role in all volcanic ash fields, although the existence of nearby areas of surviving ecosystem is also common20,27. Most volcanic explosions or ash fields result in no more than a few square kilometres of landscape being completely devastated, and isolated pockets of vegetation that survive are common27,28—in this respect the proximity of our mesocosms to natural vegetation may be fairly realistic. In natural ash deposits, upwards colonization by soil biota from buried ‘legacy soils’ is also possible20. In our experiment, upwards colonization from soil below the pots was not possible, and the plastic gauze covering may have prevented access by insects, birds or seeds that could have brought incidental soil biota. It is thus difficult to know for sure whether the overall role of dispersal limitation in our mesocosm systems is stronger or weaker than would generally be the case in natural ash fields. Since natural ash fields themselves are also very heterogenous in terms of area, depth and degree of devastation of natural vegetation, it is especially hard to generalise.
Secondly, the relatively extreme chemical and physical conditions of the volcanic ash itself are also likely play a major role in limiting the bacterial taxonomic diversity of the ash-soil biota in the mesocosms. Although the pH of the ash in our mesocosm systems was not extreme, it may be expected to be droughty due to low organic matter content, and low in available nutrients and organic matter that could sustain soil food chains. Even by 36 months, the organic carbon of the ash-soil was still orders of magnitude lower than in the surrounding forest soils (Supplementary Fig. S1)10,26. Thus, fewer niche types may be viable in the environment of the developing ash.
Nevertheless, although lower level taxonomic diversity of bacteria is clearly lower than in the established forest soils, the metagenome results from the ash soil mesocosms show that most higher level taxonomic groups of bacteria, archaea and eukaryotes are already present by the 24-month and 36-month stage, emphasizing that in some respects the establishment of soil biota has been rapid. While DNA of dead microorganisms blown as dust could have provided the impression of populations being present, it seems unlikely that dead material would be able to disperse in the same relative proportions as in a forest soil, to give a metagenome that resembled a developed soil in all its major groups, in roughly the same relative abundances (Please refer to Fig. 1 in Kerfahi et al.10).
Was there a lower diversity of categories of functional genes of soil biota than are normally found in a developed soil, indicating less functional complexity in the early ash-soil system?
Surprisingly, the richness and diversity of functional gene categories at Level 4 of the SEED Subsystem was not significantly different between the ash mesocosms and the forest soils. Around 97% of the metagenome reads in the ash mesocosms and the forest soil were bacterial, so the much lower OTU diversity of bacteria in the mesocosms would be expected to give a lower functional diversity of genes. The contrast between patterns of taxonomic and functional diversity in the ash mesocosms emphasises the redundancy of gene functions in soil organisms—such that losing a high proportion of taxonomic diversity apparently has no effect on functional diversity. If the level of functional gene diversity is high, this implies that in a general sense the ecosystem can potentially perform a wide variety of functions. Greater functional diversity is also considered to result in greater resilience of the ecosystem29.
We had also hypothesized that the distinct chemical environment of the developing ash would result in increased relative abundance of a number of specific gene categories:
Is there an increased relative abundance of genes (or of prokaryotic genera) associated with autotrophy (e.g. Rubisco gene, coxL gene) in the ash-soils?
We searched for potential taxa and genes which might indicate autotrophic carbon fixation through chemosynthetic oxidation processes. We found a higher relative abundance of Ktedonobacteraceae (Chloroflexi) in the ash soils compared to forest soils, which is a pattern that was also found in previous ash studies21,30. Ktedonobacteraceae is a novel taxonomic group that has only been recently added to the phylogenetic tree of Chloroflexi30,31. Their genome has been reported to be large and they are known to have a wide potential for different metabolic mechanisms32. Ktedonobacteraceae are mostly found in extreme environments, including volcanic ash and hydrothermal vents30.
We had hypothesized that the coxL (carbon monoxide dehydrogenase large chain) gene—which is implicated in autotrophy—would be more abundant in the ash soil samples. Likewise, the rbcL (ribulose bisphosphate carboxylase large chain) gene is involved in carbon fixation and we hypothesized its greater abundance in the ash-soil mesocosms. However, in fact both rbcL and coxL had higher relative abundances in the forest soils.
Although coxL has been mostly linked with chemotrophic organisms living in an extreme environment, due to its potential role for assisting heterotrophic growth in the environments lacking organic matter21,33, it is also one of the more abundant genes in natural forest soils34. Noting that natural forest is one of the largest global sinks of atmospheric CO34,35, the high relative abundance of coxL gene might be due to high abundance of CO in natural forests. Also, the coxL gene might have the potential to participate in other metabolic pathways. The presence of coxL genes in many different types of organisms (e.g. plant symbionts, animal pathogens, etc.) suggests other roles of CO-oxidation by the coxL gene33.
The higher abundance of rbcL in the forest soils in our study might be related to photosynthetic C fixation by cyanobacteria in both the forest soil and ash soils. rbcL gene also have been found in many natural forest sites. By contrast, Fujimura et al.3 found rbcL to be more abundant in developing volcanic ash soils, which might be attributable to differences in the chemical composition of ash or due to details of the mesoocosm system used in our study.
Is there increased relative abundance of genes that are associated with acquisition of nutrients from abiotic sources rather than decomposition of organic matter (e.g. nitrogen fixation genes)?
Contrary to expectations we found no differences in the relative abundance of nitrogen fixation gene (nifH) between the ash soils and forest soils. It is possible that this reflects nitrogen being relatively more limiting in the forest soils, where there is an abundance of organic carbon. It is also possible that in the forest soils, the abundance of labile carbon in the rhizosphere of N-limited plants encourages N fixing bacteria through root secretions36.
Is there increased relative abundance of stress response genes and dormancy related genes?
As hypothesized, we found that dormancy related genes were more abundant in the ash mesocosms than in the forest soils. This would seem to be adaptive in terms of survival of a well-drained ash-soil, low in organic matter, which is apt to dry out. This would depend, however, on the detailed microclimate. Field measurements suggested that in sunny conditions the microclimate in the static air in the trays in which our pots were held was generally around 0.5–1 °C higher than in the open air a meter away, although this difference disappeared in cloudy conditions and at night10. It is possible that our mesocosms (exposed in open sunlight, but covered by a gauze) would have either retained or lost moisture more easily than the soils, and that this might have affected the frequency of drying. We had also anticipated that stress response genes would be more common in the ash mesocosms. However, in this case the stress response category was less common than in the forest soil, surprisingly suggesting that at a cellular level stresses are in fact less common in the ash-soil.
Is there decreased relative abundance of cell–cell interaction related genes?
As anticipated, genes related to cell–cell interactions such as regulation and cell signalling genes and virulence, disease, and defense genes (Fig. 7a,b) were relatively less abundant in the ash mesocosms. This seems to emphasize that complex interactions are less common in the developing ash system than in a fully developed soil with its more abundant and diverse carbon sources. However, bacterial genes found as part of CRISPRs were relatively less abundant in the forests, implying lower intensity of defense mechanisms of bacteria against viruses in the forests compared to ash soils. The relatively low OTU diversity of the ash soils may perhaps allow greater spread and mortality of viruses through populations, necessitating greater investment in defences.
Since Odum37, it has been noted that developing ecosystems tend to be based on tighter and more effective interactions as succession continues. For example, Morriën et al.38 found that during secondary succession of old field ecosystems, co-occurrences of taxa become more predictable and carbon cycling in the decomposer chain more efficient. Empirically our findings seem to agree with the same paradigm, as we found cell–cell interaction genes found to be more abundant in the developed forest soils. It would be very interesting to directly measure decomposer carbon cycling efficiency in ash-soil mesocosm systems as they develop.
Although we focused on 16S rRNA amplicon sequence data for comparing OTU level diversity between samples as taxonomic assignment based on MG-RAST pipeline is very limited39,40, we had briefly compared the family level bacterial community composition assigned based on metagenome sequence data and based on 16S rRNA amplicon sequence data. It is still debatable if whole genome sequencing, which is free from primer bias, is superior in this respect to 16S rRNA amplicon sequencing40. Our data supports the idea that at the bacterial family level, metagenome sequencing covered a larger variety of taxonomic groups than 16S rRNA sequencing. More