How and why animals can live alongside humans

New study suggests animals can live alongside humans—if they are risk-analysis experts

MAX PLANCK INSTITUTE FOR EVOLUTIONARY ANTHROPOLOGY

 

IMAGE: 

FLOCK OF GREAT-TAILED GRACKLES ON POWERLINES.

view more 

CREDIT: © BRIAN HENDERSEN

“For animals, living alongside humans is ‘risky business’. But some species, like grackles, are clearly coping better in human-dominated environments, even seeking them out. We wanted to find out the secret to grackles’ urban-invasion success story,” said Breen.

The research is based on new analyses of grackles’ feeding behaviour. Deffner explained: “Cities are chaotic; they may have more cafes where animals like grackles can nab food, but they’re also filled with unpredictable people and their pets. To help manage this uncertainty, we thought grackles might use a specific strategy when trying to find food.”

Across three different populations, the researchers first examined how quickly grackles learned food was hidden in one particular place over another. Next, when the location of the food was swapped, the researchers examined how quickly the grackles relearned where to find it.

Better safe than sorry when leading an urban invasion

“Our key behavioural finding is that—across all three populations—male grackles were faster than female grackles at relearning the location of an out-of-sight treat. This robust result means male grackles are more efficient foragers in uncertain environments,” said Breen.

Under uncertainty, how do male grackles ‘outlearn’ female grackles? “Unlike females, males exhibit pronounced risk-sensitive learning. That is, males pay close attention to whether they recently found food, and, if so, they pretty much stick to feeding from that location, instead of gambling on exploring another location,” explained Deffner. The researchers said they were able to infer this strategy from grackles’ feeding behaviour via cognitive modelling.

“This sex differences in grackles’ learning makes biological sense,” said Breen, adding: “In this species, males are the ones that disperse and move into new territories; in other words, they lead their species’ urban invasion. So, as urban-invasion leaders, male grackles should proceed with caution—new neighbourhoods will pose new challenges”. The authors said they thought later-arriving females could overcome these same challenges by learning from the already established, and therefore presumably ‘knowledgeable’, males.   

Risk-sensitive learners are winners in unpredictable environments

On their computers, the researchers also artificially simulated evolution, to examine the kinds of learning strategies that emerge victorious from unpredictable environments like urban environments. Deffner explained: “In this urban-like environment, pretend animals need to learn to find food. The learning strategy they use to find food determines how much they get to eat. And how much they get to eat determines whether they can have babies who also learn roughly the same way. Over many generations, then, the animals with the best learning strategy will come to dominate the urban-like environment. Importantly, these ‘winners’ will give us an idea of how animals in general can thrive in the Anthropocene”.

Which learning strategy do unpredictable urban-like environments prefer? “Strikingly, in times of uncertainty, we found risk-sensitive learners were more likely to dominate over learners with other strategies. This result implies risk-sensitive learners like male grackles are better adapted to cope in chaotic settings, human-induced or otherwise”, said Breen.

Breen concluded: “Our study offers compelling evidence for how and why at least grackles are thriving in unpredictable urban environments. We link sex differences in foraging grackles’ learning strategies to sex differences in who leads their species’ invasion, and we further link the learning strategy used by these urban-invasion leaders to likely being a generally good one for any animal navigating a life shared with humans”.

To help facilitate future similar study on human-animal coexistence, the researchers created an online repository where scientists and the public alike can freely access their custom-built modelling tools.  In reference to the repository, Deffner said: “We hope this open-science resource proves useful to others”.

Male great-tailed grackle on a power line holding a sauce packet.

CREDIT

© Gary Leavens

Male great-tailed grackle foraging in a parking lot.

CREDIT

© John Mangold

JOURNAL

eLife

DOI

10.7554/eLife.89315 

ARTICLE TITLE

Risk-sensitive learning is a winning strategy for leading an urban invasion

ARTICLE PUBLICATION DATE

2-Apr-2024

 

Older trees help to protect an endangered species

When old trees are life shelters

UNIVERSITY OF BARCELONA

 

IMAGE: 

PROFESSOR SERGI MUNNÉ-BOSCH, FROM THE FACULTY OF BIOLOGY AND THE UB BIODIVERSITY RESEARCH INSTITUTE (IRBIO).

view more 

CREDIT: UNIVERSITY OF BARCELONA

The oldest trees in the forest help to prevent the disappearance of endangered species in the natural environment, according to a study led by the University of Barcelona. This is the case of the wolf lichen — threatened throughout Europe —, which now finds refuge in the oldest trees in the high mountains of the Pyrenees. This study reveals for the first time the decisive role of the oldest trees in the conservation of other living beings thanks to their characteristic and unique physiology.

Conserving the oldest trees in forests will be essential to protect biodiversity in forest ecosystems, which are increasingly affected by the impact of global change. This is stated on a new study published in the journal Proceedings of the National Academy of Sciences USA (PNAS). The study is signed by the experts Sergi Munné-Bosch and Ot Pasques, from the Faculty of Biology and the UB Biodiversity Research Institute (IRBio).

When old trees are life shelters

The wolf lichen (Letharia vulpina) is a species with a very limited distribution that is prevalent in mature forests and long-lived trees. Native to the American continent, it has also been found in Europe and the Iberian Peninsula, in medium and high mountain areas. Now, the authors have discovered that the presence of this lichen in the Pyrenees is associated with the longest-lived trees, specifically the black pine (Pinus uncinata).

“These old trees are found in the most isolated places, they grow on rocks with very little substrate and show unique characteristics regarding structure and composition. Specifically, the black pine can even live for more than a millennium, and its decay would be the most important factor facilitating the presence of the lichen”, says Professor Sergi Munné-Bosch.

“Paradoxically, the worse off these trees are, the more useful they are for the ecosystem (lichen conservation). In other words, the less important they might seem as individuals because of their decline, the more important they are for the whole ecosystem", says Munné-Bosch, cited as one of the world's most influential experts in the Clarivate Analytics' 2023 list.

The best habitat for the survival of the lichen L. vulpina is the oldest trees in the forest, the authors note. “In the case of centenarian and millenarian trees, the simplicity of their development, the modular growth that allows them to respond better to injury and damage, and the high tolerance to extreme conditions (water stress, extreme temperatures, etc.) are factors that explain their great longevity in the natural environment", explains Ot Pasques, an expert from the UB’s Department of Evolutionary Biology, Ecology and Environmental Sciences and IRBio.

“Trees have survival limits in extreme conditions, but they can survive with little water and nutrient resources. They are able to survive extreme conditions and live longer, thanks to modular growth and compartmentalisation of the damage that can affect them”, says Munné-Bosch. “Slow growth, which is associated with stress responses — such as the typical cold of high mountains or drought, which is increasingly frequent in the summer — also favours the longevity of these trees.

The most majestic trees, threatened by the human footprint

Longevity is one of the biological keys that would explain the unique ecological functions of trees, which make it essential to protect species and older trees in the most isolated mountain regions. “All individuals of a population are indispensable not only for their particular population and species, but for the whole global ecosystem. Everything is closely interconnected, and even the decline and death of trees plays an essential role in conserving biodiversity and ecosystems”, says Munné-Bosch.

These giants of the forest are threatened by the human footprint, especially the felling of trees. “Environmental conditions are not a problem for these trees, but unfortunately we as a species are. Only with a deep respect for nature and the life of other living beings can we preserve the extraordinary longevity of these trees. And as we have found in this study, this will also be decisive for the preservation of all biodiversity as we know it today”, the researchers conclude.

The longest-lived trees in the Pyrenees facilitate the survival of wolf lichen, a species threatened throughout Europe.

Old trees provide invaluable services to the forest ecosystem.

CREDIT

Ot Pasques - University of Barcelona

---

JOURNAL

Proceedings of the National Academy of Sciences

DOI

10.1073/pnas.231786612 

METHOD OF RESEARCH

Observational study

SUBJECT OF RESEARCH

Not applicable

ARTICLE TITLE

Ancient trees are essential elements for high mountain forests conservation: linking the longevity of trees to their ecological function

 

Scientists’ urgent call: end destruction and forge a just, sustainable future

UNIVERSITY OF HAWAII AT MANOA

 

IMAGE: 

UNLESS HUMAN VALUES SHIFT DRAMATICALLY AND SOON, THE RESULTING DAMAGE TO THE NATURAL WORLD WILL LIKELY BE CATASTROPHIC, WITH LONG-LASTING CONSEQUENCES FOR SPECIES AND ECOSYSTEMS, AND DEVASTATING UPHEAVALS FOR HUMANITY. A SYSTEMIC CHANGE IN HUMAN VALUES IS NEEDED THAT FOCUSES ON EARTH-CENTERED GOVERNANCE, AND ENTAILS A TRANSITION IN COLLECTIVE VALUES, BEHAVIORS, AND INSTITUTIONAL PRACTICES TO PRIORITIZE LONG-TERM ECOLOGICAL HEALTH AND SOCIAL WELL-BEING OVER IMMEDIATE GAINS. 

view more 

CREDIT: FLETCHER, ET AL., 2024.

An international team of scientists published a study today in the Proceedings of the National Academy of Sciences NEXUS emphasizing the urgent need to align political will, economic resources, and societal values to ensure a more sustainable and equitable world. Led by University of Hawai‘i at Mānoa researchers, the 18 authors combine their expertise in earth and ocean sciences, politics, law, public health, renewable energy, geography, communications, and ethnic studies to assess causes, impacts, and solutions to a multitude of worldwide crises.

“Climate change, ecological destruction, disease, pollution, and socio-economic inequality are pressing global challenges facing humanity in the 21st century,” said Chip Fletcher, lead author and interim Dean of the UH Mānoa School of Ocean and Earth Science and Technology. “These crises are not isolated problems but are interwoven, exacerbate each other, and create amplifying feedbacks that pose a grave threat to both the environment and human well-being.”

“Environmental and human health are inextricably linked,” said David Karl, co-author and professor of oceanography at UH Mānoa. “Urgent and comprehensive action is called for, including rapid decarbonization, fostering a more harmonious relationship with nature, and equitable human development.”

Global cultural shift

The authors argue that centuries of imperialism, extractive capitalism, and population growth have pushed Earth's ecosystems beyond their limits, and created a broadening pattern of social inequality. The review summarizes the grave threats facing the planet but rejects a “doom and gloom” philosophy. Instead, the authors argue, the threats should motivate swift and substantial actions.

According to the authors, a global economic model focused on wealth accumulation and profit, rather than true sustainability, is a major impediment to decarbonization, conserving natural resources, and ensuring social equity. Therefore, the authors argue, governments should enforce radical, immediate cuts in fossil fuel use, eliminate environmentally harmful subsidies, and restrict trade that generates pollution or unsustainable consumption.

The most vulnerable human populations, those who bear the least responsibility, disproportionately bear the consequences of these interwoven global crises. The broadening pattern of this inequity breeds displacement, disease, disillusionment, and dissatisfaction that ultimately erode social cohesion.

A grossly unequal distribution of wealth has coupled with the increasing consumption patterns of a rising global middle class to amplify ecological destruction. Studies show that the poorest half of the global population owns barely 2% of total global wealth, while the richest 10% owns 76% of all wealth. The poorest 50% of the global population contribute just 10% of emissions, while the richest 10% emit more than 50% total carbon emissions. Climate change, economic inequality, and rising consumption levels intertwine to amplify ecological destruction.

Marine and terrestrial biomes face critical tipping points, while escalating challenges to food and water access foreshadow a bleak outlook for global security. The consequences of these actions are disproportionately borne by vulnerable populations, further entrenching global inequities.

“To avoid these consequences, we advocate a global cultural shift that elevates kinship with nature and communal well-being, underpinned by the recognition of Earth's finite resources and the interconnectedness of its inhabitants,” said Krista Hiser, professor of English at Kapiolani Community College at the University of Hawai‘i.

Kinship with nature

The authors welcome signs that humanity is interested in changing its value system to prioritize justice and reciprocity within human societies and between humans and natural landscapes and ecosystems, which they see as the best route to true sustainability.

 

According to Phoebe Barnard, affiliate professor at the University of Washington, “The imperative is clear: to navigate away from this precipice, we must collectively harness political will, economic resources, and societal values to steer toward a future where human progress does not come at the cost of ecological integrity and social equity.”

The authors call for a global cultural shift in values, aided by education, robust policy, economic incentives, cross-sector partnerships, community empowerment, corporate accountability, technological innovation, leadership, and cultural narratives delivered through art and media. They conclude that humanity must stop treating these issues as isolated challenges and establish a systemic response based on kinship with nature that recognizes Earth as our lifeboat in the cosmic sea of space.

---

JOURNAL

PNAS Nexus

DOI

10.1093/pnasnexus/pgae106 

METHOD OF RESEARCH

Systematic review

SUBJECT OF RESEARCH

Not applicable

ARTICLE TITLE

Earth at risk: An urgent call to end the age of destruction and forge a just and sustainable future

ARTICLE PUBLICATION DATE

2-Apr-2024

 

Intergenerational altruism and climate policy support

PNAS NEXUS

 

IMAGE: 

EXPOSURE TO THE INTERGENERATIONAL DILEMMA IMPACTS CLIMATE POLICY SUPPORT AMONG WOMEN AND NON-BINARY PEOPLE BUT NOT AMONG MEN.

view more 

CREDIT: AGNEMAN ET AL

Investments in mitigating climate change in many cases benefit future generations more than those alive today. However, initial costs must be borne by those living now, so many climate mitigation policies rely on some level of intergenerational altruism for support. To investigate the strength and shape of intergenerational altruism, Gustav Agneman and colleagues asked Swedish study participants to engage in an experimental task in which they allocated fictional resources across generations, after being told how many descendants they might be expected to have in the next 250 years.  On average, participants allocated most of the resources to the present generation, and fewer and fewer resources to each subsequent generation in a nearly quasi-hyperbolic curve. Participants who allocated more resources to future generations showed stronger support for contemporary climate policies. In addition, those who engaged in the intergenerational resource allocation task supported climate policies more strongly than those who did not, suggesting that thinking about potential connections to future people reduces the perceived social distance of future people and increases willingness to bear some costs in the present to benefit people in the future. Finally, although all genders allocated resources between the generations in a similar manner, the authors find that the impact of participating in the intergenerational allocation task on support for climate policies is strongly significant for women and non-binary people, but not for men. The results could have implications for creating effective climate policy communications, according to the authors.  

---

JOURNAL

PNAS Nexus

ARTICLE TITLE

Intergenerational altruism and climate policy preferences

ARTICLE PUBLICATION DATE

2-Apr-2024

 

What are the best Nature-Based Solutions in Spain to adapt to climate change?

A new project aims to identify and catalogue the most effective proposals to better adapt the territory to climate change.

UNIVERSITAT AUTONOMA DE BARCELONA

As a country particularly vulnerable to climate change, Spain faces significant challenges, risks and impacts to which it must adapt both proactively and reactively. The scarcity of water resources, an increase in temperatures, and an increase in the intensity and volume of extreme rainfall events are causing droughts, water shortages, fires, floods and soil erosion, among other problems.

A new ICTA-UAB project titled “Systematization of nature-based solutions in Spain (E:SBN), will carry out a comprehensive identification and compilation of nature-based solutions in Spain, as a reference of good practices for adequate adaptation to climate change in each territory. The project is funded by the Biodiversity Foundation of Spanish Ministry for the Ecological Transition and the Demographic Challenge through the Grants call in competition regime for the execution of projects that contribute to implementing the 2021-2030 National Plan for Adaptation to Climate Change (PNACC).

Climate change affects ecosystems and their biodiversity, as well as human health and well-being. The extent of the impact depends on the degree of vulnerability of natural and agroforestry areas, of people and their urban environment, and on the prevention, adaptation, and resilience capacities of territories.

Strengthening the capacity to adapt to climate change is therefore an urgent task to be addressed in Spain, and Nature-Based Solutions (NBS) must play a prominent role. According to the United Nations (UN; 2022), NBSs are actions to protect, conserve, restore, use, and sustainably manage different types of ecosystems to address social, economic, and environmental challenges in an effective and adaptive manner, while providing benefits to human well-being, ecosystem services, resilience and biodiversity. The use of NBSs is considered one of the key measures to adapt to climate change. However, in Spain there is no system for cataloguing NBSs at the national level, which could be useful for their future applicability at local level.

Therefore, the E:SBN project aims to create a system for identifying, classifying and cataloguing nature-based solutions created in different types of ecosystems in Spain, from parks, green corridors, coastal and wetland restoration to climate refuges, so that their planning and implementation, both in urban and rural areas, can be carried out with a global vision and in a coherent, effective and adapted manner to each territorial reality within the framework of climate action.

To this end, a bibliographic analysis of the state of the art of NBSs at international and national level will be carried out on at least 100 scientific publications, identifying their principles, classification systems, key parameters and impact assessment indicators. Moreover, more than 50 NBS projects will be collected and characterised and 15 of these projects, representative of different territories, different types of hazards and vulnerabilities to climate change, will be analysed in depth as examples of good practice, in order to understand their characteristics, institutional realities and perceptions regarding the use of NBSs and their enablers. All these tools will be validated with key stakeholders to ensure that they meet the needs of the PNACC.

 

Tracking the virus behind India's lumpy skin cattle crisis

INDIAN INSTITUTE OF SCIENCE (IISC)

 

IMAGE: 

RESEARCH SCHOLAR PERFORMING WHOLE GENOME SEQUENCING OF LSDV

view more 

CREDIT: PADMANAIDU CHAITANYA

In May 2022, cattle across India began dying of a mysterious illness. Since then, about 1,00,000 cows have lost their lives to a devastating outbreak of what scientists have identified as lumpy skin disease. The outbreak has severely affected India's agricultural sector, leading to staggering economic losses.

"It was a calamity in some ways … a national emergency," says Utpal Tatu, Professor in the Department of Biochemistry, Indian Institute of Science (IISc).

Tatu is part of a multi-institutional team that decided to probe the cause of the outbreak. Their study, published in BMC Genomics, provides critical insights into the evolution and origins of the virus strains fueling it.

A viral infection caused by the Lumpy Skin Disease Virus (LSDV), the disease is transmitted by insects like flies and mosquitoes. It causes fever and skin nodules, and can be fatal for cattle. LSDV was first found in Zambia in 1931 and remained confined to the Sub-African region until 1989, after which it started spreading to the Middle East, Russia and other southeast European nations, before spreading to South Asia. There have been two major outbreaks of this disease in India, the first in 2019 and a more severe outbreak in 2022, infecting more than two million cows.

To investigate the current outbreak, the team collected skin nodules, blood and nasal swabs from infected cattle in various states, including Gujarat, Maharashtra, Rajasthan and Karnataka, in collaboration with veterinary institutes. They performed advanced whole-genome sequencing of DNA extracted from 22 samples.

"The biggest challenge was the lack of an established LSDV genome sequencing and analysis pipeline. We had to adapt techniques from COVID-19 research," explains Ankeet Kumar, PhD student at IISc and co-lead author. "Data was also limited, so we compiled all available global LSDV genome sequences to make our analysis robust."

Their genomic analysis revealed two distinct LSDV variants circulating in India, one with a low number of genetic variations and another with a high number of genetic variations. The sequence with fewer variations was genetically similar to the 2019 Ranchi and 2020 Hyderabad strains that were sequenced previously. The samples with high variations, however, turned out to be similar to LSDV strains from an outbreak in Russia in 2015. 

Kumar says that there are no previous reports of such highly varied LSDV strains in India. Viruses that have DNA as the genetic material – like LSDV – are generally more stable than RNA viruses. Therefore, finding so many genetic variations was quite surprising, and could explain the severity of the disease, he adds.

The team found a large number of genetic variations – over 1,800. These include deletions and insertions in various genes, single-letter changes in DNA (called SNPs), and genetic variations in regions between genes. Importantly, they found a large number of genetic variations in viral genes critical for binding to host cells, evading immune response, and replicating efficiently. This likely enhanced the virus’s ability to cause disease. "Cattle developed more severe symptoms in areas where we found highly diverse strains. This suggests that the genetic variations could elevate virulence," says Kumar.

Such insights can pave the way for improved diagnostics, vaccines and interventions to combat emerging infectious diseases that threaten livestock and livelihoods. Tatu’s research group has conducted similar studies on COVID-19 during the pandemic, and more recently on the rabies virus.

“The genomic data will prove invaluable for vaccine development by revealing molecular hotspots and genetic variations to target,” notes Tatu. “This is a first for characterising the genomic landscape of LSDV during India's outbreak on a national scale.”

The study represents an example of the One Health approach in which multidisciplinary teams, including molecular biologists, computational experts and veterinary doctors come together to address issues of national relevance. Tatu also emphasises how collaboration between veterinary experts and multiple scientific institutions was critical to tracing the variants across the country. “We learned a lot from the veterinary doctors,” he says. “They understand the field knowledge, and their perception about the disease was very important for us.”

---

JOURNAL

BMC Genomics

DOI

10.1186/s12864-024-10061-3 

ARTICLE TITLE

Unravelling the genomic origins of lumpy skin disease virus in recent outbreaks

 

The math problem that took nearly a century to solve

UC San Diego mathematicians unlock the secret to Ramsey numbers

UNIVERSITY OF CALIFORNIA - SAN DIEGO

 

IMAGE: 

RAMSEY PROBLEMS, SUCH AS R(4,5) ARE SIMPLE TO STATE, BUT AS SHOWN IN THIS GRAPH, THE POSSIBLE SOLUTIONS ARE NEARLY ENDLESS, MAKING THEM VERY DIFFICULT TO SOLVE. 

view more 

CREDIT: JACQUES VERSTRAETE / UC SAN DIEGO

We’ve all been there: staring at a math test with a problem that seems impossible to solve. What if finding the solution to a problem took almost a century? For mathematicians who dabble in Ramsey theory, this is very much the case. In fact, little progress had been made in solving Ramsey problems since the 1930s.

Now, University of California San Diego researchers Jacques Verstraete and Sam Mattheus have found the answer to r(4,t), a longstanding Ramsey problem that has perplexed the math world for decades.

What was Ramsey’s problem, anyway?

In mathematical parlance, a graph is a series of points and the lines in between those points. Ramsey theory suggests that if the graph is large enough, you’re guaranteed to find some kind of order within it — either a set of points with no lines between them or a set of points with all possible lines between them (these sets are called “cliques”). This is written as r(s,t) where s are the points with lines and t are the points without lines.

To those of us who don’t deal in graph theory, the most well-known Ramsey problem, r(3,3), is sometimes called “the theorem on friends and strangers” and is explained by way of a party: in a group of six people, you will find at least three people who all know each other or three people who all don’t know each other. The answer to r(3,3) is six.

“It’s a fact of nature, an absolute truth,” Verstraete states. “It doesn't matter what the situation is or which six people you pick — you will find three people who all know each other or three people who all don't know each other. You may be able to find more, but you are guaranteed that there will be at least three in one clique or the other.”

What happened after mathematicians found that r(3,3) = 6? Naturally, they wanted to know r(4,4), r(5,5), and r(4,t) where the number of points that are not connected is variable. The solution to r(4,4) is 18 and is proved using a theorem created by Paul Erdös and George Szekeres in the 1930s.

Currently r(5,5) is still unknown.

A good problem fights back

Why is something so simple to state so hard to solve? It turns out to be more complicated than it appears. Let’s say you knew the solution to r(5,5) was somewhere between 40-50. If you started with 45 points, there would be more than 10234 graphs to consider!

“Because these numbers are so notoriously difficult to find, mathematicians look for estimations,” Verstraete explained. “This is what Sam and I have achieved in our recent work. How do we find not the exact answer, but the best estimates for what these Ramsey numbers might be?”

Math students learn about Ramsey problems early on, so r(4,t) has been on Verstraete’s radar for most of his professional career. In fact, he first saw the problem in print in Erdös on Graphs: His Legacy of Unsolved Problems, written by two UC San Diego professors, Fan Chung and the late Ron Graham. The problem is a conjecture from Erdös, who offered $250 to the first person who could solve it.

“Many people have thought about r(4,t) — it’s been an open problem for over 90 years,” Verstraete said. “But it wasn’t something that was at the forefront of my research. Everybody knows it's hard and everyone’s tried to figure it out, so unless you have a new idea, you’re not likely to get anywhere.”

Then about four years ago, Verstraete was working on a different Ramsey problem with a mathematician at the University of Illinois-Chicago, Dhruv Mubayi. Together they discovered that pseudorandom graphs could advance the current knowledge on these old problems.

In 1937, Erdös discovered that using random graphs could give good lower bounds on Ramsey problems. What Verstraete and Mubayi discovered was that sampling from pseudorandom graphs frequently gives better bounds on Ramsey numbers than random graphs. These bounds — upper and lower limits on the possible answer — tightened the range of estimations they could make. In other words, they were getting closer to the truth.

In 2019, to the delight of the math world, Verstraete and Mubayi used pseudorandom graphs to solve r(3,t). However, Verstraete struggled to build a pseudorandom graph that could help solve r(4,t).

He began pulling in different areas of math outside of combinatorics, including finite geometry, algebra and probability. Eventually he joined forces with Mattheus, a postdoctoral scholar in his group whose background was in finite geometry. 

“It turned out that the pseudorandom graph we needed could be found in finite geometry,” Verstraete stated. “Sam was the perfect person to come along and help build what we needed.”

Once they had the pseudorandom graph in place, they still had to puzzle out several pieces of math. It took almost a year, but eventually they realized they had a solution: r(4,t) is close to a cubic function of t. If you want a party where there will always be four people who all know each other or t people who all don’t know each other, you will need roughly t3 people present. There is a small asterisk (actually an o) because, remember, this is an estimate, not an exact answer. But t3 is very close to the exact answer.

The findings are currently under review with the Annals of Mathematics. 

“It really did take us years to solve,” Verstraete stated. “And there were many times where we were stuck and wondered if we’d be able to solve it at all. But one should never give up, no matter how long it takes.”

Verstraete emphasizes the importance of perseverance — something he reminds his students of often. “If you find that the problem is hard and you're stuck, that means it's a good problem. Fan Chung said a good problem fights back. You can't expect it just to reveal itself.”

Verstraete knows such dogged determination is well-rewarded: “I got a call from Fan saying she owes me $250.”

---

JOURNAL

Annals of Mathematics

DOI

10.4007/annals.2024.199.2.8 

METHOD OF RESEARCH

Experimental study

ARTICLE TITLE

The asymptotics of r(4,t)

ARTICLE PUBLICATION DATE

5-Apr-2024