How Shannon’s Information Theory and Edward O. Wilson’s Ecological Vision Highlight the Importance of a Balanced Species Abundance

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“Nature is our most precious archive of evolutionary information. To destroy it is to burn a unique library, written over 4 billion years of trial and error.” Edward O. Wilson

Maurício Veloso Brant Pinheiro

1. Introduction: When Counting Species Is Not Enough

For a long time, measuring biodiversity was almost an arithmetic exercise: counting how many different species inhabit an area and using that number as an indicator of its natural wealth. The assumption was that the more species, the greater the biodiversity — and, therefore, the healthier and more resilient the ecosystem would be. This logic, though intuitive, has proven insufficient in the face of nature’s real complexities. In many biologically rich regions, entire systems collapse even with a high species count. What, then, explains the difference between forests that withstand fires, pests, and droughts, and others that quickly succumb to similar disturbances?

The answer, increasingly clear to ecologists, lies less in the number of species and more in how they are distributed among themselves. It is not enough to have many species if almost the entire population is concentrated in just one or two. What matters is evenness — the degree of balance in the relative abundance of the species that make up an ecosystem. A system with high evenness not only harbors a variety of life forms but allows these forms to coexist and interact functionally. It is this quiet balance that sustains food chains, regulates biogeochemical cycles, and keeps ecosystems alive in the face of the unexpected.

Interestingly, this ecological principle has a precise mathematical parallel: Information Theory, formulated by Claude Shannon in 1948. Created to solve communication problems in telegraph systems, the theory proposed that the amount of information in a message depends on its unpredictability. The more unexpected the content, the more information it carries. This same logic applies to nature: an ecosystem where each encounter with a species is a surprise carries more “ecological information” — and with it, more complexity and greater adaptive capacity.

This text explores this surprising confluence between mathematics and ecology. We will see how evenness can be measured using formulas originally devised for engineering, why this matters for the resilience of living systems, and how examples from nature — from coral reefs to soybean fields, from tropical forests to urban landscapes — reveal, in practice, the distributed intelligence of life. At the crossroads of butterflies, bits, and biodiversity, we find not just a more precise way to measure the living world, but also a deeper way to understand it.

2. When Information Became Ecology

Information theory was born far from forests and reefs, among the cables and circuits of engineering. In 1948, Claude Elwood Shannon, a young mathematician and engineer at Bell Labs, published a technical paper with a dry title — A Mathematical Theory of Communication — which ended up launching a revolution. In it, Shannon defined the fundamental principles of how messages can be encoded, transmitted, and decoded even in noisy environments. To do this, he needed a way to measure the unpredictability of a signal. This is how the concept of informational entropy emerged: the more uncertain a message, the more bits it carries.

In the following decades, the impact of the theory was explosive: from digital file compression to cryptography, from telecommunications to molecular biology. But one of its most fruitful applications would come from an unlikely field: Ecology.

In the 1960s, the Spaniard Ramon Margalef, one of the pioneers of theoretical ecology, realized that entropy could serve as a rigorous metric for biological diversity. After all, an ecosystem is also an information system: it contains units (individuals), categories (species), and a statistical distribution among them. Measuring this distribution, then, could reveal how much information — and therefore how much organized life — exists in a given natural environment.

This idea would gain momentum with the work of Edward O. Wilson, who saw biodiversity not merely as a catalog of species, but as a dynamic network of interdependent relationships. In The Diversity of Life (1992), Wilson describes biological complexity as the result of millions of accumulated evolutionary interactions — and points to evenness as one of the pillars of that complexity. The convergence between Shannon’s mathematics and Wilson’s ecology, therefore, is not an interdisciplinary curiosity: it is a powerful lens through which to see nature as an adaptive system that stores and processes information in order to stay alive.

3. Shannon’s Formula Applied to Biodiversity

The seminal equation of Shannon’s Information Theory is expressed as:

\[ H = – \sum_{i=1}^{S} p_i \log_2 p_i \]

In this formula, H represents the informational entropy — that is, the average amount of information per transmitted symbol. The summation runs over S possible categories (in the original case, the symbols or signals of a message; in ecology, the species). The term pᵢ is the probability of occurrence of each category — or, more concretely in ecology, the proportion of individuals of a given species relative to the total. The negative sign ensures the result is positive, since the logarithms of numbers smaller than 1 are negative. And the base 2 of the logarithm converts the unit of entropy into bits, the smallest measurable unit of information.

The beauty of this equation lies in its capacity for generalization. Although conceived to measure uncertainty in electronic messages, the formula adapts perfectly to any system where there is a statistical distribution among categories — including living systems. It was precisely this insight that led ecologists such as Ramon Margalef and later Edward O. Wilson to apply Shannon’s entropy to biodiversity: if each species in an ecosystem is seen as a “symbol” and individuals as occurrences, then a biologically balanced environment behaves like a message rich in information.

An analogy helps to better visualize this concept. Imagine two DNA sequences, composed of nucleotides:

The first, “AAAAAAAAAA,” repeats the same letter ten times, forming a highly predictable sequence.

The second, “AGCTTAGGCA,” combines different letters in more balanced proportions, indicating greater diversity and thus greater informational complexity.

The first sequence is completely predictable, repeating the same letter ten times without any variation. From the perspective of information theory, it carries zero bits of entropy: no surprise, only redundancy. The second sequence, on the other hand, exhibits a more balanced distribution of different letters, making each new symbol a small uncertainty. Its entropy value, approximately 1.97 bits, according to Shannon’s equation, reflects this unpredictability and reveals a much richer informational content.

More than a mathematical curiosity, this measure offers an objective way to compare different ecosystems and to predict their behavior in the face of disturbances. Ecosystems with high entropy are like distributed information systems: if one channel fails, others take over its function. Environments with low entropy, by contrast, are fragile like centralized systems — a single failure is enough to make everything collapse.

4. The Butterfly Experiment and the Surprise of Evenness

It was Edward O. Wilson who, with his characteristic didactic clarity, proposed a simple — almost playful — way to visualize the importance of evenness. In The Diversity of Life (1992), Wilson invites the reader to imagine themselves in a tropical forest, with an entomologist’s net in hand, catching butterflies. In two distinct scenarios, the total number of butterflies is the same: one million. And the number of species is also identical: one hundred. What changes radically is the distribution of these species.

In the first scenario, a single species dominates the environment with 990,000 individuals, while the remaining 99 species are squeezed into the statistical margins, together accounting for only 10,000 butterflies. The apparent diversity — one hundred species — is deceiving. The unpredictability is minimal. The entropy, calculated by Shannon’s formula, barely reaches 0.15 bits. If you catch a butterfly at random, the chances are overwhelmingly high that it belongs to the dominant species. There is little surprise, little functional diversity. It is a vulnerable, predictable system, exposed to the risk of collapse.

In the second scenario, the same one hundred species are present, but now with a perfectly balanced distribution: 10,000 individuals for each. The richness is the same, but the evenness is radically different. With each individual captured, the outcome is uncertain — it could be any of the hundred species. This unpredictability translates into an entropy value of 6.64 bits, almost at the theoretical limit for that number of categories. Here, diversity is not merely aesthetic or symbolic: it is measurable, functional, and, above all, resilient.

To understand how ecological balance manifests in nature, one only needs to observe the workings of a coral reef. In the Coral Triangle, located in the western Pacific, one of the most biodiverse marine regions on the planet, each species plays a fundamental ecological role and interacts harmoniously with the others. Parrotfish, such as Scarus niger, scrape algae growing on the corals; if these algae are not controlled, they can suffocate the reefs and hinder coral growth. The corals themselves — notably of the genus Acropora — host symbiotic microalgae of the group Symbiodinium, which perform photosynthesis and provide most of the energy required to sustain the system. Sea urchins, such as Diadema setosum, clean the substrate, helping to maintain chemical balance and prevent the excessive buildup of organic matter. None of these species completely dominates the environment. In ecological simulation models, these environments reach entropy values close to 5 bits, indicating a rich, dynamic, and highly functional ecological network. This functional diversity ensures resilience: in the face of disturbances such as storms, bleaching, or disease outbreaks, other species can temporarily take on critical ecological functions, ensuring the continuity and recovery of the ecosystem.

The opposite of a biodiverse ecosystem can be seen in the vast soybean monocultures of Brazil’s Cerrado. In these highly mechanized systems, virtually all the vegetation cover consists of a single species: soybean (Glycine max). This extreme homogeneity quickly impoverishes the soil, requiring the constant use of fertilizers and chemical amendments. Moreover, it creates an ideal environment for specialized pests, such as the soybean caterpillar (Anticarsia gemmatalis) and the brown stink bug (Euschistus heros), which encounter little or no ecological resistance there.

The uniformity of biomass also favors intense and fast-spreading fires. In such simplified ecosystems, the loss of the dominant species — whether due to market collapse, pests, or climate change — can lead to the functional failure of the entire agroecosystem, owing to the absence of species that perform complementary ecological roles.

If we estimate Shannon’s entropy (H) in this type of monoculture, the value approaches 0 bits, since nearly 100% of the biomass belongs to a single species. This value represents the maximum degree of predictability: the system is entirely dominated by a single type of organism. For comparison, in eucalyptus monocultures the situation is similar. With about 95% of the biomass concentrated in just one species, entropy drops drastically, hovering around 0.35 bits.

Both cases illustrate predictable, repetitive, and vulnerable ecosystems, with no room for ecological substitution or buffering of impacts. The loss of the dominant species — due to fire, pest outbreak, or drought — results in the near-immediate collapse of the entire biological structure.

Even in urban centers, evenness — or its absence — has concrete effects. In large cities, a few generalist species, such as pigeons and sparrows, dominate the scene, while more specialized birds disappear with the loss of green spaces and native trees. This ecological impoverishment undermines important processes such as plant pollination and seed dispersal, directly affecting air quality, ambient temperature, and the health of urban forests themselves.

In urban forests, although there is still some plant and animal diversity, evenness is also low. In São Paulo, for example, studies show that pigeons and sparrows make up more than 80% of the bird population. This is reflected in intermediate entropy values — higher than those of monocultures, but far below those of natural ecosystems. The ecological function of these birds, adaptable as it may be, does not replace the roles of missing pollinating, frugivorous, or dispersing species, such as tanagers or toucans. The simplified urban system is resilient up to a point but loses ecological efficiency as it moves away from its original balance.

Even in urban centers, evenness — or the lack of it — has tangible ecological impacts. In large cities such as São Paulo, a few generalist species dominate the scene. Pigeons (Columba livia) and sparrows (Passer domesticus), for example, account for more than 80% of the urban bird population, while specialized species vanish with the loss of green areas and native trees. Assuming pigeons and sparrows together comprise 80% of the population and the remaining 20% are evenly distributed among four other species (5% each), the estimated entropy would be 1.72 bits. This value is considerably higher than in monocultures (close to 0 bits), but still far from what is observed in balanced natural ecosystems, where entropy can exceed 2.5 bits.

This impoverishment compromises essential functions such as pollination, seed dispersal, and biological control, affecting air quality, the microclimate, and the resilience of urban forests. Although some biological diversity still exists, low evenness reduces the ecological efficiency of the system. Shannon’s entropy (H) in this context reflects this imbalance. The urban system, therefore, retains some resilience, but with reduced ecological functionality.

These mathematical analyses are not merely abstractions. They reveal profound patterns of ecological functioning. A system with high evenness offers more possibilities for interaction, more alternative pathways for energy flow, and greater resistance in the face of the unexpected. Life, after all, is a code in constant transformation — and its internal organization can be read, understood, and preserved with the help of mathematics as well.

5. Resilience: When Diversity Becomes Ecological Insurance

Evenness, often underestimated, is not merely a whim of nature — it effectively functions as an ecological insurance policy against crises and systemic collapses. Its importance becomes evident when we examine historical and contemporary examples in which the absence or restoration of diversity had profound impacts on the resilience of living systems.

One of the most tragic and illuminating cases occurred in Ireland between 1845 and 1849, during the episode known as the Great Famine. At that time, much of the population depended almost exclusively on a single variety of potato, the Lumper, for subsistence. This reliance on a single, genetically uniform crop — with extremely low entropy — left the country vulnerable to any disturbance. When the fungus Phytophthora infestans spread through the fields, there was no genetic resistance to stop the infestation. The result was devastating: approximately 99% of the crop was lost, more than a million people died of starvation, and around two million emigrated in a forced exodus. This human tragedy cruelly revealed the danger of homogeneous agricultural systems, which offer no margin of adaptability in the face of external threats.

On the other hand, the reintroduction of wolves (Canis lupus) in Yellowstone National Park, in the United States, in 1995 demonstrated the regenerative power of ecological diversity. After seven decades of absence, wolves were reintroduced into the ecosystem, triggering a trophic cascade that completely transformed the landscape. The reduction of the overabundant deer population allowed vegetation — especially willows — to regenerate, stabilizing riverbanks through strengthened root systems. This new plant structure brought back beavers, waterfowl, and a host of other organisms, reestablishing lost connections in the web of life. The degraded landscape gave way to a more balanced system, with greater functional and trophic evenness, showing how diversity can reorganize and strengthen complex ecological networks.

An even more recent and forward-looking example comes from southern Bahia, where the Swiss farmer Ernst Götsch developed an innovative approach known as syntropic agriculture. Inspired by the logic of tropical forests, Götsch created agroforestry systems in which agricultural species like cacao and coffee grow side by side with fruit trees such as mango and jamelão. In this arrangement, the diversity of plants, heights, and life cycles promotes a continuous cycling of nutrients, enriching the soil without the need for fertilizers or chemical pesticides. Moreover, the high heterogeneity of the system prevents pests from becoming dominant, as the abundance of niches reduces the likelihood of imbalances. The result is remarkable: sustainable agricultural productivity combined with a biological entropy comparable to that of natural ecosystems.

These three examples, so distinct in time and space, point to the same conclusion: evenness — understood here as the balanced distribution of functions, genes, or species — is a central element of ecological resilience. Where there is diversity, there are alternatives. And where there are alternatives, there is a future.

6. Metaphors and Machines: Explaining Ecology with Images, Data, and Artificial Intelligence

Ecological complexity often escapes immediate perception. To better understand it, we can make use of visual metaphors and analogies with technology. A biodiverse ecosystem, for example, resembles a vast living library, where each species represents a unique book, the result of millions of years of natural selection. Diversity ensures not just aesthetic richness but ecological functionality. A monoculture, on the other hand, resembles a corrupted digital file: there are thousands of copies of the same content, and a single error — such as a pest or a sudden climate change — can compromise the entire system. Resilience disappears when redundancy is merely superficial.

Similarly, we can imagine biodiversity as an ecological Wi-Fi network. In a network with many devices and communication channels, if one connection fails, others take over without loss of signal. But in a homogeneous system, where everything depends on a single channel, any interference undermines stability. This comparison helps explain why evenness — that is, the balanced distribution among species — is essential for the flows of energy, matter, and information to move freely between the components of the ecosystem.

In recent years, technology — especially artificial intelligence — has become a powerful ally of ecology. Machine learning tools are revolutionizing the way we monitor and understand life on the planet. A notable example is the use of algorithms such as MaxEnt (Maximum Entropy Modeling), which allow scientists to predict species distributions based on environmental and geographic occurrence data. This modeling has been used to map the impacts of climate change and design connectivity strategies between forest fragments, creating more effective ecological corridors for endangered species.

Another important innovation is environmental DNA (eDNA), a technique that identifies organisms through genetic fragments found in soil, water, or even air. The BioSCAN project in Los Angeles used this approach combined with neural networks to detect more than a thousand arthropod species in urban areas, about 30% of which were previously unknown to science. This demonstrates how AI can assist in mapping invisible biodiversity — that which escapes traditional observation methods.

However, while we advance technologically, human activity continues to drastically reduce the complexity of ecosystems, in a process that can be compared to data compression — but in this case, with irreversible losses. In the Amazon, for example, between 2000 and 2020, about 20% of the forest was converted to pasture. This transformation led to a sharp drop in ecological entropy, estimated from approximately 6 bits — in intact forest areas — to around 1.5 bits in single-species pastures. What is lost in this case is not just trees, but the ecological services that sustain life: climate regulation, pollination, soil fertility, and the water cycle itself.

Even in landscapes dominated by concrete and asphalt, the signs of this biological compression are visible. In cities, ecological networks become simplified, favoring generalist species such as pigeons, rats, and cockroaches, which occupy the niches left by specialist organisms. In Paris, studies on urban bats of the species Pipistrellus kuhlii showed that they adapted their hunting habits to public lighting, which altered the structure of nocturnal trophic networks. This kind of imbalance shows how evenness is eroded even in highly anthropized environments.

The use of technologies such as remote sensors, cameras with embedded artificial intelligence, predictive models, and big data analysis indeed offers a new light at the end of the tunnel for biodiversity conservation. This combination of technological advances and ecological science is allowing us not only to observe the damage more clearly and in real time, but also to anticipate threats, prevent impacts, and, in some cases, even reverse them before they become irreversible.

Conservation projects around the world are already making use of these technologies. Camera traps with computer vision systems can automatically recognize endangered or invasive species, speeding up diagnostics and facilitating data collection on forest populations. A remarkable example comes from the University of Tasmania, which uses AI-powered cameras to monitor Tasmanian devils (Sarcophilus harrisii), detecting signs of facial tumors with unprecedented accuracy.

Another emblematic case is the Conservation AI project, which applies deep neural networks to analyze images from fixed cameras and drones, identifying wildlife, illegal hunters, or habitat changes with greater efficiency than traditional methods. These tools have already been successfully deployed in nature parks in Africa, Europe, and Asia, providing a new layer of protection against biodiversity loss.

Drones equipped with multispectral cameras and thermal sensors, combined with machine learning algorithms, are being used by organizations such as Smart Parks and Conservation Drones for aerial patrols, identification of fire outbreaks, and vegetation mapping in remote areas. Brazil, for example, already has conservation units using these technologies to detect illegal deforestation with high precision — and more quickly than by human monitoring.

From space, satellites powered by artificial intelligence help map the advance of agricultural frontiers, the loss of vegetation cover, and habitat fragmentation. The use of these images in predictive models, such as MaxEnt, makes it possible to create future scenarios of species distribution under different temperature and humidity regimes — an essential tool for planning protected areas and ecological corridors.

As biologist Thomas Lovejoy, known as the “Godfather of Biodiversity”, succinctly put it, “Biodiversity is the infrastructure that supports all life on Earth.” This statement becomes even more relevant in light of the new technological tools: we now have at our disposal not just data and sensors, but true ecological prediction machines. The challenge is ethical and political: to know how to use them with wisdom, responsibility, and a sense of urgency.

8. Conclusion: Evenness in the Age of Crises

The warning issued by the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services (IPBES, 2019) is unequivocal: about one million species are at risk of extinction, many of them before even being known to science. In this scenario, conserving isolated species is no longer enough. True ecological resilience lies in preserving the living structure of ecosystems — and this includes not just diversity, but the evenness with which that diversity is distributed.

Evenness is more than a matter of numbers: it is a metric of functional balance. An ecosystem where a few species dominate, even if still rich in variety, loses its ability to self-regulate, to withstand disturbances, and to sustain essential ecological services. Protecting this invisible dimension of biodiversity requires urgent and integrated action on multiple fronts, engaging both environmental conservation and the broader global sustainability goals.

The Sustainable Development Goals (SDGs) are a global UN agenda made up of 17 interconnected targets aimed at eradicating poverty, protecting the environment, and ensuring peace and prosperity for all people by 2030. The connection with the SDGs is clear. SDG 2 (Zero Hunger) directly depends on diverse pollinators, on which 75% of global crops are functionally reliant. SDG 13 (Climate Action), in turn, benefits from structurally complex forests: areas with greater evenness can sequester up to 30% more carbon than monocultures, as well as maintain stable microclimates and better withstand extreme events.

To tackle this crisis effectively, some concrete directions can be outlined. It is crucial to incorporate metrics such as the Shannon and Simpson indices — which measure diversity and evenness in informational terms — into public policies on land use, environmental licensing, and agricultural zoning. It is also urgent to promote agroecological practices that prioritize functional diversity, such as agroforestry systems and syntropic agriculture, which combine productivity with ecological regeneration. Finally, the creation of protected areas should consider not just the number of species present, but their ecological connectivity — that is, the ability to maintain flows of energy and information between different fragments of the landscape.

In a world where environmental, climatic, and social crises are intertwined, thinking about biodiversity is thinking about vital infrastructure. And within that infrastructure, evenness is a key element. Without it, there is no balance, no adaptation — and therefore, no future.

References

• Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal.
• Wilson, E. O. (1992). A Diversidade da Vida. Companhia das Letras.
• IPBES (2019). Relatório Global sobre Biodiversidade e Serviços Ecossistêmicos.
• Margalef, R. (1968). Perspectives in Ecological Theory. University of Chicago Press.
• Gaston, K. J. (2000). Global patterns in biodiversity. Nature.

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