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Dark diversity helped solve Darwin’s 160-year-old puzzle | University of Tartu

A paper recently published in Proceedings of the National Academy of Sciences of the USA (PNAS) by an international team that included researchers from the University of Tartu, Estonia, offers a solution to a conundrum in evolutionary ecology first identified by Charles Darwin more than 160 years ago: Darwin’s naturalisation conundrum.

The problem concerns why some introduced species successfully establish themselves in a new environment while others fail. Darwin recognised two apparently contradictory possibilities, both of which make sense in evolutionary terms. On the one hand, a newcomer closely related to local species might succeed because its relatives show that the environment is suitable for that general way of life. In other words, similarity to the local community could be a sign of pre-adaptation. On the other hand, a newcomer might be more successful if it is unlike the resident species, because it avoids direct competition and exploits resources the local community is not already using.

So which is it? Should a successful immigrant species resemble the local species, or should it be different from them? That is Darwin’s naturalisation conundrum.

These are the sorts of paradoxes science thrives on because they expose a gap in understanding and invite investigation. They are not waved aside as mysteries, nor protected from scrutiny by declaring them ineffable. They are problems to be solved by evidence.

That is in stark contrast to religion, where glaring contradictions are often preserved rather than resolved. Christianity, for example, asks its followers to believe simultaneously in an omniscient god and in human free will. Yet the contradiction can be exposed with a simple question: if God has always known that you will eat fish for dinner tomorrow, can you choose steak instead? If yes, then God did not know after all; if no, then you were never free to choose. Either answer undermines a central plank of Christian theology, because without free will there can be no meaningful original sin, no need for salvation, and no coherent reason for the Jesus story.

Another awkward question is why an omniscient god supposedly waited until about 2,000 years ago to arrange the sacrifice of Jesus as the mechanism for saving humanity. If this god had always known that a blood sacrifice would be needed, why wait through countless generations of human suffering before arranging it? Why not solve the alleged problem at the beginning? Did God simply stand by while millions died without that supposed salvation, or did it merely take until the first or second century CE for priests to invent a theological explanation for the Jesus story?

And so the list goes on. Can an omnipotent god create an object too heavy for it to lift? Can God lie? If God claims to be omniscient, how can it know that there is nothing it does not know? And if it is aware of not knowing something, then it is not omniscient. Such questions are usually met not with answers but with evasion, because religions have no neutral referee. They have only opinion, assertion and authority.

Science is different because evidence can arbitrate between competing explanations. This is why science tends to converge on a single answer while religions fragment into sects, denominations and, sometimes, mutually hostile factions.

In the case of Darwin’s naturalisation conundrum, the team, including Wen-gang Zhang and Professor of Botany Meelis Pärtel of the University of Tartu, examined the evidence in the form of a remarkable 340-year dataset from Swedish lakes, recording both successful and unsuccessful fish introductions. This allowed the researchers to test, with unusual precision, what determines whether an introduced species establishes itself.

The key concept is “dark diversity”. This does not mean some mysterious or hidden force. It refers to the species that are absent from a particular local community even though, in principle, they could live there because the environmental conditions are suitable and they belong to the wider regional species pool. In simple terms, dark diversity is the missing part of a community: the species that could be there, but are not.

Add those absent-but-possible species to the species already present, and you have the potential species pool for that site. “Community completeness” then measures how much of that potential has actually been realised: what proportion of all the species that could live there are already present.

With those concepts, the apparent contradiction begins to disappear. In lakes suitable for relatively few species, where most of the possible species were already present, introduced fish closely related to local species were more likely to succeed. In those cases, similarity to the resident community was a sign that the newcomer was suited to the local conditions. But in lakes with a larger potential species pool and lower community completeness, more distantly related species were more likely to establish, presumably because there was more ecological opportunity and less direct competition for the same resources.

So the answer is not that Darwin was wrong in one of his two predictions. The answer is that both can be right, depending on the ecological context. The important factor is not merely how many species are already present, but how complete the local community is relative to the number of species that could potentially live there. It is a tribute to Darwin and his intellectual honesty that he looked for and published possible paradoxes that his theory could produce and admitted that they remained unresolved.

Some Unresolved Theological Paradoxes. Religions often contain contradictions or paradoxes that are not resolved by evidence but protected by doctrine, mystery, tradition or authority. Believers may offer apologetic answers to them, but these answers are rarely testable and are often mutually incompatible.

The problem of evil
If God is omnipotent, omniscient and perfectly good, why is there apparently pointless suffering? If God cannot prevent it, he is not omnipotent. If he does not know about it, he is not omniscient. If he knows and can prevent it but chooses not to, he is not perfectly good.

The problem of natural evil
Free will is often invoked to explain human cruelty, but it does not explain earthquakes, childhood cancers, parasites, tsunamis, birth defects, droughts, pandemics or the suffering of animals that lived and died long before humans existed. These cannot plausibly be blamed on human choice.

The Euthyphro dilemma
Is something good because God commands it, or does God command it because it is good? If it is good only because God commands it, morality becomes arbitrary. If God commands it because it is already good, then morality exists independently of God.

Divine hiddenness
If God wants humans to know him, worship him and be saved, why does he remain indistinguishable from a god who does not exist? A perfectly loving god could make his existence clear without removing human freedom, just as the existence of other people is clear without forcing us to love them.

Prayer and omniscience
If God already knows what is best and has a perfect plan, what is prayer supposed to achieve? If prayer changes God’s mind, then the original plan was not perfect. If it does not change anything, petitionary prayer appears pointless.

Divine immutability and intervention
Classical theology often claims that God is unchanging. Yet the same religion usually claims that God acts in history, responds to prayer, becomes angry, forgives, punishes, regrets, commands and intervenes. An unchanging being cannot meaningfully change its actions, intentions or emotional state.

Justice and mercy
Perfect justice requires that wrongdoing receives its due consequence. Perfect mercy requires that the consequence is withheld or reduced. A god who is perfectly just and perfectly merciful appears to be required to do two contradictory things at once.

Infinite punishment for finite offences
The doctrine of eternal punishment raises a moral contradiction. How can a finite human life, with finite errors committed under conditions of ignorance, fear, culture and biology, justly merit infinite punishment?

Original sin and inherited guilt
Christianity often claims that humans inherit the consequences, and sometimes the guilt, of Adam’s sin. But punishing descendants for the actions of an ancestor is normally regarded as unjust. It is especially difficult to reconcile with the claim that God is perfectly just.

Substitutionary atonement
The idea that Jesus had to die so that God could forgive humanity raises another contradiction. A just judge does not punish an innocent person instead of the guilty, and an omnipotent god should be able to forgive without requiring a blood sacrifice.

The Trinity
Christianity claims that the Father is God, the Son is God and the Holy Spirit is God, yet there is only one God and the three are not identical to one another. This is usually declared a mystery rather than explained in coherent terms.

The incarnation
Jesus is said to be fully God and fully human. But God is normally defined as omniscient, omnipotent, eternal and immortal, while humans are limited, ignorant, mortal and finite. Combining both sets of properties in one person produces unresolved logical tension.

Scriptural inerrancy and biblical disagreement
Many believers claim that scripture is divinely inspired or inerrant, yet sacred texts contain conflicting accounts, failed expectations, moral changes, historical problems and mutually incompatible theological claims. The contradiction is usually managed by selective interpretation.

God’s plan and human responsibility
If everything happens according to God’s plan, then evil acts also form part of that plan. But if people are morally responsible for carrying out actions God planned in advance, responsibility becomes confused. Are humans disobeying God, or fulfilling the script he wrote for them?

Miracles and divine consistency
Miracles are said to be signs of divine power, yet they also imply that God sometimes suspends or overrides the natural order he supposedly created. If the original design was perfect, why would it need occasional correction?

Unlike scientific paradoxes, which can be investigated by comparing competing explanations with evidence, theological paradoxes have no neutral method of resolution. They persist because they are protected by faith, authority and tradition rather than exposed to the corrective discipline of evidence.

The paper in PNAS was accompanied by a news item from the University of Tartu:

Dark diversity helped solve Darwin’s 160-year-old puzzle
Led by a visiting doctoral student at the University of Tartu, a solution was found for assessing which species can survive in a new habitat.

Credit: Tobias Baur / Pexels

An international research team, which included University of Tartu visiting doctoral student Wen-Gang Zhang and Professor of Botany Meelis Pärtel, has found a new solution to one of ecology’s long-standing controversies —Darwin’s naturalization conundrum, which addresses the question of why some species successfully establish in a new habitat while others do not.

In the 19th century, Charles Darwin proposed two opposing predictions. According to one, a species arriving in a new environment has a greater chance of surviving if it is closely related to local species and thus has similar environmental requirements. According to the other, species with more distant kinship should actually be more successful, as they utilize different resources and do not compete as intensely with local species. Ecologists have debated for more than 160 years when does one explanation apply and when the other.

Now, researchers have found that the answer to Darwin’s conundrum lies in dark diversity, a term which refers to species that could potentially inhabit a given location but do not actually occur there. Together with the present species, dark diversity constitutes the species pool of the study area—in other words, all species for which the habitat conditions are, in principle, suitable. It also allows for an assessment of community completeness, which indicates what proportion of the potential species pool the ecosystem under study actually contains.

The study utilized an exceptionally rich model system: a 340-year dataset from Swedish lakes, which includes both successful and unsuccessful fish introductions. Such data allow for the study, with rare precision, of the factors that determine whether species successfully establish.

The results showed that in lakes that were suitable for fewer species but where a larger proportion of the species that could live there were actually present, those species similar to local species proved more successful. In lakes that were suitable habitats for more species, but where a smaller proportion of those species were actually present, however, species that utilized resources different from those of the local species proved to be more successful.

Thus, the solution to Darwin’s paradox depends on how many species could theoretically live in the region and what proportion of them actually occur there. Importantly, the mere number of present species did not reveal such relationships, but rather, it was the species pool and community completeness, as assessed using dark diversity, that proved decisive.

The study showed that dark diversity offers a new theoretical framework for understanding species distribution and community formation. This helps reconcile previously conflicting results and improve predictions about which species will be able to establish under new conditions. As climate change, shifts in species ranges, and human activity increasingly shape the world’s biodiversity, dark diversity offers a new way to assess how ecosystems respond to these changes. This can help better guide conservation efforts and predict changes in biodiversity in a rapidly changing world.

Publication:
W. Zhang, M. Xu, S. Fan, J.A. Bennett, R.N. Cuthbert, J.T.A. Dick, M. Pärtel, & S. Li
Dark diversity framework reconciles Darwin’s naturalization conundrum for freshwater fish invasions
Proc. Natl. Acad. Sci. U.S.A. 123 (24) e2604929123, https://doi.org/10.1073/pnas.2604929123 (2026).

Significance
Predicting which exotic species will establish in new environments is a central challenge for invasion ecology. Since Darwin first posed his naturalization conundrum, ecologists have long debated whether exotic species similar or dissimilar to the native species are more likely to succeed. We argue that resolving this debate may require considering dark diversity, which comprehensively captures species pool size and community completeness. By incorporating this overlooked dimension, we showed smaller species pools and higher community completeness favor the establishment of exotic fishes closely related to native fishes in the Swedish lakes, whereas larger species pools and lower community completeness favor distant exotics. This dark diversity framework reframes Darwin’s conundrum and provides a practical tool for forecasting invasions and guiding conservation.

Abstract
The spread of invasive species poses a major threat to global biodiversity, yet predicting successful establishment of exotic species in novel environments remains challenging. Darwin’s naturalization conundrum is a longstanding debate over whether exotic species closely or distantly related to native communities are more likely to succeed. Despite its long history, empirical studies continue to yield conflicting evidence. Here, we introduce the dark diversity concept, which refers to species that could theoretically inhabit a site but are currently absent. Combined with observed diversity, dark diversity integrates information on the potential diversity (site-specific species pool size) of the resident community and how completely that pool is locally present (community completeness). Analyzing a 340-y record of successful and failed fish introductions across 516 Swedish lakes, we showed that the effect of phylogenetic relatedness on invasion outcome depends on dark diversity context. Exotics closely related to resident species were more likely to establish in communities with smaller species pools and higher completeness, whereas phylogenetically distant exotic species were more successful in communities with larger species pools and lower completeness. Models with observed species richness obtained considerably less support. Thus, integrating the dark diversity framework clarifies the contrasting effects of phylogenetic relatedness on invasion outcomes, and helps reconcile this 160-y-old conundrum.

W. Zhang, M. Xu, S. Fan, J.A. Bennett, R.N. Cuthbert, J.T.A. Dick, M. Pärtel, & S. Li
Dark diversity framework reconciles Darwin’s naturalization conundrum for freshwater fish invasions
Proc. Natl. Acad. Sci. U.S.A. 123 (24) e2604929123, https://doi.org/10.1073/pnas.2604929123 (2026).

© 2026 National Academy of Sciences of the USA.
Reprinted under the terms of s60 of the Copyright, Designs and Patents Act 1988.

And so Darwin’s naturalisation conundrum turns out not to be an embarrassment for evolutionary biology but an opportunity to refine it. The apparent contradiction was never a fatal flaw; it was a clue that something more subtle was going on. By looking more closely at the evidence, and by using the concept of dark diversity to measure not just which species are present but which species could be present, the researchers have shown why both sides of Darwin’s conundrum can be true under different ecological conditions.

That is how science deals with paradoxes. It does not protect them from scrutiny, sanctify them as mysteries, or insist that they must be accepted on faith. It tests them against reality. If the evidence shows that an explanation is incomplete, science improves the explanation. If a model fails, it is revised or discarded. The process may be slow, untidy and argumentative, but it has a self-correcting mechanism that religion conspicuously lacks: evidence.

Religion, by contrast, has no impartial referee. When doctrines collide with one another, or with observable reality, the contradiction is usually buried beneath apologetics, metaphor, “mystery”, or demands for faith. No agreed method exists for deciding which interpretation is correct, which is why religions so readily fragment into sects and denominations, each claiming access to the same divine truth while disagreeing with all the others.

The contrast could hardly be clearer. Darwin identified a genuine problem more than 160 years ago, and biologists continued to investigate it until better data and better concepts produced a clearer answer. That is not a weakness of science but one of its greatest strengths. It can admit uncertainty, expose its own difficulties, and then use evidence to resolve them.

Creationism and theology, on the other hand, begin with conclusions that must not be questioned and then try to force the evidence, or the argument, to fit. That is why scientific paradoxes tend to become discoveries, while religious paradoxes remain exactly where they have always been: unresolved, unexplained and protected from the one thing most likely to expose them — honest enquiry.

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