In the last few decades, the debate on climate change has assumed global importance with consequences on national and global policies. Many factors due to human activity are considered as possible responsible of the observed changes: among these water and air contamination (mostly greenhouse effect) and deforestation are the mostly cited. While the extent of human contribution to the greenhouse effect and temperature changes is still a matter of discussion, the deforestation is an undeniable fact. Indeed before the development of human civilisations, our planet was covered by 60 million square kilometres of forest¹. As a result of deforestation, less than 40 million square kilometres currently remain². In this paper, we focus on the consequence of indiscriminate deforestation.

Trees’ services to our planet range from carbon storage, oxygen production to soil conservation and water cycle regulation. They support natural and human food systems and provide homes for countless species, including us, through building materials. Trees and forests are our best atmosphere cleaners and, due to the key role they play in the terrestrial ecosystem, it is highly unlikely to imagine the survival of many species, including ours, on Earth without them. In this sense, the debate on climate change will be almost obsolete in case of a global deforestation of the planet. Starting from this almost obvious observation, we investigate the problem of the survival of humanity from a statistical point of view. We model the interaction between forests and humans based on a deterministic logistic-like dynamics, while we assume a stochastic model for the technological development of the human civilisation. The former model has already been applied in similar contexts^3,4 while the latter is based on data and model of global energy consumption^5,6 used as a proxy for the technological development of a society. This gives solidity to our discussion and we show that, keeping the current rate of deforestation, statistically the probability to survive without facing a catastrophic collapse, is very low. We connect such probability to survive to the capability of humankind to spread and exploit the resources of the full solar system. According to Kardashev scale^7,8, which measures a civilisation’s level of technological advancement based on the amount of energy they are able to use, in order to spread through the solar system we need to be able to harness the energy radiated by the Sun at a rate of ≈4 × 10²⁶ Watt. Our current energy consumption rate is estimated in ≈10¹³ Watt⁹. As showed in the subsections “Statistical Model of technological development” and “Numerical results” of the following section, a successful outcome has a well defined threshold and we conclude that the probability of avoiding a catastrophic collapse is very low, less than 10% in the most optimistic estimate.

Deforestation

The deforestation of the planet is a fact². Between 2000 and 2012, 2.3 million Km² of forests around the world were cut down¹⁰ which amounts to 2 × 10⁵ Km² per year. At this rate all the forests would disappear approximatively in 100–200 years. Clearly it is unrealistic to imagine that the human society would start to be affected by the deforestation only when the last tree would be cut down. The progressive degradation of the environment due to deforestation would heavily affect human society and consequently the human collapse would start much earlier.

Curiously enough, the current situation of our planet has a lot in common with the deforestation of Easter Island as described in³. We therefore use the model introduced in that reference to roughly describe the humans-forest interaction. Admittedly, we are not aiming here for an exact exhaustive model. It is probably impossible to build such a model. What we propose and illustrate in the following sections, is a simplified model which nonetheless allows us to extrapolate the time scales of the processes involved: i.e. the deterministic process describing human population and resource (forest) consumption and the stochastic process defining the economic and technological growth of societies. Adopting the model in³ (see also¹¹) we have for the humans-forest dynamics

whereN represent the world population andR the Earth surface covered by forest.β is a positive constant related to the carrying capacity of the planet for human population,r is the growth rate for humans (estimated asr ~ 0.01 years⁻¹)¹²,a₀ may be identified as the technological parameter measuring the rate at which humans can extract the resources from the environment, as a consequence of their reached technological level.r’ is the renewability parameter representing the capability of the resources to regenerate, (estimated asr’ ~ 0.001 years⁻¹)¹³,R_c the resources carrying capacity that in our case may be identified with the initial 60 million square kilometres of forest. A closer look at this simplified model and at the analogy with Easter Island on which is based, shows nonetheless, strong similarities with our current situation. Like the old inhabitants of Easter Island we too, at least for few more decades, cannot leave the planet. The consumption of the natural resources, in particular the forests, is in competition with our technological level. Higher technological level leads to growing population and higher forest consumption (largera₀) but also to a more effective use of resources. With higher technological level we can in principle develop technical solutions to avoid/prevent the ecological collapse of our planet or, as last chance, to rebuild a civilisation in the extraterrestrial space (see section on the Fermi paradox). The dynamics of our model for humans-forest interaction in Eqs. (1,2), is typically characterised by a growing human population until a maximum is reached after which a rapid disastrous collapse in population occurs before eventually reaching a low population steady state or total extinction. We will use this maximum as a reference for reaching a disastrous condition. We call this point in time the “no-return point” because if the deforestation rate is not changed before this time the human population will not be able to sustain itself and a disastrous collapse or even extinction will occur. As a first approximation³, since the capability of the resources to regenerate,r′, is an order of magnitude smaller than the growing rate for humans,r, we may neglect the first term in the right hand-side of Eq. (2). Therefore, working in a regime of the exploitation of the resources governed essentially by the deforestation, from Eq. (2) we can derive the rate of tree extinction as

The actual population of the Earth isN ~ 7.5 × 10⁹ inhabitants with a maximum carrying capacity estimated¹⁴ ofN_c ~ 10¹⁰ inhabitants. The forest carrying capacity may be taken as¹R_c ~ 6 × 10⁷ Km² while the actual surface of forest is\(R\lesssim 4\times {10}^{7}\) Km². Assuming thatβ is constant, we may estimate this parameter evaluating the equalityN_c(t) = βR(t) at the time when the forests were intact. HereN_c(t) is the instantaneous human carrying capacity given by Eq. (1). We obtainβ ~ N_c/R_c ~ 170.

In alternative we may evaluateβ using actual data of the population growth¹⁵ and inserting it in Eq. (1). In this case we obtain a range\(700\lesssim \beta \lesssim 900\) that gives a slightly favourable scenario for the human kind (see below and Fig. 4). We stress anyway that this second scenario depends on many factors not least the fact that the period examined in¹⁵ is relatively short. On the contraryβ ~ 170 is based on the accepted value for the maximum human carrying capacity. With respect to the value of parametera₀, adopting the data relative to years 2000–2012 of ref.¹⁰,we have

The time evolution of system (1) and (2) is plotted in Figs. 1 and2. We note that in Fig. 1 the numerical value of the maximum of the functionN(t) isN_M ~ 10¹⁰ estimated as the carrying capacity for the Earth population¹⁴. Again we have to stress that it is unrealistic to think that the decline of the population in a situation of strong environmental degradation would be a non-chaotic and well-ordered decline, that is also way we take the maximum in population and the time at which occurs as the point of reference for the occurrence of an irreversible catastrophic collapse, namely a ‘no-return’ point.

On the left: plot of the solution of Eq. (1) with the initial conditionN₀ = 6 × 10⁹ at initial timet = 2000 A.C. On the right: plot of the solution of Eq. (2) with the initial conditionR₀ = 4 × 10⁷. Hereβ = 700 anda₀ = 10⁻¹².

Full size image

On the left: plot of the solution of Eq. (1) with the initial conditionN₀ = 6 × 10⁹ at initial timet = 2000 A.C. On the right: plot of the solution of Eq. (2) with the initial conditionR₀ = 4 × 10⁷. Hereβ = 170 anda₀ = 10⁻¹².

Full size image

Statistical model of technological development

According to Kardashev scale^7,8, in order to be able to spread through the solar system, a civilisation must be capable to build a Dyson sphere¹⁶, i.e. a maximal technological exploitation of most the energy from its local star, which in the case of the Earth with the Sun would correspond to an energy consumption ofE_D ≈ 4 × 10²⁶ Watts, we call this value Dyson limit. Our actual energy consumption is estimated inE_c ≈ 10¹³ Watts (Statistical Review of World Energy source)⁹. To describe our technological evolution, we may roughly schematise the development as a dichotomous random process

whereT is the level of technological development of human civilisation that we can also identify with the energy consumption.α is a constant parameter describing the technological growth rate (i.e. ofT) andξ(t) a random variable with values 0, 1. We consider therefore, based on data of global energy consumption^5,6 an exponential growth with fluctuations mainly reflecting changes in global economy. We therefore consider a modulated exponential growth process where the fluctuations in the growth rate are captured by the variableξ(t). This variable switches between values 0, 1 with waiting times between switches distributed with densityψ(t). Whenξ(t) = 0 the growth stops and resumes whenξ switches toξ(t) = 1. If we considerT more strictly as describing the technological development,ξ(t) reflects the fact that investments in research can have interruptions as a consequence of alternation of periods of economic growth and crisis. With the following transformation,

differentiating both sides respect tot and using Eq. (5), we obtain for the transformed variableW

where\(\bar{\xi }(t)=2[\xi (t)-\langle \xi \rangle ]\) and〈ξ〉 is the average ofξ(t) so that\(\bar{\xi }(t)\) takes the values ±1.

The above equation has been intensively studied, and a general solution for the probability distributionP(W,t) generated by a generic waiting time distribution can be found in literature¹⁷. Knowing the distribution we may evaluate the first passage time distribution in reaching the necessary level of technology to e.g. live in the extraterrestrial space or develop any other way to sustain population of the planet. This characteristic time has to be compared with the time that it will take to reach the no-return point. Knowing the first passage time distribution¹⁸ we will be able to evaluate the probability to survive for our civilisation.

If the dichotomous process is a Poissonian process with rateγ then the correlation function is an exponential, i.e.

and Eq. (7) generates for the probability density the well known telegrapher’s equation

We note that the approach that we are following is based on the assumption that at random times, exponentially distributed with rateγ, the dichotomous variable\(\bar{\xi }\) changes its value. With this assumption the solution to Eq. (9) is

whereI_n(z) are the modified Bessel function of the first kind. Transforming back to the variableT we have

where for sake of compactness we set

In Laplace transform we have

The first passage time distribution, in laplace transform, is evaluated as¹⁹

Inverting the Laplace transform we obtain

which is confirmed (see Fig. 3) by numerical simulations. The time average to get the pointx for the first time is given by

which interestingly is double the time it would take if a pure exponential growth occurred, depends on the ratio between final and initial value ofT and is independent ofγ. We also stress that this result depends on parameters directly related to the stage of development of the considered civilisation, namely the starting valueT₁, that we assume to be the energy consumptionE_c of the fully industrialised stage of the civilisation evolution and the final valueT, that we assume to be the Dyson limitE_D, and the technological growth rateα. For the latter we may, rather optimistically, choose the valueα = 0.345, following the Moore Law²⁰ (see next section). Using the data above, relative to our planet’s scenario, we obtain the estimate of 〈t〉 ≈ 180 years. From Figs. 1 and2 we see that the estimate for the no-return time are 130 and 22 years forβ = 700 andβ = 170 respectively, with the latter being the most realistic value. In either case, these estimates based on average values, being less than 180 years, already portend not a favourable outcome for avoiding a catastrophic collapse. Nonetheless, in order to estimate the actual probability for avoiding collapse we cannot rely on average values, but we need to evaluate the single trajectories, and count the ones that manage to reach the Dyson limit before the ‘no-return point’. We implement this numerically as explained in the following.

(Left) Comparison between theoretical prediction of Eq. (15) (black curve) and numerical simulation of Eq. (3) (cyan curve) forγ = 4 (arbitrary units). (Right) Comparison between theoretical prediction of Eq. (15) (red curve) and numerical simulation of Eq. (3) (black curve) forγ = 1/4 (arbitrary units).

Full size image

(Left panel) Probabilityp_suc of reaching Dyson value before reaching “no-return” point as function ofα anda forβ = 170. Parametera is expressed in Km² ys⁻¹. (Right panel) 2D plot ofp_suc fora = 1.5 × 10⁻⁴ Km² ys⁻¹ as a function ofα. Red line isp_suc forβ = 170. Black continuous lines (indistinguishable) arep_suc forβ = 300 and 700 respectively (see also Fig. 6). Green dashed line indicates the value ofα corresponding to Moore’s law.

Full size image

Numerical results

We run simulations of Eqs. (1), (2) and (5) simultaneously for different values of of parametersa₀ andα for fixedβ and we count the number of trajectories that reach Dyson limit before the population level reaches the “no-return point” after which rapid collapse occurs. More precisely, the evolution ofT is stochastic due to the dichotomous random processξ(t), so we generate theT(t) trajectories and at the same time we follow the evolution of the population and forest density dictated by the dynamics of Eqs. (1), (2)³ until the latter dynamics reaches the no-return point (maximum in population followed by collapse). When this happens, if the trajectory inT(t) has reached the Dyson limit we count it as a success, otherwise as failure. This way we determine the probabilities and relative mean times in Figs. 5,6 and7. Adopting a weak sustainability point of view our model does not specify the technological mechanism by which the successful trajectories are able to find an alternative to forests and avoid collapse, we leave this undefined and link it exclusively and probabilistically to the attainment of the Dyson limit. It is important to notice that we link the technological growth process described by Eq. (5) to the economic growth and therefore we consider, for both economic and technological growth, a random sequence of growth and stagnation cycles, with mean periods of about 1 and 4 years in accordance with estimates for the driving world economy, i.e. the United States according to the National Bureau of Economic Research²¹.

Average timeτ (in years) to reach Dyson value before hitting “no-return” point (success, left) and without meeting Dyson value (failure, right) as function ofα anda forβ = 170. Plateau region (left panel) whereτ ≥ 50 corresponds to divergingτ, i.e. Dyson value not being reached before hitting “no-return” point and therefore failure. Plateau region atτ = 0 (right panel), corresponds to failure not occurring, i.e. success. Parametera is expressed in Km² ys⁻¹.

Full size image

Probabilityp_suc of reaching Dyson value before hitting “no-return” point as function ofα anda forβ = 300 (left) and 700 (right). Parametera is expressed in Km² ys⁻¹.

Full size image

Probability of reaching Dyson valuep_suc before reaching “no-return” point as function ofβ andα fora = 1.5 × 10⁻⁴ Km² ys⁻¹.

Full size image

In Eq. (1,2) we redefine the variables asN′ = N/R_W andR′ = R/R_W with\({R}_{W}\simeq 150\times {10}^{6}\,K{m}^{2}\) the total continental area, and replace parametera₀ accordingly witha = a₀ × R_W = 1.5 × 10⁻⁴ Km² ys⁻¹. We run simulations accordingly starting from values\({R{\prime} }_{0}\) and\({N{\prime} }_{0}\), based respectively on the current forest surface and human population. We take values ofa from 10⁻⁵ to 3 × 10⁻⁴ Km² ys⁻¹ and forα from 0.01 ys⁻¹ to 4.4 ys⁻¹. Results are shown in Figs. 4 and6. Figure 4 shows a threshold value for the parameterα, the technological growth rate, above which there is a non-zero probability of success. This threshold value increases with the value of the other parametera. As shown in Fig. 7 this values depends as well on the value ofβ and higher values ofβ correspond to a more favourable scenario where the transition to a non-zero probability of success occurs for smallerα, i.e. for smaller, more accessible values, of technological growth rate. More specifically, left panel of Fig. 4 shows that, for the more realistic valueβ = 170, a region of parameter values with non-zero probability of avoiding collapse corresponds to values ofα larger than 0.5. Even assuming that the technological growth rate be comparable to the valueα = log(2)/2 = 0.345 ys⁻¹, given by the Moore Law (corresponding to a doubling in size every two years), therefore, it is unlikely in this regime to avoid reaching the the catastrophic ‘no-return point’. When the realistic value ofa = 1.5 × 10⁴ Km² ys⁻¹ estimated from Eq. (4), is adopted, in fact, a probability less than 10% is obtained for avoiding collapse with a Moore growth rate, even when adopting the more optimistic scenario corresponding toβ = 700 (black curve in right panel of Fig. 4). While anα larger than 1.5 is needed to have a non-zero probability of avoiding collapse whenβ = 170 (red curve, same panel). As far as time scales are concerned, right panel of Fig. 5 shows forβ = 170 that even in the rangeα > 0.5, corresponding to a non-zero probability of avoiding collapse, collapse is still possible, and when this occurs, the average time to the ‘no-return point’ ranges from 20 to 40 years. Left panel in same figure, shows for the same parameters, that in order to avoid catastrophe, our society has to reach the Dyson’s limit in the same average amount of time of 20–40 years.

In Fig. 7 we show the dependence of the model on the parameterβ fora = 1.5 × 10⁻⁴.

We run simulations of Eqs. (1), (2) and (5) simultaneously for different values of of parametersa₀ andα depending onβ as explained in Methods and Results to generate Figs. 5,6 and7. Equations (1), (2) are integrated via standard Euler method. Eq. (5) is integrated as well via standard Euler method between the random changes of the variableξ. The stochastic dichotomous processξ is generated numerically in the following way: using the random number generator from gsl library we generate the times intervals between the changes of the dichotomous variableξ = 0, 1, with an exponential distribution(with mean values of 1 and 4 years respectively), we therefore obtain a time series of 0 and 1 for each trajectory. We then integrate Eq. (5) in time using this time series and we average overN = 10000 trajectories. The latter procedure is used to carry out simulations in Figs. 3 and4 as well in order to evaluate the first passage time probabilities. All simulations are implemented in C++.

Fermi paradox

In this section we briefly discuss a few considerations about the so called Fermi paradox that can be drawn from our model. We may in fact relate the Fermi paradox to the problem of resource consumption and self destruction of a civilisation. The origin of Fermi paradox dates back to a casual conversation about extraterrestrial life that Enrico Fermi had with E. Konopinski, E. Teller and H. York in 1950, during which Fermi asked the famous question: “where is everybody?”, since then become eponymous for the paradox. Starting from the closely related Drake equation^22,23, used to estimate the number of extraterrestrial civilisations in the Milky Way, the debate around this topic has been particularly intense in the past (for a more comprehensive covering we refer to Hart²⁴, Freitas²⁵ and reference therein). Hart’s conclusion is that there are no other advanced or ‘technological’ civilisations in our galaxy as also supported recently by²⁶ based on a careful reexamination of Drake’s equation. In other words the terrestrial civilisation should be the only one living in the Milk Way. Such conclusions are still debated, but many of Hart’s arguments are undoubtedly still valid while some of them need to be rediscussed or updated. For example, there is also the possibility that avoiding communication might actually be an ‘intelligent’ choice and a possible explanation of the paradox. On several public occasions, in fact, Professor Stephen Hawking suggested human kind should be very cautious about making contact with extraterrestrial life. More precisely when questioned about planet Gliese 832c’s potential for alien life he once said: “One day, we might receive a signal from a planet like this, but we should be wary of answering back”. Human history has in fact been punctuated by clashes between different civilisations and cultures which should serve as caveat. From the relatively soft replacement between Neanderthals and Homo Sapiens (Kolodny²⁷) up to the violent confrontation between native Americans and Europeans, the historical examples of clashes and extinctions of cultures and civilisations have been quite numerous. Looking at human history Hawking’s suggestion appears as a wise warning and we cannot role out the possibility that extraterrestrial societies are following similar advice coming from their best minds.

With the help of new technologies capable of observing extrasolar planetary systems, searching and contacting alien life is becoming a concrete possibility (see for example Grimaldi²⁸ for a study on the chance of detecting extraterrestrial intelligence), therefore a discussion on the probability of this occurring is an important opportunity to assess also our current situation as a civilisation. Among Hart’s arguments, the self-destruction hypothesis especially needs to be rediscussed at a deeper level. Self-destruction following environmental degradation is becoming more and more an alarming possibility. While violent events, such as global war or natural catastrophic events, are of immediate concern to everyone, a relatively slow consumption of the planetary resources may be not perceived as strongly as a mortal danger for the human civilisation. Modern societies are in fact driven by Economy, and, without giving here a well detailed definition of “economical society”, we may agree that such a kind of society privileges the interest of its components with less or no concern for the whole ecosystem that hosts them (for more details see²⁹ for a review on Ecological Economics and its criticisms to mainstream Economics). Clear examples of the consequences of this type of societies are the international agreements about Climate Change. The Paris climate agreement^30,31 is in fact, just the last example of a weak agreement due to its strong subordination to the economic interests of the single individual countries. In contraposition to this type of society we may have to redefine a different model of society, a “cultural society”, that in some way privileges the interest of the ecosystem above the individual interest of its components, but eventually in accordance with the overall communal interest. This consideration suggests a statistical explanation of Fermi paradox: even if intelligent life forms were very common (in agreement with the mediocrity principle in one of its version³²: “there is nothing special about the solar system and the planet Earth”) only very few civilisations would be able to reach a sufficient technological level so as to spread in their own solar system before collapsing due to resource consumption.

We are aware that several objections can be raised against this argument and we discuss below the one that we believe to be the most important. The main objection is that we do not know anything about extraterrestrial life. Consequently, we do not know the role that a hypothetical intelligence plays in the ecosystem of the planet. For example not necessarily the planet needs trees (or the equivalent of trees) for its ecosystem. Furthermore the intelligent form of life could be itself the analogous of our trees, so avoiding the problem of the “deforestation” (or its analogous). But if we assume that we are not an exception (mediocrity principle) then independently of the structure of the alien ecosystem, the intelligent life form would exploit every kind of resources, from rocks to organic resources (animal/vegetal/etc), evolving towards a critical situation. Even if we are at the beginning of the extrasolar planetology, we have strong indications that Earth-like planets have the volume magnitude of the order of our planet. In other words, the resources that alien civilisations have at their disposal are, as order of magnitude, the same for all of them, including ourselves. Furthermore the mean time to reach the Dyson limit as derived in Eq. 6 depends only on the ratio between final and initial value ofT and therefore would be independent of the size of the planet, if we assume as a proxy forT energy consumption (which scales with the size of the planet), producing a rather general result which can be extended to other civilisations. Along this line of thinking, if we are an exception in the Universe we have a high probability to collapse or become extinct, while if we assume the mediocrity principle we are led to conclude that very few civilisations are able to reach a sufficient technological level so as to spread in their own solar system before the consumption of their planet’s resources triggers a catastrophic population collapse. The mediocrity principle has been questioned (see for example Kukla³³ for a critical discussion about it) but on the other hand the idea that the humankind is in some way “special” in the universe has historically been challenged several times. Starting with the idea of the Earth at the centre of the universe (geocentrism), then of the solar system as centre of the universe (Heliocentrism) and finally our galaxy as centre of the universe. All these beliefs have been denied by the facts. Our discussion, being focused on the resource consumption, shows that whether we assume the mediocrity principle or our “uniqueness” as an intelligent species in the universe, the conclusion does not change. Giving a very broad meaning to the concept of cultural civilisation as a civilisation not strongly ruled by economy, we suggest for avoiding collapse³⁴ that only civilisations capable of such a switch from an economical society to a sort of “cultural” society in a timely manner, may survive. This discussion leads us to the conclusion that, even assuming the mediocrity principle, the answer to “Where is everybody?” could be a lugubrious “(almost) everyone is dead”.

In conclusion our model shows that a catastrophic collapse in human population, due to resource consumption, is the most likely scenario of the dynamical evolution based on current parameters. Adopting a combined deterministic and stochastic model we conclude from a statistical point of view that the probability that our civilisation survives itself is less than 10% in the most optimistic scenario. Calculations show that, maintaining the actual rate of population growth and resource consumption, in particular forest consumption, we have a few decades left before an irreversible collapse of our civilisation (see Fig. 5). Making the situation even worse, we stress once again that it is unrealistic to think that the decline of the population in a situation of strong environmental degradation would be a non-chaotic and well-ordered decline. This consideration leads to an even shorter remaining time. Admittedly, in our analysis, we assume parameters such as population growth and deforestation rate in our model as constant. This is a rough approximation which allows us to predict future scenarios based on current conditions. Nonetheless the resulting mean-times for a catastrophic outcome to occur, which are of the order of 2–4 decades (see Fig. 5), make this approximation acceptable, as it is hard to imagine, in absence of very strong collective efforts, big changes of these parameters to occur in such time scale. This interval of time seems to be out of our reach and incompatible with the actual rate of the resource consumption on Earth, although some fluctuations around this trend are possible³⁵ not only due to unforeseen effects of climate change but also to desirable human-driven reforestation. This scenario offers as well a plausible additional explanation to the fact that no signals from other civilisations are detected. In fact according to Eq. (16) the mean time to reach Dyson sphere depends on the ratio of the technological levelT and therefore, assuming energy consumption (which scales with the size of the planet) as a proxy forT, such ratio is approximately independent of the size of the planet. Based on this observation and on the mediocrity principle, one could extend the results shown in this paper, and conclude that a generic civilisation has approximatively two centuries starting from its fully developed industrial age to reach the capability to spread through its own solar system. In fact, giving a very broad meaning to the concept of cultural civilisation as a civilisation not strongly ruled by economy, we suggest that only civilisations capable of a switch from an economical society to a sort of “cultural” society in a timely manner, may survive.

M.B. and G.A. acknowledge Phy. C.A. for logistical support.

1. These authors contributed equally: Mauro Bologna and Gerardo Aquino.

Authors and Affiliations

1. Departamento de Ingeniería Eléctrica-Electrónica, Universidad de Tarapacá, Arica, Chile

   Mauro Bologna

2. The Alan Turing Institute, London, UK

   Gerardo Aquino

3. University of Surrey, Guildford, UK

   Gerardo Aquino

4. Goldsmiths, University of London, London, UK

   Gerardo Aquino

Contributions

M.B. and G.A. equally contributed and reviewed the manuscript.

Corresponding author

Correspondence toGerardo Aquino.

Competing interests

The authors declare no competing interests.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visithttp://creativecommons.org/licenses/by/4.0/.

Reprints and permissions