Human migration is the movement of people from one region (called the region/country of origin) to another region (called the host region/country). This movement can be temporary, where migrants return to their regions of origin, or permanent, where migrants and their future generations settle down permanently in the host region. Migration can occur within a country (domestic), or between countries (international). The reasons for migration are myriad. People can do so to seek better economic opportunities or better environments for their offspring (pull factors). It can also be to escape from criminal or political violence and oppression (push factors). Migration can also be classified as voluntary or involuntary. In the latter, migrants are classified as refugees.

To navigate the contemporary scholarly literature on human migration, we start from the 2017 paper by Sirkeci, Cohen, and Privara surveying the most influential papers and authors in migration studies [9]. This list is objective, since the ranking is created based on citations obtained from the Google Scholar database. Within the 100 most cited works, the earliest was in the late 1800s [10, 11] and the early 1900s [12]. There was then a long lapse, before the literature exploded after 1985, to reach a high around the year 2000 (see Figure 2). Thereafter, the number of highly-cited works decreased. Putting aside the early works, and looking at the post-2000 publications by the most influential migration scholars, we find them accepting migration as an ongoing phenomenon, with their papers investigating specific issues related to migration, without pronouncing whether migration is desirable or not.

Given this stance amongst leading scholars, it is difficult to understand why there is a one-sided opinion on migration as a good thing in traditional or social media. To clarify this, we surveyed opinions published in the media, starting with those who sing praises about human migration, before touching on those who object (and why they object). Wherever possible, we identify scholarly research these opinions are based off. Here, let us warn that opinion pieces do not cite references (opinions of previous writers), are not as comprehensively archived and indexed as scholarly publications, and hence we are likely to miss earlier articles (especially if they pre-date the Google search engine).

Amongst the many advocates of migration, we find international organizations such as the International Organization on Migration (IOM). The IOM’s views on migration are understandably positive, since it is an organization created to serve migrants. Their support for migration is first and foremost based on human rights, but IOM argued that there are also other benefits. Another international organization that leans positively on migration is the Organization for Economic Co-operation and Development (OECD), who urges the public to accept more open immigration policies [13]. The World Economic Forum also argues that meaningful policies must balance the longer-term economic benefits that immigration brings with local and short-term costs [14].

The greatest divide in opinions about immigration occur at the level of think tanks. Advocates of immigration includes the non-profit IZA Institute of Labour Economics based in Bonn, Germany [15], and the Center for Global Liberty and Prosperity in the CATO Institute [16], an American libertarian think tank with headquarters in Washington DC, founded in 1977 by private philanthropists. Opponents to immigration tend to be think tanks strongly influenced by colorful individuals. These include advocacy groups such as NumbersUSA, and the Center for Immigration Studies, who make their cases in the form of books [17]. Opponents of migration appear to be the minority.

Biological invasions happen when an organism (the invasive species) arrives from its distant native habitat. This can happen as a result of human actions (also known as human dispersals), either deliberately or accidentally. The invasive species can also be transported by mammals, birds, insects, and plants. According to the 1996 book Biological Invasions by Williamson [18], the invasion process consists of a series of steps (or stages), including transport, establishment, spread, and impact. Others have proposed four different stages, i.e., arrival, establishment, spread, and adjustment [19, 20]. Henderson [21], on the other hand, proposed six stages of biological invasion, namely, introduction, establishment, naturalization, dispersal, population distribution, and invasive spread.

The impact caused by biological invasions can be harmful to our health or our economy. Economically, Pimentel et al. [22] estimated in 2005 that invasive species cause environmental damages and losses adding up to almost $120 billion per year in the United States Policy and management options differ at different stages of a biological invasion, but it has been recognized once an invasion has started, the efforts to reverse it will be enormous. Therefore, preventive steps for stopping biological invasions are deemed more effective. They include early detection, rapid response, and eradication before the invasive species spreads. This is why United States President Bill Clinton signed Executive Order 13,751 to deal with invasive species in 1999.

But how did the ecology community become fixated on biological invasions as bad? To understand this, we reviewed literature going back to the mid-1700s, when the deliberate transportation of plants and animals by humans was first documented. According to Chew [23], Pehr Kalm traveled to North America seeking new plants that might be brought back to Sweden and grown commercially for economic benefit. Thereafter in the 1800s, a host of botanists and zoologist (including Charles Darwin and Alfred Russell Wallace) went around documenting the distribution of the world’s biota, and brought samples back home with them. These data sets and collections laid the conceptual groundwork for the modern sciences of evolutionary biology as well as ecology in the 20th century. This was also when native and non-native species were first formally defined. However, in those days no one was of the opinion that the deliberate introduction of non-native species into various ecosystems for economic purposes was bad.

According to Cadotte [24], North American agricultural scientists in the middle of the 19th century started noticing the negative impacts of non-native species [25]. By the end of the 19th century, such commentaries became more common [26–28]. The notion that movements of species between ecosystems were bad was popularized by Charles Elton (who is considered the forefather of the field of biological invasions), who in 1958 wrote a book titled The Ecology of Invasions by Animals and Plants [29], and also coined the term invasive species. Over in Europe, ecologists were also becoming aware of the impacts of non-native species, but adopted a neutral attitude towards them. In particular, they deemed that the introduction of non-native species as just one of many factors that could cause the decline of native species [30]. In fact, 6 years after the publication of Elton’s book, the International Union of Biological Scientists (IUBS) held its first Biological Sciences Symposium in Asilomar, California, to facilitate discussions on “the kinds of evolutionary change which take place when organisms are introduced into new territories” amongst top geneticists, ecologists, taxonomists, and applied scientists working in the area of pest control [31].

The two views were balanced until 1980, when the Third International Conference on Mediterranean Ecosystems was held in Stellenbosch, South Africa. At this conference, the idea of biological invasions appealed to many participants, who deemed biological invasions to inevitably cause an impact to human societies and ecosystems if preventive and mitigation measures were not implemented promptly. Since then, books, conferences, and organizations on biological invasions have emerged. The issue was frequently discussed in mass media and also appeared in government policies in many countries. In short, the negative impressions towards non-native species may be attributed to Elton’s 1958 book, and also the 1980 South Africa conference. A complete account of the historical developments of this field can be found in Davis’s book on Invasion Biology [32].

Human migration introduces new communities into an existing society with many established communities, whereas biological invasion involves new non-native species being introduced into an ecosystem with many existing species. Despite this similarity, human migration is largely considered as a positive change, while biological invasion is seen negatively. Between these two extremes, the real situation may actually be more complex. In fact, the history of human migration is effectively the history of our Homo sapiens species. Prehistorically, the earliest H. sapiens appeared to have occupied all of Africa about 150,000 years ago [33]. Around 70,000 years ago, humans started moving out of Africa into Asia and Europe [34, 35], across Australia, Asia, and Europe by 40,000 BCE [34, 35], and finally to the Americas 20,000 to 15,000 years ago [36]. Using historical records of human migration, McNeill classified them into four types, namely, (1) radical displacement via systematic exercise of force; (2) conquest of one population by another, (3) infiltration-type migration, and (4) slavery or exploitation-type migration [37]. Our modern definition of human migration is closest to types (3) and (4) (but less the slavery component).

Human migration of types 1 and 2 are rare in modern times, but common in our historic past. For example, nomads such as the Huns, Mongols, Turks, and many others raided each other in the Eurasian Steppe whenever opportunities presented themselves. The patterns of movements resulting from these skirmishes are classified as type 1 by McNeill. In contrast, human migration of type 2 occurs when a nomadic group encounters and overwhelms a farming society, and eventually the two communities become one [38–40]. However, itinerant peoples were not always raiders and conquerors. They also included merchants and traders, artisans with exotic skills, as well as scavengers and street food vendors. Their contact with local communities were welcomed, because they provided exclusive goods and services. Over time, these ‘strangers’ integrated into their host communities in what McNeill called type 3 human migration. Finally, there is type 4 human migration, which can be distinguished from type 3 by the involuntary displacement of large groups of peoples, either as slaves, or as cheap sources of labour.

As we can see, human migrations of types 1, 2, and 4 are clearly not acceptable today. If there are any good and desirable human migration, it must be of type 3. Besides the integration of various practical expertise into the host community through the assimilation of a small proportion of ‘outsiders’, human migration of this type also brought missionaries, teachers, medical and military experts and their knowledge to various communities. This infusion of knowledge increased the wealth of a host community without sacrificing social coherence. Certainly, this form of human migration plays an important role in shaping civilization as we know it today.

Moreover, the movements of human communities also resulted in the spread of plants and animals numerous times in pre-historic and historic times. The effects of these past movements were not documented, so it is difficult to assess what their social and ecological impacts were. In this survey of the literature, we do not aim to paint a comprehensive picture of all episodes of human migrations and the biological invasions that followed them, but to highlight the possibility that impacts of specific human migrations can be decidedly bad (the Eurasian Steppe example given above), and specific episodes where non-native species could be introduced without destroying or compensating host ecosystems. One example is the cultivation of rice, Oryza sativa. This plant was first domesticated in China between 13,500 and 8,200 years ago [41], then spread to the Korean Peninsula latest by 2,000 BCE [42], and to Japan by 1,000 BCE [43]. It was hypothesized that rice was domesticated a second time in India [44]. Today, rice is the staple food crop for more than 3.5 billion people around the world, and has historically supported the growth of human population.

Another example would be the pig, Sus scrofa, which was first domesticated from wild boars in Eastern Turkey 10,000 to 9,000 years ago [45, 46]. The pig was also independently domesticated in China between 10,000 and 8,000 years ago [47, 48]. From Eastern Turkey, domestic pigs spread to Northern Turkey [49], and throughout Europe by 5,500 BCE [50]. Thereafter, between 5,000 and 4,000 years ago, Austronesian-speaking rice agriculturalists from southern China migrated through Taiwan and Sundaland into southeast Asia and Oceania as well as westward to Madagascar, bringing with them domesticated pigs [51]. Today, the pig is an important source of animal protein for the world, but it is also one of the largest source of zoonotic diseases [52]. From the perspectives given above, the pig is thus both good (food) and bad (disease).

The immigration issue came to the fore during the 2016 United States Presidential Elections between Democrat candidate Hillary Clinton and Republican candidate Donald Trump. The debate grew so polarizing that in the September/October 2016 issue of Politico [53], an United States news outlet specializing in politics and policy, George Borjas explained how Donald Trump used half of his findings (that admitting large numbers of immigrants over many decades have led to lower wages and unemployment, especially for African and Hispanic Americans [54]) to justify tougher immigration policies and building the border wall, while Hillary Clinton used the other half of his findings (that both legal and illegal immigrants helped improve economic outcomes for everyone) to justify immigration policies to date. In fact, anti-immigrant sentiments are on the rise in many countries that accept foreign-born citizens. Unfortunately, contrary to calls for “a more balanced and evidence-based debate about migration, where the real facts are presented and discussed openly” [55], this is an ethical issue that cannot be settled with hard facts alone. We cannot keep telling the segments of our society negatively impacted by immigration that immigrants make the economic pie bigger, when these benefits do not actually go to them.

There is a similar set of considerations surrounding biological invasions by non-native species, and that is, who decides which non-natives species can or cannot be introduced. According to many ecologists, we would not introduce any non-native species at all. However, we also know from the history of humankind that our success on this planet was strongly influenced by our spreading of non-native plant and animal species. Given this backdrop, we argue that it is reasonable to measure the benefits of introducing non-native species into an ecosystem (or a foreign community into society), against the potential biodiversity loss (or cultural diversity loss) that these might produce. In this paper, we are not advocating for the cessation of all movements of human communities and non-native plant and animal species, but to suggest how we can debate the ethics of allowing some such movements, and at the same time barring or intervening in others.

While some might argue that such ethical discussions are beyond the realm of science, we believe the scientific approach can be the basis for such debates, by providing not just data and hard evidence, but also compelling narratives derived from quantitative models. In the real world, we can either shut out immigrants, or let them in. If we have chosen one path of action, we will never know what happens for other paths of action. Thus this is where modelling comes in. The biggest advantage that models can offer is for us to simulate both scenarios, and measure quantities we are interested in. More importantly, different immigration policies can be compared first through simulations, before their outcomes are put on the table for policy discussions. Ultimately, the policy with the best economic outcome is not automatically selected, because we must also decide whether its social cost is acceptable. In the end, we may opt for a compromise, and go with a policy with reduced economic benefits, but whose social cost we decide that we are able to bear.

We proceed to describe a common modelling framework for human migration and biological invasions, because there are strong similarities between the two phenomena. Could it be that human migration can also be bad? Or perhaps the introduction of non-native species sometimes good? To find answers to these questions, we need to first use the same performance metric, instead of using economic benefits for one, and biodiversity for the other. To quantify diversity, it is customary to use the entropy function S p → = p 1 , … , p i , … , p N = − ∑ i = 1 N p i ⁡ log ⁡ p i . For example, if we have N communities that are equally represented, then the probability of finding an individual from a given community i would be p i = 1 / N . Such a society/ecosystem would have entropy S = ∑ i = 1 N log ⁡ N N = log ⁡ N , which is the maximum possible for a system with N communities. In contrast, if the first community has overwhelmingly many individuals, while the other communities are represented by a few individuals, then S ≈ 0 . When we go from a society or ecosystem with N communities to one with N + 1 communities, we ought to compare S N + 1 against S N . Depending on the detail distribution p → = p i , S N + 1 is not automatically larger than S N .

In the Supplementary Material, we reviewed the literatures on ecological and evolutionary models of niches, as well as their applications to culture, technology and innovation. In the former, we find the work by May dealing with many interacting species exploiting a single resource type distributed in space [56]. For the ecosystem to be stable, May argued that the distributions of species will eventually become non-overlapping. These can then be thought of as niches for the different species. In the latter, Laland et al. [57] investigated how a single species’ fitness is determined by how strongly it modifies its environment with an unspecified number of resource types. They showed that niche construction allows even deleterious genes to persist in the population. In these literatures, the niche occupied by a species is a region of space (its habitat) that it has modified to favor itself (and disadvantage other species) and its offspring (inheritance). Since much of the debate on human migration and biological invasion is focused on introduced individuals and the first few generations of their offspring, we will not consider the effects of evolution in this paper. However, we do wish to explicitly model how introduced individuals interact with natives, by exploiting the native niches. This network of niches is implicitly assumed in May’s model, and in this paper we make their interactions explicit by writing down simple network models based on ordinary differential equations.

When an initial population N 6 0 of species 6 invades the periphery niche K 2 0 of species 2, we found from our simulations three different types of equilibria post-invasion: (1) the invasion fails ( N 6 * = 0 ); (2) the invasion succeeds ( N 6 * > 0 ), and there is a partial collapse in the ecosystem; and (3) the invasion succeeds ( N 6 * > 0 ) and all other species remain alive. In the first situation, which occurs when ϵ < 1 and for all initial populations N 6 0 as far as we can tell, K 2 * = 0 if μ 6 ≤ μ 2 , and species 2 also dies ( N 2 * = 0 ) (see Figures 6A,B). This is slightly surprising, as we did not expect N 2 to also collapse. On the other hand, if μ 6 > μ 2 , K 2 decreases to a new equilibrium value, and species 2 remains alive ( N 2 * > 0 ) (see Figures 6C,D). The carrying capacity lost by node 2 is absorbed by node 1 (the core). We find this last result unintuitive, because according to the standard Lotka-Volterra equation, the species with the larger reproduction rate μ should survive, but our simulations showed otherwise. In this first situation, the biodiversity decreases slightly.

The second situation occurs when ϵ ≳ 1 , where species 1 (the core) dies (even when μ 1 = 20 ), whether μ 6 ≤ μ 2 < μ 1 or μ 2 < μ 6 < μ 1 , whatever N 6 0 is. For μ 6 ≤ μ 2 < μ 1 , we have N 2 * > N 6 * (Figures 7A,B, in agreement with the reproductive advantage μ 2 > μ 6 ), whereas for μ 2 < μ 6 < μ 1 , we have N 6 * > N 2 * (Figures 7C,D, again in agreement with the reproductive advantage μ 6 > μ 2 ). In the standard Lotka-Volterra model, co-existence is possible only in the exceptional case when 1 − N 2 * + N 6 * K 2 = 0 . In our model, K 2 t can evolve with time, and in this second situation, it reaches the equilibrium value associated with 1 − N 2 * + N 6 * K 2 * = 0 , whenever ϵ ≳ 1 . This explains why species 2 and 6 can co-exist. In this scenario, full ecological collapse is averted by the fragmentation of the ecosystem ( K 1 * = 0 ). In this second situation, the biodiversity also decreases slightly.

Finally, we find the third situation, which occurs for ϵ = 1 . In this situation shown in Figure 8, the invasion is successful, and species 6 establishes itself, at the expense of species 1 (core) and species 2 (periphery node invaded), but all species are alive. For μ 6 < μ 2 , we end up with N 6 * > N 2 * if N 6 0 ≥ N 2 0 , but N 6 * < N 2 * if N 6 0 < N 2 0 . On the other hand, for μ 6 > μ 2 , we have N 2 * > N 6 * whatever value N 6 0 takes. In either case, K 2 increases to a new equilibrium value, and its increase is at the expense of node 1 (core). In this third situation, we find either the biodiversity remaining more or less constant, or increasing slightly.

In view of our discussions earlier in this paper, this is the best-case scenario for biological invasion because the biodiversity is slightly increased. However, it only occurs for ϵ = 1 , which is related to the special case of the Lotka-Volterra equation where K 2 * = N 2 * + N 6 * , allowing the old species 2 and the new species 6 to coexist on niche K 2 . However, this scenario remains special, because it requires the invasive species 6 to be identical in exploration efficiency as species 2.

When species 6 invades the core (species 1), the situation becomes more complex for μ 6 ≤ μ 1 . There are four distinct regimes: (1) for ϵ = 0.3 , K 1 * > 0 , K 2 * = K 3 * = K 4 * = K 5 * = 0 , N 1 * > N 6 * > 0 , N 2 * = N 3 * = N 4 * = N 5 * = 0 (independent of N 6 0 ) (near complete ecological collapse, see Figures 9A,B); (2) for 0.4 < ϵ < 0.6 , we have N 6 * > 0 , N 1 * = N 2 * = N 3 * = N 4 * = N 5 * = 0 for larger N 6 0 , but N 1 * > 0 also for smaller N 6 0 (see Figures 9C–F); (3) for ϵ > 0.73 , K 1 * > 0 , K 2 * = K 3 * = K 4 * = K 5 * = 0 , N 6 * > 0 , N 1 * = N 2 * = N 3 * = N 4 * = N 5 * = 0 (complete ecological collapse, independent of N 6 0 , see Figures 9G,H). To summarize, for μ 6 < μ 1 , we end up either with N 1 * > N 6 * > 0 (near complete ecological collapse) or N 6 * > N 1 * = 0 (complete ecological collapse). For smaller μ 6 , this transition occurs at smaller value of ϵ (between 0.3 and 0.4 for μ 6 = 0.01 , and between 0.6 and 0.9 for μ 6 = 1 ). For μ 6 < μ 1 , there is (4) an additional nonlinear oscillation regime between the two equilibrium phases (see Figures 9I,J, and Section 6 in the Supplementary Material for their phase portraits). This last scenario corresponds to all species co-existing, and therefore biodiversity can potentially increase.

For μ 6 > μ 1 , the invasion fails with N 1 * > N 6 * = 0 (complete ecological collapse) independent of N 6 0 (see Figures 9K,L)). We found no signs of nonlinear oscillations whatever ϵ is. We suspect that ecologists may not be aware of this possibility, where the invasion fails, but the ecosystem collapses nonetheless. If we compare this μ 6 > μ 1 core invasion to the μ 6 > μ 2 periphery invasion, we find in the latter the invasion also fails, but the ecosystem fragmented, and thus did not collapse. This system of non-overlapping niches is what May foresaw can be accomplished slowly through gradual competition, but it seems like it can also be accomplished rapidly through a failed periphery invasion.