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Knowledge based analysis of continental population and migration dynamics
Technological Forecasting & Social Change 151 (2020) 119848
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Knowledge based analysis of continental population and migration dynamics
T
Mustafa M. Aral Civil Engineering Department, Bartin University, Bartin 74100, Turkey
A R T I C LE I N FO
A B S T R A C T
Keywords: Population dynamics Continental population Continental migration Mathematical model
Continental migration studies range from elaborate recording of periodic migration data to regression analysis to statistical models that may combine several sources of quantitative and qualitative data. It is the writer's observation that continuous mathematical modeling has not been attempted to estimate continental migration because of the complexity of the governing mathematical models. In this study the writer proposes a continuous mathematical model to estimate continental population and migration trends. The proposed model is based on knowledge-based population dynamics model developed earlier which was used to estimate global population levels and stability of world population under various stress scenarios. In this study one of these models are extended to include continental population and continental migration concepts. Resulting mathematical model is calibrated using historical continental population data which is a reliable data source. If historical continental migration is a zero-sum process, the outcome of the calibrated model yields continental population growth and intercontinental migration estimates. Results obtained are in line with global projections that are made in other studies. The proposed model is also used for future projections.
1. Introduction Historical demographic data analysis and future projections of population trends are not only useful but necessary data sources that are extensively used in social, economic and infrastructure planning of nations. The United Nations Development Program (UNDP) introduced the concept of human security as an important component of national and territorial security, which involves economic, environmental, health, food, personal/community and political aspects of people's wellbeing (Commission on Human Security, 2003). Since its introduction, this interdisciplinary concept has increasingly been scrutinized, but the consensus is that it provides a good road map for our understanding of the reasons behind continental migration and its effects on continental population (Paris and Human Security, 2001). International migration data is scarcely available, not well documented and appear in various databanks under variable standards. Lack of consistent and reliable availability of this data is the main source of uncertainty in global population projections. As stated in (Abel, 2018): “The accurate prediction of future international migration is one of the most difficult challenges in long-run population projections.” Yet, as fertility and mortality rates continue to fall in the developing world, migration is going to be more and more important in shaping continental trends in world demographics (Lee, 2011). Main drivers of population dynamics of a
region in terms of birth rates and mortality excluding migration are reasonably well understood. However, why people move from one region or country to several other possible destinations depends on so many factors and parameters that it is almost impossible to analyze these trends in micro scale terms and there lies the difficulty in modeling efforts (Massey et al., 1993; Bijak and Wiśniowski, 2010; Bijak, 2011, 2012). From this perspective, continental migration problem can be a good example of a complex system problem. Complex systems, in addition to being composed of many unknown variables, as in continental migration case, due to their internal links and feedback mechanisms, the behavior of complex systems is difficult predict when the system is stressed. When stressed, the dynamic interaction of the components of complex systems may yield surprising and unexpected system responses. Over long periods complex systems not only experience change unpredictably, but also, they change how they change (Aral, 2014). Similarly, since world migration trends depend on factors such as lack of adequate infrastructure, violent conflict, public health, climate change and economic poverty trap, and since it is equally difficult to predict future trends of these parameters, it seems predicting migration patterns that depend on these parameters would be a more arduous task. As of now world population trends are in stable range and population dynamics analysis does not necessitate the tipping point
E-mail address: [email protected]. https://doi.org/10.1016/j.techfore.2019.119848 Received 27 July 2019; Received in revised form 12 November 2019; Accepted 16 November 2019 0040-1625/ Published by Elsevier Inc.
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(Commission on Human Security, 2003). While refugees can be provided with some economic rights and a path to full citizenship, asylum seekers cannot. Thus, migrants, refugees and asylum seekers are not necessarily the same group of people from a legal standpoint in reporting in Turkey. There are several other criteria and definitions in other nations. Noting these differences, this study is using “human migration” and “migrant” in the inclusive sense for all these categories since the model developed in this study does not provide for distinction among the categories that are described above. In the contemporary literature the three principles that are used in the development of deterministic population models are as follows: (i) demographic models in which rate of change of population is a function of population (Foerster et al., 1960); (ii) information based models that are built on (i) in which it is assumed that populations recognize, store and process information but does not create knowledge from information and this process effects population growth (Akaev and Sadovnichy, 2010; Akaev and Sadovnichy, 2011; Kapitza, 1992; Kapitza, 1996; Miranda and Lima, 2010; Miranda and Lima, 2011); and, (iii) knowledge based models that are again built on (i) but in this case populations produce knowledge for their survival based on the information recognized, stored and processed (Dolgonosov, 2012; Dolgonosov and Naidenov, 2006; Dolgonosov, 2016; Okuducu and Aral, 2017). In this study, the third category of modeling procedure is used to develop deterministic models for continental population growth and migration. In this choice the writer does not claim that knowledgebased population models will produce the best results for the near- or long-term population trends. As indicated in (Aral, 2013), that would be a rather difficult proposition. The writer also acknowledges that there is no other alternative to computer simulations if one wants to predict the future. Given these observations, although there are other modeling alternatives, the writer chose to proceed with the use of knowledge-based models to address the goals of this study. The recent statistics on global migration indicate that there were around 244 million international migrants in the world in 2015. This equates to 3.3 percent of the global population (International Organization for Migration, 2018). It is important to note that this is a small percentage of global population. Thus, remaining within one's country of birth seems to be the norm. Moreover, majority of migration does not occur across continental borders. Much larger numbers migrate within countries of a continent which is estimated to be 740 million internal migrants in 2009 (International Organization for Migration, 2018). Although these numbers seem small relative to world population, they are significant numbers for some destination countries in which fertility and mortality rates are in continuous decline. Further, over time cross-border migration numbers are volatile and show an increasing trend which is also alarming for destination countries. Thus, continental migration is going to be on the agenda of many developed nations and will shape the trends in world demographics. Good statistical data exist on global migration patterns which is extensively used in this study for comparison (International Organization for Migration, 2018). Other continental migration study outcomes that appear in the literature cover a range from elaborate recording and displaying of periodic migration data (Abel, 2013; Abel and Sander, 2014) to regression analysis (Kupiszewska and Nowok, 2008; Willekens, 1994) to stochastic models (Ševčíková and Raftery, 2016) that may combine and analyze several sources of quantitative and qualitative data. These topics are out of the scope of the current study.
applications and concepts which is a characteristic methodology for complex systems analysis. Thus, continental migration estimation and its consequences can be handled through risk characterization and adaptation methodologies assuming that the behavior of the system is in stable equilibrium range (Aral, 2013, 2014). Based on this assumption, in this study the purpose is to develop continuous mathematical models that rely on classical knowledgebased models that exist in the literature (Dolgonosov, 2012; Dolgonosov and Naidenov, 2006; Dolgonosov, 2016; Okuducu and Aral, 2017). In this study, first the global population dynamics models are adopted to continental population model concept without any modification in its system definition. Next, continental migration terms are included to the analysis with the assumption that the population system modeled is a zero-sum model. In other words, due to continental migration populations are not lost. Arguably this is a restriction to the model developed in this study. However, since the yearly migration levels are in the order of hundreds of thousands and the loss to migrating population is expected to be much less than thousands during migration, the zero-sum definition used in this study is a reasonable assumption. Resulting mathematical model is calibrated using only the historical continental population data which is a reliable database. Continental migration data, which is scarcely available and not reliable is not used during calibration. Finally, the resulting calibrated zero-sum model yields the continental migration estimates as the outcome from which future predictions may also be made. The proposed model does not suffer from convergence towards a zero net migration assumption that is used in the literature but hardly justified (Abel, 2018; United Nations, DESA/Population Division, 2017). The result is a continuous model that can be used for future projections based on the assumption that the use of the historical trends on continental population is justified. 2. Literature review and definitions Being human-centric (as opposed to state-centric), human security concept adopted by UNDP (Commission on Human Security, 2003) is not in conflict with the conventional understandings of national security, which is arguably a necessary but insufficient condition for the former. Historically, several authoritarian and totalitarian states have proved that their citizens’ personal and community security may cease to exist even when national borders are effectively protected. The Commission on Human Security (CHS) has studied human security as it pertains to poverty, environment, violent conflict, migration, health, education, and governance (Commission on Human Security, 2003), all of which has a cause and effect relation to internal or continental migration. One of the likely outcomes of human insecurity is clearly the migration outcome. The International Organization for Migration (IOM) (Commission on Human Security, 2003), defines the term migrant as, “any person who is moving or has moved across an international border or within a State away from his/her habitual place of residence, regardless of (1) the person's legal status; (2) whether the movement is voluntary or involuntary; (3) what the causes for the movement are; or (4) what the length of the stay is.” On the other hand, a refugee is someone “who has been forced to flee his or her country because of persecution, war or violence,” and an asylum seeker is someone “whose request for sanctuary has yet to be processed” (Commission on Human Security, 2003). Although the term “migrant” seems to include “refugee” and “asylum seeker,” the legal frameworks of different countries can make a significant difference in migrant data preparation and outcome. This is one of the reasons for inaccurate and incompatible databases that exists in the literature on migration, which makes continental migration analysis based on this data extremely difficult. For example, Turkey considers only migrants coming from Europe as refugees, whereas it considers migrants coming from “East” including Africa and other underdeveloped countries as asylum seekers
3. Mathematical model Knowledge based mathematical model for world population can be associated with the minimization principle of a knowledge function over time (Dolgonosov, 2016),
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Technological Forecasting & Social Change 151 (2020) 119848
M.M. Aral t2
∫ L (q, q˙ , t ) dt = min
calibration constants. When these definitions are substituted in Eqs. (9, (8) one may obtain,
(1)
t1
⎛ N˙ = (c1 w (q) − w′ (q)) N 2 ⎜1 − ⎜ ⎝
where L (q, q˙ , t ) is a knowledge production function and q(t) is the knowledge function. The minimization problem given in Eq. (1) may also be stated as the identification of a function L (q, q˙ ) which satisfies the Lagrangian,
d dL dL − =0 dt dq˙ dq
w (q) = b1 αqtotal + b1
It is shown in (Dolgonosov, 2016) that the nontrivial solutions of Eq. (2) is only associated with quadratic and higher order terms of the L (q, q˙ ) function which can be given as an infinite series, (3)
a (q) q˙ 2 + O (q˙ 4 ) (1 − c (q) q˙
(4) a3 (q) a2 (q)
> 0 , are idenwhere the functions a(q) ≡ a2(q) > 0 and c (q) = tified as resource consumption and breaking knowledge productions functions respectively. Substituting Eq. (4) into Eq. (2) and omitting fourth and higher order terms the generalized knowledge dynamics equation can be obtained as (Dolgonosov, 2016), q¨ = k (q) q˙ 2 [1 − b (q) q˙]
a′ (q) 2a (q)
;
c′ (q) k (q)
(6)
(7)
Substituting Eq. (7) into Eq. (5), the knowledge-based population model, or the so-called N-K equation can be obtained as follows,
N ⎞ ⎟ N˙ = r (q) N 2 ⎜⎛1 − K (q) ⎠ ⎝
(8)
where K(q) and r(q) are identified as the potential carrying capacity of Earth and growth coefficient at knowledge level q, respectively. These functions can be derived as,
r (q) = k (q) w (q) − w′ (q);
K (q) =
r (q) k (q) b (q) w (q)2
(12)
With increasing population, since knowledge level production becomes a function of technologic innovations, the humanity may not maintain the homeostasis between nature and human populations, and the equilibrium breaks down due to environmental problems that may be created by the uncontrolled application of the high rate of knowledge created. This outcome can be tied to the current issues’ humans are facing, i.e. global warming, sea level rise, ozone depletion, proliferation of diseases etc. (Aral, 2013, 2014). To solve these problems, one may argue that humanity must increase its productivity and produce environmentally friendly technologies to overcome the problems and create a sustainable balance between population growth and Earth's resources. This analysis was treated in (Aral, 2013, 2014; Okuducu and Aral, 2017) and will not be repeated here. The global population dynamics model described in Eq. (10) may also be utilized for continental population growth including the migration dynamics that may develop between continents. We will identify this model as the N-K-C model where the letter “C” is used as the continent identifier. Although the mathematical definition of this model is straight forward, which is based on the above described knowledgebased model concept, one must be careful with the calibration process that will be used in the identifications of the constants of the resulting model. The reason behind this observation is associated with the limited availability and reliability of long-term continental migration data. As discussed in the earlier section, this database is not generally available. If it is available, it is not reliable due to the reasons explained earlier or if available it is not sufficiently long term to justify its use during the calibration of the N-K-C model. Whereas, as it is well known that, historical world population and continental population data is readily available, and it is reliable. First, we present the continental mathematical Model A which is based on the sequence of Eqs. (7–12) as given above. Given Eq. (8) we can write,
In Eq. (6) the superscript prime refers to the derivative of the function with respect to q, b(q) is a function of resource limitation and resource consumption parameters, and k(q) is given as the ratio of the rate of resource consumption to resource consumption. Since knowledge production is a function of population and productivity of humans, the rate of knowledge production can be defined as a function of a productivity function w(q) and population N(t),
q˙ (t ) = w (q) N (t )
∫ w (q) N (t ) dt 0
(5)
b (q) = c (q) +
(11)
tn
qtotal =
where,
k (q) = −
(10)
where the coefficient α is interpreted as the proportion of the total knowledge produced that is environmentally friendly, which yields technologic knowledge qtech = αqtotal ; 0 < α < 1, and b1 is defined as average person's human productivity independent of technologic innovations which may represent the knowledge level of civilizations. At this constant productivity level, humanity may sustain its existence in a homeostasis with the environment at a certain population level (Dolgonosov, 2016; Okuducu and Aral, 2017). Given Eq. (7) we can define,
where the coefficients of this series a2(q) and a3(q) are functions of q. Eq. (3) can be written as,
L (q, q˙ ) =
c1 c 2 w (q)2
⎞ ⎟ ⎟ ⎠
Further, without loss of generality, among several possible choices (Okuducu and Aral, 2017), the following linear definition of the productivity function will be considered here since w(q) need to be defined,
(2)
L (q, q˙ ) = a2 (q) q˙ 2 + a3 (q) q˙ 3 + O (q˙ 4 )
N c1 w (q) − w′ (q)
(9)
In these equations r(q) > 0 and K(q) > 0 by definition of w(q) > 0 and w′ < w. Given Eq. (7) it is possible to define several productivity functions to solve for the total knowledge that maybe generated at time tn. Using these productivity functions and Eq. (8) there are three possible models that can be formulated which are identified as: (i) the classical logistic function model; (ii) carrying capacity independent Model A; and, (iii) carrying capacity independent Model B. These three models and the analysis based on these models has been demonstrated in (Okuducu and Aral, 2017) and will not be repeated here. In this study the writer has selected to use Model A of Okuducu and Aral, 2017) since it is easier to follow and adapt. With the definitions and simplifications given in (Okuducu and Aral, 2017), in Model A, k (q) = c1 and b (q) = c2 where these functions were treated as
Nj ⎞ ⎤ ⎡ ⎛ ; j = af , as, eu, na, sa oc N˙ j = ⎢r j (qj )(Nj )2 ⎜1 − Kj (qj ) ⎟ ⎥ ⎝ ⎠⎦ ⎣
(13)
where the subscript j refers to the continents, Africa (af), Asia (as), Europe (eu), North America (na), South America (sa) and Oceania (oc). In this mathematical form the governing equation for the continents is the same as the world population model given in Eq. (8) or (10). As such all underlying assumptions and definitions will follow the concepts defined in the world population model which yields, 3
Technological Forecasting & Social Change 151 (2020) 119848
M.M. Aral
Fig. 1. Continental population trends obtained from the calibrated mathematical model: (a) Africa Population; (b) Asia Population; (c) Europe Population; (d) North America Population; (e) South America Population; and, (f) Oceania Population.
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linked at the migration flow terms which can be solved numerically. One should also notice that each ordinary differential equation component of the simultaneous system of equations also has an internal ordinary differential equation to solve for the knowledge function given in Eq. (17). In conclusion the outcome is a rather complicated nonlinear simultaneous system of equations representing continental population growth and inter-continental migration. One should notice that the population growth component of the model is already calibrated in (Okuducu and Aral, 2017). The only difference for the continental application is the initial knowledge value qjo of the continents which is the only calibration coefficient of the growth model. This leaves only the djk and dkj constants as the additional calibration parameters of Eq. (16). Calibration of Eq. (16) will be performed based on continental population data which is available and reliable. Migration flow data is not used in this calibration process since that data is not reliable as described earlier. Since this is a zero-sum model, i.e. migration outflow from one continent towards another continent is an inflow migration to the other continent without loss of population, one should notice that an outflow term (−djk Nj ) for one continent will be an inflow term (+dkj Nk ) for another continent for all (j, k) where (j ≠ k). The calibrated model will not only yield population growth of the continents but will also yield the migration fluxes between continents. The outcome of this analysis is presented in the next section.
Fig. 2. Total World Population trend obtained from the mathematical model.
r j (qj ) = c1 w (qj ) − w′ (qj ) ; Kj (qj ) =
c1 w (qj ) − w′ (qj )
; j = af , as,
c1 c2 w (qj )2
(14)
eu, na, sa oc
4. Results and discussion
where c1, c2 and w(qj) are as defined earlier but now qj represent continental knowledge generation based on continental population, Eq. (7). In this study, not only the assumptions and definition that are used for Model A are the same but also the calibrated model coefficient for Model A will not be modified and used as is, as given in (Okuducu and Aral, 2017). For example, the coefficients used in (Okuducu and Aral, 2017), such as,
The calibrated model given in Eq. (16) yields the trends shown in Fig. 1 for continental population. One should notice that in these figures the data range between 1860 and 2018 are the recorded population data (Okuducu and Aral, 2017; United Nations, DESA/Population Division, 2017) (shown as red dots in decades) that is used for calibration and statistical analysis. The data beyond year 2018 and in the range between 2020 and 2100 are the estimated data obtained from (Statista, 2019) (shown as green dots in decades). Since this data set is an estimation of continental population it is not used in the calibration of the mathematical model and it is not included to the statistical analysis given below. This data is shown here for visual comparison of the outcome of the mathematical model developed in this study and the estimated outcome obtained by some other means in another study (Statista, 2019). The total population shown in Fig. 2 is simply obtained as the sum of continental population results obtained from Eq. (16). The black dots represent the analytical model results and this data is not used during calibration of the mathematical model developed in this study. As can be visually seen in Fig. 1, the outcome of the mathematical model follows the trend of the historical recorded data for each continent and for the world population as shown in Fig. 2 rather well. A statistical analysis is also performed to quantify this observation using the coefficient of determination analysis and Root Mean Square Error (RMSE). The coefficient of determination (denoted by R2 in Table 1) is a key output to evaluate the proportion of the variance between a variable that is predicted based on another independent variable and RMSE
(15)
b1 = 0.0007 ; c1 = 6.994 ; c2 = 97.94 ; α = 0.6
are kept as is and are not used as calibration parameters. This is based on the observation that population growth for each continent will only be a function of knowledge produced in each continent based on Eq. (12) and will no longer depend on the calibration constants determined in (Okuducu and Aral, 2017). Only the initial value of the knowledge function, qjo , is adjusted for each continent as the calibration parameter of the growth model since starting knowledge value of each continent is expected to be different. In the next step the continental migration terms will be added to Eq. (13) to yield population dynamics model for the continents with continental migration flows.
Nj ⎞ ⎤ ⎡ ⎛ N˙ j = ⎢r j (qj )(Nj )2 ⎜1 − − Kj (qj ) ⎟ ⎥ ⎝ ⎠⎦ ⎣ ⎧ j = af , as, eu, na, sa oc ⎫ k = af , as, eu, na, sa oc ⎨ ⎬ j≠k ⎩ ⎭
∑ djk Nj + ∑ dkj Nk k
;
k
(16)
where, rj(qj) and Kj(qj) are as given in Eq. (14), migration outflow (negative summation terms) and migration inflow (positive summation terms) are associated with the coefficients djk and dkj are chosen as the calibration constants in addition to initial knowledge function value of each continent qjo . In the outflow terms the superscript denotes the destination continent. In the inflow terms the subscript denotes the origination continent. Given Eq. (7) we also notice that,
q˙ j = w (qj ) Nj
; j = af , as, eu, na, sa oc
Table 1 Coefficient of Determination and RMSE for Continental and Total Population Estimates.
(17)
and,
w (qj ) = b1 qj + b1
; j = af , as, eu, na, sa oc
(18)
Eq. (16) is a simultaneous ordinary differential equation that are 5
Continental Population (billions)
qjo
R2
RMSE
Africa Pop. Asia Pop. Europe Pop. North Am. Pop. South Am. Pop. Oceania Pop. Total Pop.
1.88 1.04 15.5 30.0 18.0 0.03 –
0.94 0.98 0.98 0.99 0.99 0.91 0.98
0.095 0.194 0.023 0.009 0.002 0.006 0.310
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Table 2 Calibrated Coefficients of the Continental Migration Model. djk
Africa
Africa Asia Europe N. America S. America Oceania
– 4.9 4.5 2.0 1.0 1.0
× × × × ×
Asia
10−4 10−3 10−11 10−7 10−10
1.1 – 1.0 1.2 5.1 6.3
Europe
× 10−12 × × × ×
10−11 10−12 10−9 10−9
1.2 1.0 – 5.2 5.0 1.2
× 10−11 × 10−12 × 10−12 × 10−6 × 10−6
quantifies how different the two data sets are. As such, coefficient of determination is an indicator of the correlation between the two data sets. The range of R2 is (0–1) and results close to 1 indicate good correlation. RMSE quantifies how different a set of values are. The smaller an RMSE value, the closer predicted and observed values are. Both results are given in Table 1, which indicates good correlation. Since the population of Africa and Asia are very large (billions) the coefficients of these continents are small but the products representing the migration trends are in the order of thousands. The population of Oceania is very small relative to the other continents and thus its plot appears as a step function (Table 2). Given these results, it is predicted that Africa will show an increasing population trend and will reach ~4 billion people around 2100, Fig. 1(a). Asia's maximum population is estimated to be ~5.2 billion and will be reached around 2040. After that a decline in Asia population is predicted, Fig. 1(b). European population reaches a peak of ~0.7 billion in 2030 and a slight decline is observed after that until 2100. This predicted value is slightly below observed values in 2018. The decline in European population predicted in (Statista, 2019) is much sharper than the one predicted in this study, Fig. 1(c). North American population reaches an estimated value of ~0.5 billion people, which is higher than the predicted values given in (Statista, 2019) and it is reached earlier as seen in Fig. 1(d). South America population flattens out at ~0.75 billion people in year 2050 and shows a steady level until 2100, Fig. 1(e). In (Statista, 2019) a decline in South American population is predicted which is not seen in the results predicted in this study until 2100. Oceania is continuing with its increasing trend and reaching ~0.07 billion people in year 2100, Fig. 1(f). All these results are in expected rages of continental population trends. The results for the total population are given in Fig. 2, which is calculated as the yearly sum of all continental population estimates. This outcome is also good with an R2 value of 0.98 and RMSE value of 0.31. With this outcome the total population estimate for the world reaches to ~11 billion people in year 2100 which is in the range of most predictions made in the literature. A comparison of the estimated values obtained in (Statista, 2019) (green dots) and analytical model results is also shown in Fig. 2. The yearly population growth for each continent excluding migration inflow and out flow is also calculated as shown in Fig. 3. It is emphasized that the results shown in Fig. 3 are not cumulative values of population growth but yearly estimates. As seen in Fig. 3 yearly population growth in Asia and Africa is initially in a sharp increasing trend. In 2010 a peak yearly increase of ~0.06 billion people is estimated for Asia and the peak for Africa is ~0.051 billion people and it is reached in 2060. After that a sharp decline of yearly population is predicted in both continents reaching negative population growth in Asia after 2040 and in Africa after 2090. The yearly population growth in Europe is slightly increasing initially and this turns into a declining trend after 1950. South America, North America and Oceania yearly population growth is mild and stable initially and for North Amerian this trend goes negative after 2050. This implies that any increase in the population of these continents are attributed to migration inflows. The yearly net migration outflow estimated from each continent is shown in Fig. 4. It is again emphasized that these are yearly values and
N. America
S. America
4.2 × 10−11 3.35 × 10−4 1.35 × 10−3 – 1.1 × 10−5 1.2 × 10−9
1.0 1.0 2.3 7.2 – 1.1
× × × ×
10−11 10−12 10−3 10−9
× 10−9
Oceania 1.4 1.3 4.5 2.0 1.1 –
× × × × ×
10−12 10−11 10−4 10−9 10−6
Fig. 3. Yearly continental population growth estimates.
Fig. 4. Yearly continental migration outflow estimates.
are not cumulative. The cumulative estimates yield the results that are given in Fig. 1. As seen in Fig. 4 historically the net migration outflow is the highest in Europe until 1940s. After that a sharp decline is followed by steady outflow after 2050. Feeder continents like Africa and Asia is in a continuously increasing trend until 2050 for africa and 2100 for Asia. Net outflow in North and South America is small relative to Asia, Africa and Europe. For Europe to maintain its high net outflow migration status, it seems Europe is going to be a gate way continent to other continents in a zero sum population trend. Oceania net outflow migration estimate is negligible when compared to the other continents.
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5. Conclusion
Bijak, J., Wiśniowski, A., 2010. Bayesian forecasting of immigration to selected European countries by using expert knowledge. J. R. Stat. Soc. Series A Stat. Soc. 173 (4), 775–796. https://doi.org/10.1111/j.1467985X.2009.00635.x. Bijak, J., 2011. Forecasting International Migration in Europe: A Bayesian View. Springer Netherlands, Dordrecht. https://doi.org/10.1007/978-90-481-8897-0. Bijak, J., 2012. Migration Assumptions in the UK National Population Projections: Methodology review [electronic resource]. Office for National Statistics, Southampton. http://www.ons.gov.uk/ons/guide-method/method-quality/specific/ population-and-migration/population-projections/npp-migrationassumptionsmethodology-review/index.html. Aral, M.M., 2014a. Perspectives and challenges on climate change and its effects on water quality and health. Water Qual. Health. https://doi.org/10.1007/s12403-0140125-7. Aral, M.M., 2013. Climate change and human population dynamics. Water Qual. Health. https://doi.org/10.1007/s12403-013-0091-5. Aral, M.M.2014. Climate change and persistent high temperatures: does it matter?2(45):1–8. doi: 10.3389/fenvs.2014.00045. Dolgonosov, B.M., 2012. An informational dynamics of civilizations. Biosphere 4 (3), 263–279. Dolgonosov, B.M., Naidenov, V.I., 2006. An informational framework for human population dynamics. Ecol. Model. 198, 375–386. Dolgonosov, B.M., 2016. Knowledge production and world population dynamics. Tech. Forcast. Soc. Change 103, 127–141. Okuducu, M.B., Aral, M.M., 2017. Knowledge based dynamic human population models. Tech. Forecast. Soc. Change 122, 1–11. http://dx.doi.org/10.1016/j.techfore.2017. 05.008. United Nations, DESA/Population Division. 2017. World Population Prospects. https:// population.un.org/wpp/. (Accessed, May 8, 2019). Commission on Human Security, 2003. Human Security Now. CHS, New York Available online: https://reliefweb.int/sites/reliefweb.int/files/resources/ 91BAEEDBA50C6907C1256D19006A9353-chs-security-may03.pdf (Accessed on 22.03.2019). Foerster, H., Mora, P.M., Amiot, L.W., 1960. Doomsday: friday, 13 November, A.D. 2026. Science 132, 1291–1295. Akaev, A.A., Sadovnichy, V.A., 2010. Mathematical model of population dynamics with the world population size stabilizing about a stationary level. Dokl. Math. 82 (3), 978–981. Akaev, A.A., Sadovnichy, V.A., 2011. Global demographic models as the basis for strategic forecast. Projects and Risks of the Future: Concepts, Models, Instruments, Forecasts. Krasand, Moscow, pp. 17–44. Kapitza, S.P., 1992. Mathematical model of world population growth. Math. Model. 4 (6), 65–79. Kapitza, S.P., 1996. Phenomenological theory of world population growth. PhysicsUspekhi 166 (1), 63–80. Miranda, L.C.M., Lima, C.A.S., 2010. On the logistic modeling and forecasting of evolutionary processes: application to human population dynamics. Technol. Forecast. Soc. Chang. 77, 699–711. Miranda, L.C.M., Lima, C.A.S., 2011. On the forecasting of the challenging world future scenarios. Technol. Forecast. Soc. Chang. 78, 1445–1470. International Organization for Migration. 2018. World Migration Report – 2018. The United Nations Migration Agency, 17 route des Morillons, P.O. Box 17, 1211 Geneva 19, Switzerland. 347p. ISBN 978-92-9068-742-9. Abel, G.J., 2013. Estimating global migration flow tables using place of birth data. Demogr. Res. 28 (18), 505–546. https://doi.org/10.4054/DemRes.2013.28.18. Abel, G.J., Sander, N., 2014. Quantifying global international migration flows. Science 343 (6178), 1520–1522. https://doi.org/10.1126/science.1248676. Kupiszewska, D., Nowok, B., 2008. Comparability of statistics on international migration flows in the European Union. In: Willekens, F., Raymer, J. (Eds.), International Migration in Europe: Data, Models and Estimates. Wiley, London, pp. 41–73. Willekens, F., 1994. Monitoring international migration flows in Europe. Eur. J. Population 10 (1), 1–42. https://doi.org/10.1007/BF01268210. Ševčíková, H., Raftery, A.E., 2016. bayesPop: probabilistic population projections. J. Stat. Softw. 75 (5). https://doi.org/10.18637/jss.v075.i05. Statista. 2019. Continental Population Estimates:https://www.statista.com/statistics/ 272789/world-population-by-continent/(Accessed July 18, 2019).
A knowledge based analytical model developed earlier (Okuducu and Aral, 2017) is used to estimate continental migration trends in the world. To the best knowledge of the author this is the first use of a continuous analytical model to obtain continental migration estimates in the world. Other applications in this field of study include statistical models and regression models as they are summarized in the literature review section of the paper. The analytical model developed assumes that continental migration is a zero-sum event and the inherent implication of the use of the calibrated model in predictive analysis assumes that historical trends on migration flows will be representative of the future events as well. These are not that restrictive assumptions and they are used in all predictive models of population analysis. The statistical accuracy of the model calibration is satisfactory indicating that the calibrated model produces a good fit to the historical data. Predictive results show that world population may reach ~11 billion people in year 2100. The Africa and Asia continents will continue to be the main feeder of migration flows to other continents in years to come. The European continent is going to be the gateway continent to North and South America for migration flows. Oceania is going to show a steady but very mild increase in population mainly due to migration inflows. The results presented in this study are inline and confirming the trends that are reported in the literature. However, a continuous analytical model may have some advantages over other approaches in that a calibrated model may easily be used to analyze what if scenarios to estimate the effects of changing conditions. For example, as demonstrated in other studies (Aral, 2013, 2014), inclusion of the effects of climate change on continental migration would be relatively easy to analyze. This type of an analysis can be done as a global climate trend analysis or the analysis may be broken down to the continental climate effects analysis as well. These studies are currently under development and out of the context of the current paper. Author contributions M.M.A. is the sole author of the paper. The concept, mathematical model development and coding, calibration of the model and preparation of this manuscript is done by M.M.A. Declaration of Competing Interest The author declares no conflict of interest. References Commission on Human Security, 2003. Human Security Now. CHS, New York Available online: https://reliefweb.int/sites/reliefweb.int/files/resources/ 91BAEEDBA50C6907C1256D19006A9353-chs-security-may03.pdf (accessed on 24.03.2019). Paris, E.G., Human security, R., 2001. Paradigm shift or hot air. Int. Secur. 26 (2), 87–102. Abel, G.J., 2018. Non-zero trajectories for long-run net migration assumptions in global population projection models. Demogr. Res. 38 (54), 1635–1662. https://doi.org/10. 4054/DemRes.2018.38.54. Lee, R.D., 2011. The outlook for population growth. Science 333 (6042), 569–573. https://doi.org/10.1126/science.1208859. Massey, D.S., Arango, Hugo, J., Kouaouci, G.J., Pellegrino, A., Taylor, J.E., 1993. Theories of international migration: a review and appraisal. Popul. Dev. Rev. 19 (3), 431–466.
Dr. Aral specializes in large scale environmental simulations in surface water and groundwater specialization areas. A licensed professional engineer (PE), he also has expertise in environmental exposure analysis, exposure-dose reconstruction, health risk assessment, population dynamics analysis, climate change effects on the environment. He has over 100 publications in these areas and actively pursues a state-of-the-art research program in these topics within the activities of the Multimedia Environmental Simulations Laboratory (MESL) at Georgia Institute of Technology USA and abroad.
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Technological Forecasting & Social Change journal homepage: www.elsevier.com/locate/techfore
Knowledge based analysis of continental population and migration dynamics
T
Mustafa M. Aral Civil Engineering Department, Bartin University, Bartin 74100, Turkey
A R T I C LE I N FO
A B S T R A C T
Keywords: Population dynamics Continental population Continental migration Mathematical model
Continental migration studies range from elaborate recording of periodic migration data to regression analysis to statistical models that may combine several sources of quantitative and qualitative data. It is the writer's observation that continuous mathematical modeling has not been attempted to estimate continental migration because of the complexity of the governing mathematical models. In this study the writer proposes a continuous mathematical model to estimate continental population and migration trends. The proposed model is based on knowledge-based population dynamics model developed earlier which was used to estimate global population levels and stability of world population under various stress scenarios. In this study one of these models are extended to include continental population and continental migration concepts. Resulting mathematical model is calibrated using historical continental population data which is a reliable data source. If historical continental migration is a zero-sum process, the outcome of the calibrated model yields continental population growth and intercontinental migration estimates. Results obtained are in line with global projections that are made in other studies. The proposed model is also used for future projections.
1. Introduction Historical demographic data analysis and future projections of population trends are not only useful but necessary data sources that are extensively used in social, economic and infrastructure planning of nations. The United Nations Development Program (UNDP) introduced the concept of human security as an important component of national and territorial security, which involves economic, environmental, health, food, personal/community and political aspects of people's wellbeing (Commission on Human Security, 2003). Since its introduction, this interdisciplinary concept has increasingly been scrutinized, but the consensus is that it provides a good road map for our understanding of the reasons behind continental migration and its effects on continental population (Paris and Human Security, 2001). International migration data is scarcely available, not well documented and appear in various databanks under variable standards. Lack of consistent and reliable availability of this data is the main source of uncertainty in global population projections. As stated in (Abel, 2018): “The accurate prediction of future international migration is one of the most difficult challenges in long-run population projections.” Yet, as fertility and mortality rates continue to fall in the developing world, migration is going to be more and more important in shaping continental trends in world demographics (Lee, 2011). Main drivers of population dynamics of a
region in terms of birth rates and mortality excluding migration are reasonably well understood. However, why people move from one region or country to several other possible destinations depends on so many factors and parameters that it is almost impossible to analyze these trends in micro scale terms and there lies the difficulty in modeling efforts (Massey et al., 1993; Bijak and Wiśniowski, 2010; Bijak, 2011, 2012). From this perspective, continental migration problem can be a good example of a complex system problem. Complex systems, in addition to being composed of many unknown variables, as in continental migration case, due to their internal links and feedback mechanisms, the behavior of complex systems is difficult predict when the system is stressed. When stressed, the dynamic interaction of the components of complex systems may yield surprising and unexpected system responses. Over long periods complex systems not only experience change unpredictably, but also, they change how they change (Aral, 2014). Similarly, since world migration trends depend on factors such as lack of adequate infrastructure, violent conflict, public health, climate change and economic poverty trap, and since it is equally difficult to predict future trends of these parameters, it seems predicting migration patterns that depend on these parameters would be a more arduous task. As of now world population trends are in stable range and population dynamics analysis does not necessitate the tipping point
E-mail address: [email protected]. https://doi.org/10.1016/j.techfore.2019.119848 Received 27 July 2019; Received in revised form 12 November 2019; Accepted 16 November 2019 0040-1625/ Published by Elsevier Inc.
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(Commission on Human Security, 2003). While refugees can be provided with some economic rights and a path to full citizenship, asylum seekers cannot. Thus, migrants, refugees and asylum seekers are not necessarily the same group of people from a legal standpoint in reporting in Turkey. There are several other criteria and definitions in other nations. Noting these differences, this study is using “human migration” and “migrant” in the inclusive sense for all these categories since the model developed in this study does not provide for distinction among the categories that are described above. In the contemporary literature the three principles that are used in the development of deterministic population models are as follows: (i) demographic models in which rate of change of population is a function of population (Foerster et al., 1960); (ii) information based models that are built on (i) in which it is assumed that populations recognize, store and process information but does not create knowledge from information and this process effects population growth (Akaev and Sadovnichy, 2010; Akaev and Sadovnichy, 2011; Kapitza, 1992; Kapitza, 1996; Miranda and Lima, 2010; Miranda and Lima, 2011); and, (iii) knowledge based models that are again built on (i) but in this case populations produce knowledge for their survival based on the information recognized, stored and processed (Dolgonosov, 2012; Dolgonosov and Naidenov, 2006; Dolgonosov, 2016; Okuducu and Aral, 2017). In this study, the third category of modeling procedure is used to develop deterministic models for continental population growth and migration. In this choice the writer does not claim that knowledgebased population models will produce the best results for the near- or long-term population trends. As indicated in (Aral, 2013), that would be a rather difficult proposition. The writer also acknowledges that there is no other alternative to computer simulations if one wants to predict the future. Given these observations, although there are other modeling alternatives, the writer chose to proceed with the use of knowledge-based models to address the goals of this study. The recent statistics on global migration indicate that there were around 244 million international migrants in the world in 2015. This equates to 3.3 percent of the global population (International Organization for Migration, 2018). It is important to note that this is a small percentage of global population. Thus, remaining within one's country of birth seems to be the norm. Moreover, majority of migration does not occur across continental borders. Much larger numbers migrate within countries of a continent which is estimated to be 740 million internal migrants in 2009 (International Organization for Migration, 2018). Although these numbers seem small relative to world population, they are significant numbers for some destination countries in which fertility and mortality rates are in continuous decline. Further, over time cross-border migration numbers are volatile and show an increasing trend which is also alarming for destination countries. Thus, continental migration is going to be on the agenda of many developed nations and will shape the trends in world demographics. Good statistical data exist on global migration patterns which is extensively used in this study for comparison (International Organization for Migration, 2018). Other continental migration study outcomes that appear in the literature cover a range from elaborate recording and displaying of periodic migration data (Abel, 2013; Abel and Sander, 2014) to regression analysis (Kupiszewska and Nowok, 2008; Willekens, 1994) to stochastic models (Ševčíková and Raftery, 2016) that may combine and analyze several sources of quantitative and qualitative data. These topics are out of the scope of the current study.
applications and concepts which is a characteristic methodology for complex systems analysis. Thus, continental migration estimation and its consequences can be handled through risk characterization and adaptation methodologies assuming that the behavior of the system is in stable equilibrium range (Aral, 2013, 2014). Based on this assumption, in this study the purpose is to develop continuous mathematical models that rely on classical knowledgebased models that exist in the literature (Dolgonosov, 2012; Dolgonosov and Naidenov, 2006; Dolgonosov, 2016; Okuducu and Aral, 2017). In this study, first the global population dynamics models are adopted to continental population model concept without any modification in its system definition. Next, continental migration terms are included to the analysis with the assumption that the population system modeled is a zero-sum model. In other words, due to continental migration populations are not lost. Arguably this is a restriction to the model developed in this study. However, since the yearly migration levels are in the order of hundreds of thousands and the loss to migrating population is expected to be much less than thousands during migration, the zero-sum definition used in this study is a reasonable assumption. Resulting mathematical model is calibrated using only the historical continental population data which is a reliable database. Continental migration data, which is scarcely available and not reliable is not used during calibration. Finally, the resulting calibrated zero-sum model yields the continental migration estimates as the outcome from which future predictions may also be made. The proposed model does not suffer from convergence towards a zero net migration assumption that is used in the literature but hardly justified (Abel, 2018; United Nations, DESA/Population Division, 2017). The result is a continuous model that can be used for future projections based on the assumption that the use of the historical trends on continental population is justified. 2. Literature review and definitions Being human-centric (as opposed to state-centric), human security concept adopted by UNDP (Commission on Human Security, 2003) is not in conflict with the conventional understandings of national security, which is arguably a necessary but insufficient condition for the former. Historically, several authoritarian and totalitarian states have proved that their citizens’ personal and community security may cease to exist even when national borders are effectively protected. The Commission on Human Security (CHS) has studied human security as it pertains to poverty, environment, violent conflict, migration, health, education, and governance (Commission on Human Security, 2003), all of which has a cause and effect relation to internal or continental migration. One of the likely outcomes of human insecurity is clearly the migration outcome. The International Organization for Migration (IOM) (Commission on Human Security, 2003), defines the term migrant as, “any person who is moving or has moved across an international border or within a State away from his/her habitual place of residence, regardless of (1) the person's legal status; (2) whether the movement is voluntary or involuntary; (3) what the causes for the movement are; or (4) what the length of the stay is.” On the other hand, a refugee is someone “who has been forced to flee his or her country because of persecution, war or violence,” and an asylum seeker is someone “whose request for sanctuary has yet to be processed” (Commission on Human Security, 2003). Although the term “migrant” seems to include “refugee” and “asylum seeker,” the legal frameworks of different countries can make a significant difference in migrant data preparation and outcome. This is one of the reasons for inaccurate and incompatible databases that exists in the literature on migration, which makes continental migration analysis based on this data extremely difficult. For example, Turkey considers only migrants coming from Europe as refugees, whereas it considers migrants coming from “East” including Africa and other underdeveloped countries as asylum seekers
3. Mathematical model Knowledge based mathematical model for world population can be associated with the minimization principle of a knowledge function over time (Dolgonosov, 2016),
2
Technological Forecasting & Social Change 151 (2020) 119848
M.M. Aral t2
∫ L (q, q˙ , t ) dt = min
calibration constants. When these definitions are substituted in Eqs. (9, (8) one may obtain,
(1)
t1
⎛ N˙ = (c1 w (q) − w′ (q)) N 2 ⎜1 − ⎜ ⎝
where L (q, q˙ , t ) is a knowledge production function and q(t) is the knowledge function. The minimization problem given in Eq. (1) may also be stated as the identification of a function L (q, q˙ ) which satisfies the Lagrangian,
d dL dL − =0 dt dq˙ dq
w (q) = b1 αqtotal + b1
It is shown in (Dolgonosov, 2016) that the nontrivial solutions of Eq. (2) is only associated with quadratic and higher order terms of the L (q, q˙ ) function which can be given as an infinite series, (3)
a (q) q˙ 2 + O (q˙ 4 ) (1 − c (q) q˙
(4) a3 (q) a2 (q)
> 0 , are idenwhere the functions a(q) ≡ a2(q) > 0 and c (q) = tified as resource consumption and breaking knowledge productions functions respectively. Substituting Eq. (4) into Eq. (2) and omitting fourth and higher order terms the generalized knowledge dynamics equation can be obtained as (Dolgonosov, 2016), q¨ = k (q) q˙ 2 [1 − b (q) q˙]
a′ (q) 2a (q)
;
c′ (q) k (q)
(6)
(7)
Substituting Eq. (7) into Eq. (5), the knowledge-based population model, or the so-called N-K equation can be obtained as follows,
N ⎞ ⎟ N˙ = r (q) N 2 ⎜⎛1 − K (q) ⎠ ⎝
(8)
where K(q) and r(q) are identified as the potential carrying capacity of Earth and growth coefficient at knowledge level q, respectively. These functions can be derived as,
r (q) = k (q) w (q) − w′ (q);
K (q) =
r (q) k (q) b (q) w (q)2
(12)
With increasing population, since knowledge level production becomes a function of technologic innovations, the humanity may not maintain the homeostasis between nature and human populations, and the equilibrium breaks down due to environmental problems that may be created by the uncontrolled application of the high rate of knowledge created. This outcome can be tied to the current issues’ humans are facing, i.e. global warming, sea level rise, ozone depletion, proliferation of diseases etc. (Aral, 2013, 2014). To solve these problems, one may argue that humanity must increase its productivity and produce environmentally friendly technologies to overcome the problems and create a sustainable balance between population growth and Earth's resources. This analysis was treated in (Aral, 2013, 2014; Okuducu and Aral, 2017) and will not be repeated here. The global population dynamics model described in Eq. (10) may also be utilized for continental population growth including the migration dynamics that may develop between continents. We will identify this model as the N-K-C model where the letter “C” is used as the continent identifier. Although the mathematical definition of this model is straight forward, which is based on the above described knowledgebased model concept, one must be careful with the calibration process that will be used in the identifications of the constants of the resulting model. The reason behind this observation is associated with the limited availability and reliability of long-term continental migration data. As discussed in the earlier section, this database is not generally available. If it is available, it is not reliable due to the reasons explained earlier or if available it is not sufficiently long term to justify its use during the calibration of the N-K-C model. Whereas, as it is well known that, historical world population and continental population data is readily available, and it is reliable. First, we present the continental mathematical Model A which is based on the sequence of Eqs. (7–12) as given above. Given Eq. (8) we can write,
In Eq. (6) the superscript prime refers to the derivative of the function with respect to q, b(q) is a function of resource limitation and resource consumption parameters, and k(q) is given as the ratio of the rate of resource consumption to resource consumption. Since knowledge production is a function of population and productivity of humans, the rate of knowledge production can be defined as a function of a productivity function w(q) and population N(t),
q˙ (t ) = w (q) N (t )
∫ w (q) N (t ) dt 0
(5)
b (q) = c (q) +
(11)
tn
qtotal =
where,
k (q) = −
(10)
where the coefficient α is interpreted as the proportion of the total knowledge produced that is environmentally friendly, which yields technologic knowledge qtech = αqtotal ; 0 < α < 1, and b1 is defined as average person's human productivity independent of technologic innovations which may represent the knowledge level of civilizations. At this constant productivity level, humanity may sustain its existence in a homeostasis with the environment at a certain population level (Dolgonosov, 2016; Okuducu and Aral, 2017). Given Eq. (7) we can define,
where the coefficients of this series a2(q) and a3(q) are functions of q. Eq. (3) can be written as,
L (q, q˙ ) =
c1 c 2 w (q)2
⎞ ⎟ ⎟ ⎠
Further, without loss of generality, among several possible choices (Okuducu and Aral, 2017), the following linear definition of the productivity function will be considered here since w(q) need to be defined,
(2)
L (q, q˙ ) = a2 (q) q˙ 2 + a3 (q) q˙ 3 + O (q˙ 4 )
N c1 w (q) − w′ (q)
(9)
In these equations r(q) > 0 and K(q) > 0 by definition of w(q) > 0 and w′ < w. Given Eq. (7) it is possible to define several productivity functions to solve for the total knowledge that maybe generated at time tn. Using these productivity functions and Eq. (8) there are three possible models that can be formulated which are identified as: (i) the classical logistic function model; (ii) carrying capacity independent Model A; and, (iii) carrying capacity independent Model B. These three models and the analysis based on these models has been demonstrated in (Okuducu and Aral, 2017) and will not be repeated here. In this study the writer has selected to use Model A of Okuducu and Aral, 2017) since it is easier to follow and adapt. With the definitions and simplifications given in (Okuducu and Aral, 2017), in Model A, k (q) = c1 and b (q) = c2 where these functions were treated as
Nj ⎞ ⎤ ⎡ ⎛ ; j = af , as, eu, na, sa oc N˙ j = ⎢r j (qj )(Nj )2 ⎜1 − Kj (qj ) ⎟ ⎥ ⎝ ⎠⎦ ⎣
(13)
where the subscript j refers to the continents, Africa (af), Asia (as), Europe (eu), North America (na), South America (sa) and Oceania (oc). In this mathematical form the governing equation for the continents is the same as the world population model given in Eq. (8) or (10). As such all underlying assumptions and definitions will follow the concepts defined in the world population model which yields, 3
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Fig. 1. Continental population trends obtained from the calibrated mathematical model: (a) Africa Population; (b) Asia Population; (c) Europe Population; (d) North America Population; (e) South America Population; and, (f) Oceania Population.
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linked at the migration flow terms which can be solved numerically. One should also notice that each ordinary differential equation component of the simultaneous system of equations also has an internal ordinary differential equation to solve for the knowledge function given in Eq. (17). In conclusion the outcome is a rather complicated nonlinear simultaneous system of equations representing continental population growth and inter-continental migration. One should notice that the population growth component of the model is already calibrated in (Okuducu and Aral, 2017). The only difference for the continental application is the initial knowledge value qjo of the continents which is the only calibration coefficient of the growth model. This leaves only the djk and dkj constants as the additional calibration parameters of Eq. (16). Calibration of Eq. (16) will be performed based on continental population data which is available and reliable. Migration flow data is not used in this calibration process since that data is not reliable as described earlier. Since this is a zero-sum model, i.e. migration outflow from one continent towards another continent is an inflow migration to the other continent without loss of population, one should notice that an outflow term (−djk Nj ) for one continent will be an inflow term (+dkj Nk ) for another continent for all (j, k) where (j ≠ k). The calibrated model will not only yield population growth of the continents but will also yield the migration fluxes between continents. The outcome of this analysis is presented in the next section.
Fig. 2. Total World Population trend obtained from the mathematical model.
r j (qj ) = c1 w (qj ) − w′ (qj ) ; Kj (qj ) =
c1 w (qj ) − w′ (qj )
; j = af , as,
c1 c2 w (qj )2
(14)
eu, na, sa oc
4. Results and discussion
where c1, c2 and w(qj) are as defined earlier but now qj represent continental knowledge generation based on continental population, Eq. (7). In this study, not only the assumptions and definition that are used for Model A are the same but also the calibrated model coefficient for Model A will not be modified and used as is, as given in (Okuducu and Aral, 2017). For example, the coefficients used in (Okuducu and Aral, 2017), such as,
The calibrated model given in Eq. (16) yields the trends shown in Fig. 1 for continental population. One should notice that in these figures the data range between 1860 and 2018 are the recorded population data (Okuducu and Aral, 2017; United Nations, DESA/Population Division, 2017) (shown as red dots in decades) that is used for calibration and statistical analysis. The data beyond year 2018 and in the range between 2020 and 2100 are the estimated data obtained from (Statista, 2019) (shown as green dots in decades). Since this data set is an estimation of continental population it is not used in the calibration of the mathematical model and it is not included to the statistical analysis given below. This data is shown here for visual comparison of the outcome of the mathematical model developed in this study and the estimated outcome obtained by some other means in another study (Statista, 2019). The total population shown in Fig. 2 is simply obtained as the sum of continental population results obtained from Eq. (16). The black dots represent the analytical model results and this data is not used during calibration of the mathematical model developed in this study. As can be visually seen in Fig. 1, the outcome of the mathematical model follows the trend of the historical recorded data for each continent and for the world population as shown in Fig. 2 rather well. A statistical analysis is also performed to quantify this observation using the coefficient of determination analysis and Root Mean Square Error (RMSE). The coefficient of determination (denoted by R2 in Table 1) is a key output to evaluate the proportion of the variance between a variable that is predicted based on another independent variable and RMSE
(15)
b1 = 0.0007 ; c1 = 6.994 ; c2 = 97.94 ; α = 0.6
are kept as is and are not used as calibration parameters. This is based on the observation that population growth for each continent will only be a function of knowledge produced in each continent based on Eq. (12) and will no longer depend on the calibration constants determined in (Okuducu and Aral, 2017). Only the initial value of the knowledge function, qjo , is adjusted for each continent as the calibration parameter of the growth model since starting knowledge value of each continent is expected to be different. In the next step the continental migration terms will be added to Eq. (13) to yield population dynamics model for the continents with continental migration flows.
Nj ⎞ ⎤ ⎡ ⎛ N˙ j = ⎢r j (qj )(Nj )2 ⎜1 − − Kj (qj ) ⎟ ⎥ ⎝ ⎠⎦ ⎣ ⎧ j = af , as, eu, na, sa oc ⎫ k = af , as, eu, na, sa oc ⎨ ⎬ j≠k ⎩ ⎭
∑ djk Nj + ∑ dkj Nk k
;
k
(16)
where, rj(qj) and Kj(qj) are as given in Eq. (14), migration outflow (negative summation terms) and migration inflow (positive summation terms) are associated with the coefficients djk and dkj are chosen as the calibration constants in addition to initial knowledge function value of each continent qjo . In the outflow terms the superscript denotes the destination continent. In the inflow terms the subscript denotes the origination continent. Given Eq. (7) we also notice that,
q˙ j = w (qj ) Nj
; j = af , as, eu, na, sa oc
Table 1 Coefficient of Determination and RMSE for Continental and Total Population Estimates.
(17)
and,
w (qj ) = b1 qj + b1
; j = af , as, eu, na, sa oc
(18)
Eq. (16) is a simultaneous ordinary differential equation that are 5
Continental Population (billions)
qjo
R2
RMSE
Africa Pop. Asia Pop. Europe Pop. North Am. Pop. South Am. Pop. Oceania Pop. Total Pop.
1.88 1.04 15.5 30.0 18.0 0.03 –
0.94 0.98 0.98 0.99 0.99 0.91 0.98
0.095 0.194 0.023 0.009 0.002 0.006 0.310
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Table 2 Calibrated Coefficients of the Continental Migration Model. djk
Africa
Africa Asia Europe N. America S. America Oceania
– 4.9 4.5 2.0 1.0 1.0
× × × × ×
Asia
10−4 10−3 10−11 10−7 10−10
1.1 – 1.0 1.2 5.1 6.3
Europe
× 10−12 × × × ×
10−11 10−12 10−9 10−9
1.2 1.0 – 5.2 5.0 1.2
× 10−11 × 10−12 × 10−12 × 10−6 × 10−6
quantifies how different the two data sets are. As such, coefficient of determination is an indicator of the correlation between the two data sets. The range of R2 is (0–1) and results close to 1 indicate good correlation. RMSE quantifies how different a set of values are. The smaller an RMSE value, the closer predicted and observed values are. Both results are given in Table 1, which indicates good correlation. Since the population of Africa and Asia are very large (billions) the coefficients of these continents are small but the products representing the migration trends are in the order of thousands. The population of Oceania is very small relative to the other continents and thus its plot appears as a step function (Table 2). Given these results, it is predicted that Africa will show an increasing population trend and will reach ~4 billion people around 2100, Fig. 1(a). Asia's maximum population is estimated to be ~5.2 billion and will be reached around 2040. After that a decline in Asia population is predicted, Fig. 1(b). European population reaches a peak of ~0.7 billion in 2030 and a slight decline is observed after that until 2100. This predicted value is slightly below observed values in 2018. The decline in European population predicted in (Statista, 2019) is much sharper than the one predicted in this study, Fig. 1(c). North American population reaches an estimated value of ~0.5 billion people, which is higher than the predicted values given in (Statista, 2019) and it is reached earlier as seen in Fig. 1(d). South America population flattens out at ~0.75 billion people in year 2050 and shows a steady level until 2100, Fig. 1(e). In (Statista, 2019) a decline in South American population is predicted which is not seen in the results predicted in this study until 2100. Oceania is continuing with its increasing trend and reaching ~0.07 billion people in year 2100, Fig. 1(f). All these results are in expected rages of continental population trends. The results for the total population are given in Fig. 2, which is calculated as the yearly sum of all continental population estimates. This outcome is also good with an R2 value of 0.98 and RMSE value of 0.31. With this outcome the total population estimate for the world reaches to ~11 billion people in year 2100 which is in the range of most predictions made in the literature. A comparison of the estimated values obtained in (Statista, 2019) (green dots) and analytical model results is also shown in Fig. 2. The yearly population growth for each continent excluding migration inflow and out flow is also calculated as shown in Fig. 3. It is emphasized that the results shown in Fig. 3 are not cumulative values of population growth but yearly estimates. As seen in Fig. 3 yearly population growth in Asia and Africa is initially in a sharp increasing trend. In 2010 a peak yearly increase of ~0.06 billion people is estimated for Asia and the peak for Africa is ~0.051 billion people and it is reached in 2060. After that a sharp decline of yearly population is predicted in both continents reaching negative population growth in Asia after 2040 and in Africa after 2090. The yearly population growth in Europe is slightly increasing initially and this turns into a declining trend after 1950. South America, North America and Oceania yearly population growth is mild and stable initially and for North Amerian this trend goes negative after 2050. This implies that any increase in the population of these continents are attributed to migration inflows. The yearly net migration outflow estimated from each continent is shown in Fig. 4. It is again emphasized that these are yearly values and
N. America
S. America
4.2 × 10−11 3.35 × 10−4 1.35 × 10−3 – 1.1 × 10−5 1.2 × 10−9
1.0 1.0 2.3 7.2 – 1.1
× × × ×
10−11 10−12 10−3 10−9
× 10−9
Oceania 1.4 1.3 4.5 2.0 1.1 –
× × × × ×
10−12 10−11 10−4 10−9 10−6
Fig. 3. Yearly continental population growth estimates.
Fig. 4. Yearly continental migration outflow estimates.
are not cumulative. The cumulative estimates yield the results that are given in Fig. 1. As seen in Fig. 4 historically the net migration outflow is the highest in Europe until 1940s. After that a sharp decline is followed by steady outflow after 2050. Feeder continents like Africa and Asia is in a continuously increasing trend until 2050 for africa and 2100 for Asia. Net outflow in North and South America is small relative to Asia, Africa and Europe. For Europe to maintain its high net outflow migration status, it seems Europe is going to be a gate way continent to other continents in a zero sum population trend. Oceania net outflow migration estimate is negligible when compared to the other continents.
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Technological Forecasting & Social Change 151 (2020) 119848
M.M. Aral
5. Conclusion
Bijak, J., Wiśniowski, A., 2010. Bayesian forecasting of immigration to selected European countries by using expert knowledge. J. R. Stat. Soc. Series A Stat. Soc. 173 (4), 775–796. https://doi.org/10.1111/j.1467985X.2009.00635.x. Bijak, J., 2011. Forecasting International Migration in Europe: A Bayesian View. Springer Netherlands, Dordrecht. https://doi.org/10.1007/978-90-481-8897-0. Bijak, J., 2012. Migration Assumptions in the UK National Population Projections: Methodology review [electronic resource]. Office for National Statistics, Southampton. http://www.ons.gov.uk/ons/guide-method/method-quality/specific/ population-and-migration/population-projections/npp-migrationassumptionsmethodology-review/index.html. Aral, M.M., 2014a. Perspectives and challenges on climate change and its effects on water quality and health. Water Qual. Health. https://doi.org/10.1007/s12403-0140125-7. Aral, M.M., 2013. Climate change and human population dynamics. Water Qual. Health. https://doi.org/10.1007/s12403-013-0091-5. Aral, M.M.2014. Climate change and persistent high temperatures: does it matter?2(45):1–8. doi: 10.3389/fenvs.2014.00045. Dolgonosov, B.M., 2012. An informational dynamics of civilizations. Biosphere 4 (3), 263–279. Dolgonosov, B.M., Naidenov, V.I., 2006. An informational framework for human population dynamics. Ecol. Model. 198, 375–386. Dolgonosov, B.M., 2016. Knowledge production and world population dynamics. Tech. Forcast. Soc. Change 103, 127–141. Okuducu, M.B., Aral, M.M., 2017. Knowledge based dynamic human population models. Tech. Forecast. Soc. Change 122, 1–11. http://dx.doi.org/10.1016/j.techfore.2017. 05.008. United Nations, DESA/Population Division. 2017. World Population Prospects. https:// population.un.org/wpp/. (Accessed, May 8, 2019). Commission on Human Security, 2003. Human Security Now. CHS, New York Available online: https://reliefweb.int/sites/reliefweb.int/files/resources/ 91BAEEDBA50C6907C1256D19006A9353-chs-security-may03.pdf (Accessed on 22.03.2019). Foerster, H., Mora, P.M., Amiot, L.W., 1960. Doomsday: friday, 13 November, A.D. 2026. Science 132, 1291–1295. Akaev, A.A., Sadovnichy, V.A., 2010. Mathematical model of population dynamics with the world population size stabilizing about a stationary level. Dokl. Math. 82 (3), 978–981. Akaev, A.A., Sadovnichy, V.A., 2011. Global demographic models as the basis for strategic forecast. Projects and Risks of the Future: Concepts, Models, Instruments, Forecasts. Krasand, Moscow, pp. 17–44. Kapitza, S.P., 1992. Mathematical model of world population growth. Math. Model. 4 (6), 65–79. Kapitza, S.P., 1996. Phenomenological theory of world population growth. PhysicsUspekhi 166 (1), 63–80. Miranda, L.C.M., Lima, C.A.S., 2010. On the logistic modeling and forecasting of evolutionary processes: application to human population dynamics. Technol. Forecast. Soc. Chang. 77, 699–711. Miranda, L.C.M., Lima, C.A.S., 2011. On the forecasting of the challenging world future scenarios. Technol. Forecast. Soc. Chang. 78, 1445–1470. International Organization for Migration. 2018. World Migration Report – 2018. The United Nations Migration Agency, 17 route des Morillons, P.O. Box 17, 1211 Geneva 19, Switzerland. 347p. ISBN 978-92-9068-742-9. Abel, G.J., 2013. Estimating global migration flow tables using place of birth data. Demogr. Res. 28 (18), 505–546. https://doi.org/10.4054/DemRes.2013.28.18. Abel, G.J., Sander, N., 2014. Quantifying global international migration flows. Science 343 (6178), 1520–1522. https://doi.org/10.1126/science.1248676. Kupiszewska, D., Nowok, B., 2008. Comparability of statistics on international migration flows in the European Union. In: Willekens, F., Raymer, J. (Eds.), International Migration in Europe: Data, Models and Estimates. Wiley, London, pp. 41–73. Willekens, F., 1994. Monitoring international migration flows in Europe. Eur. J. Population 10 (1), 1–42. https://doi.org/10.1007/BF01268210. Ševčíková, H., Raftery, A.E., 2016. bayesPop: probabilistic population projections. J. Stat. Softw. 75 (5). https://doi.org/10.18637/jss.v075.i05. Statista. 2019. Continental Population Estimates:https://www.statista.com/statistics/ 272789/world-population-by-continent/(Accessed July 18, 2019).
A knowledge based analytical model developed earlier (Okuducu and Aral, 2017) is used to estimate continental migration trends in the world. To the best knowledge of the author this is the first use of a continuous analytical model to obtain continental migration estimates in the world. Other applications in this field of study include statistical models and regression models as they are summarized in the literature review section of the paper. The analytical model developed assumes that continental migration is a zero-sum event and the inherent implication of the use of the calibrated model in predictive analysis assumes that historical trends on migration flows will be representative of the future events as well. These are not that restrictive assumptions and they are used in all predictive models of population analysis. The statistical accuracy of the model calibration is satisfactory indicating that the calibrated model produces a good fit to the historical data. Predictive results show that world population may reach ~11 billion people in year 2100. The Africa and Asia continents will continue to be the main feeder of migration flows to other continents in years to come. The European continent is going to be the gateway continent to North and South America for migration flows. Oceania is going to show a steady but very mild increase in population mainly due to migration inflows. The results presented in this study are inline and confirming the trends that are reported in the literature. However, a continuous analytical model may have some advantages over other approaches in that a calibrated model may easily be used to analyze what if scenarios to estimate the effects of changing conditions. For example, as demonstrated in other studies (Aral, 2013, 2014), inclusion of the effects of climate change on continental migration would be relatively easy to analyze. This type of an analysis can be done as a global climate trend analysis or the analysis may be broken down to the continental climate effects analysis as well. These studies are currently under development and out of the context of the current paper. Author contributions M.M.A. is the sole author of the paper. The concept, mathematical model development and coding, calibration of the model and preparation of this manuscript is done by M.M.A. Declaration of Competing Interest The author declares no conflict of interest. References Commission on Human Security, 2003. Human Security Now. CHS, New York Available online: https://reliefweb.int/sites/reliefweb.int/files/resources/ 91BAEEDBA50C6907C1256D19006A9353-chs-security-may03.pdf (accessed on 24.03.2019). Paris, E.G., Human security, R., 2001. Paradigm shift or hot air. Int. Secur. 26 (2), 87–102. Abel, G.J., 2018. Non-zero trajectories for long-run net migration assumptions in global population projection models. Demogr. Res. 38 (54), 1635–1662. https://doi.org/10. 4054/DemRes.2018.38.54. Lee, R.D., 2011. The outlook for population growth. Science 333 (6042), 569–573. https://doi.org/10.1126/science.1208859. Massey, D.S., Arango, Hugo, J., Kouaouci, G.J., Pellegrino, A., Taylor, J.E., 1993. Theories of international migration: a review and appraisal. Popul. Dev. Rev. 19 (3), 431–466.
Dr. Aral specializes in large scale environmental simulations in surface water and groundwater specialization areas. A licensed professional engineer (PE), he also has expertise in environmental exposure analysis, exposure-dose reconstruction, health risk assessment, population dynamics analysis, climate change effects on the environment. He has over 100 publications in these areas and actively pursues a state-of-the-art research program in these topics within the activities of the Multimedia Environmental Simulations Laboratory (MESL) at Georgia Institute of Technology USA and abroad.
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