Chapter 1

POPULATION DESIGN

1. Introduction

I propose the concept of population design and analyze the conditions for population design. Population design refers to the conditions the population has to satisfy in order to become self-sustainable from the physiological, economical, educational, cultural and scientific point of view. Beyond economic viability, several other criteria should be satisfied for the overall viability, including several conditions for the population. Conditions are not limited to economical viability.

In the second section of this chapter, I deal with the main conditions for the population design. The third part deals with the population composition and statistics. The fourth part deals with population growth models.

STATE OF THE ART

The settlement’s population may be evaluated differently in respect to its autonomy and to what it is expected to produce. In previous designs, like [1], [2], [3], [4] scarce or not entirely realistic designs have been proposed. For example, in our own past project ([2]), a scarce model was presented, as only the initial population structure has been analyzed (the population during the construction phase). The design [1] presented a population growth a bit too optimistic. Some designs focused only on the physiological, psychological and recreational needs of a society, rather than on its industrial needs ([3], [4]). Previous designs proposed as a solution to population growth just to provide extra space and to bring initially a lower population than the total settlement capacity ([4]), but have only approximated the required extra space. Many designs focused on settlement construction and life support and did not treat the actual population repartition regarding activity domains ([2], [4], [5]). We assessed these conditions and did our best to analyze all of them in detail, as they are of vital importance for the social organization of a space colony. Different population growth models have been analyzed. A proposal for how much space would be needed for settlement extension has been given.

Various designs proposed a self-sustainable space settlement [1, 2, 3, 4, 5]. Several previous designs limit the self-sustainability of the settlement to economical and physiological survivability. The expected degree of self-sustainability of a space colony has not been precisely stated. The concepts of social, cultural and scientific self-sustainability have not been yet introduced. These notions are discussed in this chapter.

2. Feasibility analysis of population self-sustainment

The feasibility analysis of a self-sustainable space settlement from social, economical and industrial points of view has been ignored in past designs. Also, the population requirements that have to be satisfied in order to ensure self-sustainability have not been thoroughly analyzed in past designs.

The aim of the feasibility analysis is to pinpoint the requirements in order to build a space colony in the near future (<60 years).

A self-sustainable space station must fulfill all of the following fundamental needs of people living in space:

· Basic biological requirements;

· Physiological needs

- atmosphere;

- water;

- food;

- thermal comfort;

- the need to live in a clean, proper environment;

- health needs.

· The need for security;

· The need for social relationships, for communication and for relaxing environments;

· The need for culture and for scientific development;

· Economical survivability.

These needs should be fulfilled by the population onboard the space settlement if it is fully self-sustainable. This means that the people onboard will be able to provide themselves with food, and construction materials, to develop culture, media, and industry, to have economical exchanges and to develop social relationships. The settlement society will need to progress in scientific and cultural fields at least at the same rate as the population on Earth in order to become economically viable and competitive.

BASIC BIOLOGIC REQUIREMENTS

We first deal with the minimal permanent population on the settlement, as determined by biologic requirements. If the population would be lower than 1000, then in 3-4 generations hereditary diseases will have a significant impact on the colony. This is according to Gregor Mendel’s theory and has been experimentally proven with various animal populations (such as tigers). The biologically viable minimal population should be at least 1000 strong.

SELF-SUSTAINABILITY REQUIREMENTS

Consider the settlement’s community as having autonomy from a cultural or scientific point of view. A population of 10’000 (as given in many past designs without significant justification [3], [4], including our own design [2]) cannot sustain a complete university (with all faculties, including Medicine and Law), a complete industry and education centers and schools in which to train people for all the activities a developed society needs. A population in the range of 10’000-40’000 would not be able to self-sustain educationally, culturally and scientifically, because it could not include a complete university. A complete university would simply not justify the cost for a population under 100’000 (as there would not be sufficient students for all faculties – economically speaking at least 10’000 students per university, according to standards on the Earth). Consider here a university preparing Ph.D. and Bachelor students in specific fields of importance for space exploration and engineering, such as: Aerospace engineering, Astrobiology, Space Medicine, Space Geology, Electronics (super conductibility, semiconductors), Astronomy.

The too small settlements would have to “import” specialists – doctors, lawyers and researchers on narrow fields in order to survive economically and technologically. To train all these specialists on the settlement would require much higher costs than to bring them from Earth, as a university that has faculties with fewer than 100 students per year is not profitable. In fact, operating a complete faculty for less than 100 students per year does not justify the costs.

THE NEED FOR CULTURE AND FOR SCIENTIFIC DEVELOPMENT

In order to become self-sustainable from a cultural point of view, the settlement would require artists, writers, philosophers and its own media. Without a university to train, inspire and learn people in all these fields, the station would simply have to “import” them as well.

A society will not become good enough in any field without competitive spirit. If people are not constantly in competition with others in their field, they would not have enough motivation to complete their work at the highest level. Researchers, artists, even sellers and manufacturers must be maintained in a competitive environment. 10’000, 40’000, even 100’000 people are not enough to ensure competition in all activity fields. I consider that competitive spirit is one of the basic mechanisms of modern society. Without it, a society may not excel. Looking at it otherwise is not realistic.

By analyzing the economical/industrial/cultural needs of a town with a population under 100’000, we find that it is not self-sustainable. It is not autonomous either from a scientific/cultural point of view (it has no or just a small university, that does not cover all fields) and either from agricultural/industrial points of view. Such a society cannot produce everything, because there are simply not enough people to support all industrial or research fields. This means that it cannot become industrially self-sustainable. The space settlement is just like a small town in space – only that it is rather isolated and it needs to produce by itself everything a modern society requires to survive.

ECONOMICAL SURVIVABILITY

There is no state having sufficient raw materials to sustain itself in all industrial fields. The settlement may obtain the raw materials required for its industry by extracting them from the Moon/asteroids. It may request periodically shipments of a specific raw material that cannot be extracted in sufficient amounts from the Moon/asteroids – but that would mean it is not self-sustainable and is not acceptable as a long-term solution.

The settlement must have an operational industry and may “import” during the construction period from Earth only the tools/materials that are too expensive to be produced in space. The settlement should offer – during its operational period – research, the possibility to train specialists in space in very narrow research fields, the possibility to launch cheaply and with a higher frequency space missions and the possibility of developing a community interested in space studies. Having the possibility to build and send spacecraft directly from space would mean sparing large quantities of fuel. It would turn both manned and unmanned space missions more affordable and frequent. Another advantage is commercial space tourism, that has been recently proven possible by the results of the X-Prize contest.

CONCLUDING ON CONDITIONS

It is feasible that the space settlement self-sustains physiologically and may fulfill its security and social needs, but it is not realistic to think of it as culturally, scientifically and industrially all-at-once self-sustainable society. To be able to self-sustain from all points of view, including the above three, the population of the settlement should be in the range 100’000-1’000’000. Even so, after completion it would still require a source of raw materials (the lunar extraction facility) for its aerospace industry, so it would not be fully independent from a resource point of view. In order to ensure self-sustainment of the settlement, we propose its population of at least 100’000.

3. Population composition and statistics

The population composition is determined based on economical viability and self-sustainment criteria. These include:

· Capability of a population living at a remote area in space to have an internal economy;

· Capability of industrial self-sustainment;

· Viability of research and education.

The space settlement’s society should not have a significantly different population composition than a highly developed society on Earth. The colony’s population should cover all activity fields in order to have its own internal economy. It has to produce goods for internal use and for export (satellites, spacecraft, robotics for unmanned space missions and so on). It must have its own administration, government services, and social, security maintenance services in order to cover all the needs of a modern society. All industries required for manufacturing modern society goods should also be represented in order to ensure economical viability.

There are two population compositions to consider. The first on is for the construction phase of the settlement. It has been presented in numerous past designs, including our own ([2]) and it is discussed in detail in a different approach (in relation to supplies needs and project timeline) in Chapter II.

The population composition for the operational phase of the settlement is relevant for the analysis, as it reflects the capability of self-sustainment of an orbital space colony.

In this phase, the employed population is considered as in the US Survey [6] and is of 64.1%. The rest of 35.9% is comprised of students (5.5%), children (15.3%) and retired persons (15.1%). Notice that the students’ ratio may rise up to 10%, considering that many may be employed in research while completing their Bachelor or Ph.D. degrees. Unemployment should be maintained below 0.1%, as almost everyone will be needed.

The population repartition on activity fields is presented in Table I.1 and in Fig. I.1 and I.2. The industry, agriculture and services activities are represented with their subsections. There are two types of ratios presented: per activity domain and per occupation. The categories cover largely the development needs of a modern society.

Table I.1. Population repartition per occupation. Based on the US Employment survey 2000 [6].

Occupation	Percentage	Notes
Ratios per activity domain	-
Civilian labor force	64.1
Agriculture	2.51	Out of total employed population
Non-agricultural industry	97.49	Out of employed population
Ratios per occupation	-	Out of total labor force
Managerial and professional specialty	30.61
Technical, sales & administrative support	28.8
Service occupations	13.34
Precision production, craft and repairs	10.88
Operators, laborers and fabricators	13.86
Farming	2.51
Per activity (excluding agriculture)	-
Industry	97.49
Goods manufacturing	19.32	Out of which:
Mining	0.41	Provided by the lunar extraction facility
Construction	5.01
Manufacturing	13.9
Durable goods	8.31
Non-durable goods	5.59
Food industry	23.1	Out of non-durable goods industry employment
Food industry	1.29	Out of total employed population [*]
Recycling industry	3	[*]
Services (1) - producing	75.17	[*]
Transportation	3.35	[*]
Communications & public utilities	1.81	[*]
Wholesale trades	5.21	[*]
Retail trades	17.14	[*]
Finance & insurance	5.86	[*]
Services (2)	26.51	[*], part of the services employed population (1)
Health services	4	[*]
Engineering services	7	Including space engineering, [*]
Recreation services	1.2	Including parks’ and theatres’ management and maintenance, [*]
Business services	6.8	[*]
Computer and data processing services	45	Percentage out of the business services’ employed population
Social services	2	Residential care, child care etc. [*]
Settlement maintenance services	3
Security services	0.5
Tourism	1.51	Hotel personnel, guides and so on; necessary for development of space tourism [*]
Miscellaneous	0.5	[*]
Government services	15.29	[*]
Education services	12.5
Other government services	2.79	Including defense and Meteor collision prevention system

[*]=out of total employed population

The ratios computed in Table I.1 are according to the scientific needs of the settlement. A higher employment rate was considered for education, engineering and some business services (computer and data processing services). Some specific services are included (such as the Meteor collision prevention system). The total number of medical personnel has also been recalculated, according to the colony’s needs.

Figure I.1. Population composition considering employment status. Includes employed persons, retired, children and unemployed students.

Figure I.2. Population composition considering the major activity domains.

COMPUTATION OF SPECIFIC EMPLOYMENT REQUIREMENTS

Media

To satisfy its cultural and communication needs, the settlement will need its own media. The population of the settlement being of 100’000 will afford a local TV studio, radio studio and a local newspaper. A local TV studio has largely the same employment requirements as a radio studio – 30 people minimum. A local newspaper has an employment requirement of 15 people (ten people for the editorial board and five more people for the printing house).

Medical personnel

As people onboard the settlement will live in a relatively isolated environment, with tense deadlines (in R&D, for example) and higher stresses, they will need periodical psychological counseling and examinations. It is simply more difficult to live in a closed environment, relatively far from Earth and with tenser deadlines than living on Earth. People will need to maintain their society as elite, in order to preserve its economical viability. Usual relaxation requirements include parks, restaurants and theatres. Counseling may be a medical requirement. A higher number of psychologists may be required. People will likely need an examination every six months. An examination/counseling session takes on average one hour. Thus per year we will need 2000 hours of counseling/examination sessions per 1000 people.

For the total population of 100’000 200’000 hours of counseling/examination sessions are needed yearly. One year has in average 260 workdays. A usual work shift takes eight hours. Thus, the total work time per year [average] is 2085 hours. We will need approximately 95 psychologists for the entire 100’000 population.

For the total medical personnel, we should take into account that specialists should represent all major fields (ophthalmologists, dentists, pediatricians, family and general practitioners, anesthesiologists, surgeons, audiologists, internists, obstetricians and so on). An emergency medical system must be included. The minimal number of highly qualified medical personnel should be three doctors per field per 10’000 people. Each doctor may be supported by 2-3 assistants on average and by two more maintenance personnel. Pharmacists are at least 15 per 10’000 people. Thus, the minimal number of medical personnel for the 10’000 population cell is in the order of 165. The minimal employed population in the health care system is 1.75%. The recommended employment in the health sector is of about 4%, after [6].

Defense and security

An asteroid/meteor collision prevention system should be developed for the settlement’s society. This defense system should look for potentially hazardous meteors/asteroids (using a radar system). Large objects on an impact course could be deflected or destroyed using a laser system or other methods.

The settlement should be protected also against any disastrous situation. Highly qualified and trained personnel should be able to deal with any extreme security problem or hazardous situation (such as a fire). These should be the elite defense personnel. The defense sector will cover 2% of the employed population

Basic security needs are ensured by security personnel (0.5% out of total population). These should also be trained as firemen and some as emergency medical personnel.

4. Population growth models

Various models have been proposed in the past in order to express the growth of a specific population. Each model is discussed and analyzed in order to determine which one is best suited for computing the settlement’s population growth.

THE FIBONACCI MODEL

This model does not apply to human populations. It applies to rabbit populations. It is important, as it was the first population growth model.

The model is defined using a linear second-degree recurrence:

, (1)

where is the population at the moment of time n.

Equation (1) has the general solutions stated in the following expression:

,

where and are constants determined from the initial conditions (2), while and are the solutions of the characteristic equation for recurrence (1):

The initial conditions for this model are:

(2)

We do not insist further on this model, as it does not apply to human population.

EXPONENTIAL GROWTH MODEL (MALTHUSIAN MODEL)

The natural growth model or exponential growth model in its discrete form states:

(3)

where is the initial population, n the moment of time and k the growth rate.

From (3) the model of natural growth is determined in its continuous form:

(4)

Divide expression (4) to the time variation in order to obtain:

(5)

By multiplying (5) with and then dividing the expression with we obtain:

(6)

Equation (6) is the differential growth equation. By integration, the equation states:

(7)

where c is a constant, determined from the initial condition. The initial condition states:

(8)

Change c from expression (8) into equation (7) in order to obtain:

(9)

which is the Natural Growth Model in its continuous form.

An important theorem of natural growth is:

A population following the Natural Growth Model will double in a constant amount of time, regardless of the initial population.

To prove the theorem, we first consider two different moments of time, and . is the amount of time in which the population doubles. The following notation is used for further calculus: .

The population doubles in time, stating that:

(10)

Equation (10) proves that the time in which the population doubles is a constant regardless of the initial population. Notice that this model does not reflect realistic population growth. As will be seen in the next model, other factors influence population growth. This model is widely used for the radioactivity law (in order to model the decay rate of radionuclides population). The decay rate is obtained from equation (6):

(11)

If the decay rate is known for a specific radionuclide population, the coefficient may be determined:

(12)

The coefficient is <0 for radionuclide populations (as it expresses the decay) and is >0 for human populations (as it expresses growth).

However, this model has its limitations. It is applied for determining the decay of radionuclide populations, but for human populations it is just a fair approximation. Notice in Table I.2 that the population does not double at exact intervals. Figure I.3 is based on the world population census for the past century. Notice that significant variations occur in the real model in respect to the exponential growth model. The Malthusian Model is, however, widely used.

Table I.2. World population growth versus time for the period 1900-1985. Data from [10].

Figure I.3. World population growth for the past century. Notice that the real growth may be approximated with an exponential growth, but significant variations appear in the real model.

The population does not follow exactly the exponential growth, as other factors intervene in growth. For example, if a population grows, its efficiency and self-sustainment capacity will also grow, but up to a limit. The limit is determined from the fact that a population will not have enough food or space to grow indefinitely. These are only some of the natural limiting factors for population growth. In a realistic model, we have to take into account that as the efficiency of the population grows, so does its growth rate.

These factors are taken into account by the Heinz von Foester model.

THE COALITION MODEL (HEINZ VON FOESTER)

We restate the differential growth equation from the Natural Growth Model:

Notice that is the growth rate. If the growth rate is also dependent with the population growth (and thus time-dependent), then we have the following law:

(13)

In (13) h is a constant, . (13) is the von Foester model in its differential form. Notice that if (13) is reduced to the natural growth model. The coefficients are dependent to the development capacity and productivity of a specific society. The values of these coefficients for the settlement population should be determined from direct experimental analysis of a large population’s growth in a closed environment – like a large colony in space. In our numerical applications, we used the growth rates as resulting from US Survey [10].

The continuous form of the von Foester model can be determined from equation (13) by integration:

(14)

where is a constant resulting from the integration. (14) is equivalent to:

(15)

Equation (15) is the continuous form of the von Foester model.

THE LOGISTIC GROWTH MODEL (VERHULST)

The Verhulst model considers that if resources decline in respect to the growth of the population, we have to add to the natural growth model (6) a negative factor proportional to the square of the population number:

(16)

The equation (16) is the continuous-time logistic model. In a different form, it is written as:

(17)

Model expressed in (17) is the classical logistic model, proposed by Verhulst in the 19^th century. It has a solution in the form:

.

The equation (18),

, (18)

is the discrete form of equation (17). The recurrent equation (18) has no analytical solution. Its solutions have to be determined numerically. The process in equation (18) may be chaotic.

NUMERICAL APPLICATION FOR US AND WORLD POPULATION GROWTH

Data is taken from various censuses ([13], [14], [15]) and the real population growth is plotted. Predictions are made using the exponential growth model and several logistics models. The results are then compared.

Table I.3. US population growth from 1790 up to 2005. Data for population growth before 2000 from [13], data for 2005 from [14].

Year	Population
1790	3.929
1800	5.308
1810	7.24
1820	9.638
1830	12.866
1840	17.069
1850	23.192
1860	31.443
1870	38.558
1880	50.156
1890	62.948
1900	75.996
1910	91.972
1920	105.711
1930	122.775
1940	131.669
1950	150.697
1960	179.323
1970	203.185
1980	226.546
1990	248.71
2005	295.229

Figure I.4. US population growth for the period 1790-1990 according to table I.3.

The exponential growth model for the world population with three different coefficients is shown in table I.4 and the corresponding graph in figure I.5. Data from [14] is also used.

Table I.4. World population growth approximated using the exponential growth model for three different coefficients;

Year	World population	Exponential model coefficient k=1.01	Exponential model coefficient k=1.015	Exponential model coefficient k=1.0012
1900	1608	1608	1608	1608
1910	1750	1776.232	1866.15	1811.72
1920	1834	1962.066	2165.743	2041.25
1930	2070	2167.341	2513.433	2299.86
1940	2295	2394.093	2916.942	2591.233
1950	2517	2644.568	3385.23	2919.521
1955	2780	2779.468	3646.854	3098.948
1960	3005	2921.248	3928.697	3289.401
1965	3345	3070.261	4232.323	3491.559
1970	3707	3226.875	4559.414	3706.141
1975	4086	3391.479	4911.783	3933.911
1980	4454	3564.478	5291.386	4175.678
1985	4850	3746.302	5700.325	4432.305
2005	6411	4571.201	7677.512	5626.52

Figure I.5. Comparison between the actual world population growth and predictions using three different coefficients for the Malthusian model.

Population growth is more accurately predicted using logistic models. A numerical application is given for predicting the US population growth. The logistic models used differ in parameters.

Table I.5. US population and predictions by several logistic models (from H.N. Teodorescu, with permission)

Year	US population
1790	3.929	3.93	3.93
1800	5.308	5.03498	4.98538
1810	7.24	6.446604	6.320566
1820	9.638	8.247401	8.007557
1830	12.866	10.54049	10.13557
1840	17.069	13.4537	12.81438
1850	23.192	17.14388	16.1778
1860	31.443	21.80086	20.38709
1870	38.558	27.65044	25.63356
1880	50.156	34.95484	32.1397
1890	62.948	44.00905	40.1574
1900	75.996	55.13051	49.96163
1910	91.972	68.6394	61.83762
1920	105.711	84.82727	76.05947
1930	122.775	103.9132	92.85898
1940	131.669	125.9902	112.3854
1950	150.697	150.9699	134.6598
1960	179.323	178.538	159.5319
1970	203.185	208.1383	186.6509
1980	226.546	238.9974	215.4626
1990	248.71	270.1962	245.2409
2005	295.229	315.5481	289.8963
2010		329.846	304.3585
2020		356.6967	332.0838
2030		380.8409	357.7168
2040		402.0345	380.8409
2050		420.2479	401.2444
2060		435.6175	418.8982
2070		448.3888	433.9159
2080		458.866	446.5079
2090		467.371	456.9386
2100		474.2163	465.4926

The model used to plot fig. I.4 is the logistic equation solution with parameters chosen, for example

(19)

where t is the time in years, t >1790.

Figure I.4. Actual US population growth and prediction using two logistic models that differ in parameters.

Figure I.4 shows that the logistic model predicts much more accurately population growth than the Malthusian model. Figure I.5 is from [11] and shows predictions for US population growth using all three models.

Figure I.5. Population growth models used in discrete form to approximate the US population. The census data is plotted in order to depict model accuracy. From [11].

NUMERICAL APPLICATION FOR COLONY POPULATION GROWTH

In average in developed countries the population growth is 0,2% per year. This ratio is adopted for colony population prediction using the Malthusian model. The problem is to determine after how many years the colony’s population grows significantly such that extension is needed. The amount of supplementary space required for population extension is computed. The Malthusian model is used just as an example for predicting the colony’s population growth.

The coefficients for the von Foester or Verhulst models are dependent on the development capability of the society. It is thus rather hazardous to approximate them or to take the same values as for the US population growth, as we cannot predict how exactly the settlement’s society will evolve. These should be determined experimentally in at least 40 years after the settlement’s operational period has commenced.

The growth ratio is 0,2%. is the population at a given time, n the time [in years]. is the initial population. The growth model is (natural growth, discrete form):

(20)

The values for population growth versus time have been computed from (20) for various moments of time (0-100 [years]). The results are shown in Table I.6.

Table I.6. Population growth over a period of 0 to 100 years after to the construction phase. The time increment is five years. An exponential model is assumed.

Time	Percentage of initial population	Growth [%]
0	100	0
5	101.004008	1.004008008
10	102.0180963	2.018096337
15	103.0423662	3.042366194
20	104.0769198	4.076919802
25	105.1218604	5.121860411
30	106.1772923	6.177292308
35	107.2433208	7.243320825
40	108.3200524	8.320052354
45	109.4075944	9.407594354
50	110.5060554	10.50605536
55	111.615545	11.61554501
60	112.736174	12.73617402
65	113.8680542	13.86805423
70	115.0112986	15.01129862
75	116.1660213	16.16602126
80	117.3323374	17.33233742
85	118.5103635	18.51036348
90	119.700217	19.70021702
95	120.9020168	20.90201679
100	122.1158827	22.11588272

Notice that in 25 years the population will grow with 5%. In 50 years, the population will grow with 10,5%. We consider necessary to include 10,5% more habitable space in the settlement from its construction phase to ensure that sufficient space is provided for population extension. The settlement should start its structural extension 45 years after to its construction.

5. Conclusions

As no significant emphasis was provided in literature regarding to the social/cultural/technical/industrial/scientific feasibility of a large population living onboard a space colony, I did my best to analyze this problem and to depict its importance. The analysis did not focus only on the economical viability of such a society, but also on the social and cultural aspects that should be satisfied by the colony. An estimate of the minimal population to ensure self-sustainability of the colony in all of these aspects was presented. Based on economical, technological, social, educational and scientific viability, the population repartition regarding employment and activity has been analyzed.

Moreover, we found in past designs scarce or no estimates of population growth for a space colony. Various models have been presented in order to state the importance of correctly determining the population growth of the settlement. Population growth is an important concern – if the amount of additional space required for extension is not precisely determined, the population may run out of space or the society will stall its development. However, I can only make predictions on how the settlement’s population will evolve. The three known population growth models (Malthusian, von Foester, Verhulst) are presented, along with a discussion of their use for space applications.

I did my best to pinpoint these problems, which are vital for the existence of any modern society.

FURTHER WORK

There is a degree of uncertainty in predicting the population growth of a space colony. If a better model than the Malthusian is used, experimental data are required. The relationship growth-development and growth-resource depletion has to be analyzed for a large population in a closed environment (such as the space colony). We cannot make predictions based on the coefficients determined for the US population or for other countries. The conditions differ – and the state of art does not present any analysis with large populations in closed environments. This lack of knowledge hinders predictions. Experimental data will have to be gathered based on, for example, the development/growth ratio for the first space colony. Until experimental data on this topic is available, our predictions will remain at the state of crude approximations.

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