An Essay on the Principle of Sustainable Population [1st ed.] 9789811336539, 9789811336546

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SPRINGER BRIEFS IN POPULATION STUDIES POPULATION STUDIES OF JAPAN

Toshihiko Hara

An Essay on the Principle of Sustainable Population 123

SpringerBriefs in Population Studies Population Studies of Japan

Editor-in-Chief Toshihiko Hara, School of Design, Sapporo City University, Sapporo, Hokkaido, Japan Series Editors Shinji Anzo, Tokyo, Japan Hisakazu Kato, Tokyo, Japan Noriko Tsuya, Tokyo, Japan Toru Suzuki, Tokyo, Japan Kohei Wada, Tokyo, Japan Hisashi Inaba, Tokyo, Japan Minato Nakazawa, Kobe, Japan Jim Raymo, Madison, USA Ryuichi Kaneko, Tokyo, Japan Satomi Kurosu, Chiba, Japan Reiko Hayashi, Tokyo, Japan Hiroshi Kojima, Tokyo, Japan Takashi Inoue, Tokyo, Japan

The world population is expected to expand by 39.4% to 9.6 billion in 2060 (UN World Population Prospects, revised 2010). Meanwhile, Japan is expected to see its population contract by nearly one third to 86.7 million, and its proportion of the elderly (65 years of age and over) will account for no less than 39.9% (National Institute of Population and Social Security Research in Japan, Population Projections for Japan 2012). Japan has entered the post-demographic transitional phase and will be the fastest-shrinking country in the world, followed by former Eastern bloc nations, leading other Asian countries that are experiencing drastic changes. A declining population that is rapidly aging impacts a country’s economic growth, labor market, pensions, taxation, health care, and housing. The social structure and geographical distribution in the country will drastically change, and short-term as well as long-term solutions for economic and social consequences of this trend will be required. This series aims to draw attention to Japan’s entering the post-demographic transition phase and to present cutting-edge research in Japanese population studies. It will include compact monographs under the editorial supervision of the Population Association of Japan (PAJ). The PAJ was established in 1948 and organizes researchers with a wide range of interests in population studies of Japan. The major fields are (1) population structure and aging; (2) migration, urbanization, and distribution; (3) fertility; (4) mortality and morbidity; (5) nuptiality, family, and households; (6) labor force and unemployment; (7) population projection and population policy (including family planning); and (8) historical demography. Since 1978, the PAJ has been publishing the academic journal Jinkogaku Kenkyu (The Journal of Population Studies), in which most of the articles are written in Japanese. Thus, the scope of this series spans the entire field of population issues in Japan, impacts on socioeconomic change, and implications for policy measures. It includes population aging, fertility and family formation, household structures, population health, mortality, human geography and regional population, and comparative studies with other countries. This series will be of great interest to a wide range of researchers in other countries confronting a post-demographic transition stage, demographers, population geographers, sociologists, economists, political scientists, health researchers, and practitioners across a broad spectrum of social sciences. Editor-in-chief Toshihiko Hara, Sapporo, Japan

More information about this subseries at http://www.springer.com/series/13101

Toshihiko Hara

An Essay on the Principle of Sustainable Population

123

Toshihiko Hara (Emeritus), Sapporo City University Sapporo, Hokkaido, Japan

ISSN 2211-3215 ISSN 2211-3223 (electronic) SpringerBriefs in Population Studies ISSN 2198-2724 ISSN 2198-2732 (electronic) Population Studies of Japan ISBN 978-981-13-3653-9 ISBN 978-981-13-3654-6 (eBook) https://doi.org/10.1007/978-981-13-3654-6 © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. This Springer imprint is published by the registered company Springer Nature Singapore Pte Ltd. The registered company address is: 152 Beach Road, #21-01/04 Gateway East, Singapore 189721, Singapore

Acknowledgements

I would like to thank Prof. Dr. Tilman Mayer, Prof. Dr. Franz-Xaver Kaufmann, Dr. Martin Bujard, Prof. Dr. Hans Bertram, and Prof. Dr. Hans Hoch for our meaningful dialogues on sustainable population development of our societies in Germany in October 2018, which gave me many important additional ideas for this book. I also thank Dr. Ling Sze Nancy Leung for her advices to improve my text as same as my previous work. This research was supported by JSPS KAKENHI Grant Number 23330173 (Study on the Population and Life Course Dynamics in the First and Second Demographic Transition and Their Future Prospects)/26285128 (Study on the New Population Trends and Life Course Changes based on a Contemporary Re-examination of the Demographic Transition Theory). This is Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Chief researcher: Ryuichi Kaneko, Vice-Director of National Institute of Population and Social Security Research, Population Statistics of Japan.

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Contents

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1 Introduction: The Sustainability of the World Population 1.1 World’s Increasing Population and Japan’s Decreasing Population . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 World’s Next 4 Billion People . . . . . . . . . . . . . . . . . 1.3 Demographic Transition of World Population . . . . . . . 1.4 Extinction Scenario of Human Society . . . . . . . . . . . . 1.5 About This Book . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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2 The Principle of Sustainable Population . . . . . . . . 2.1 Extinction Curve . . . . . . . . . . . . . . . . . . . . . . 2.2 Population Wave Model . . . . . . . . . . . . . . . . 2.3 What Malthus Says . . . . . . . . . . . . . . . . . . . . 2.4 Exponential Growth and Exponential Decay . . 2.5 Limit of Growth and Logistic Curve . . . . . . . 2.6 Demographic Transition of Human Population 2.7 The Principle of Sustainable Population . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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3 Japan’s Demographic Transition (JDT) . . . . . . . . . . . . . . . . . . . 3.1 Classical Demographic Transition (DT) . . . . . . . . . . . . . . . . 3.2 Second Demographic Transition (SDT) . . . . . . . . . . . . . . . . 3.3 Elucidation of Causality . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Japan’s Demographic Transition (JDT) . . . . . . . . . . . . . . . . 3.5 Total Fertility and Life Expectancy . . . . . . . . . . . . . . . . . . . 3.6 Timing Shift of Marriage and Effective Use of Reproductive Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.7 A Causal Model of Demographic Transition in Japan . . . . . . 3.8 Major Feedback Loops to Promote the Transition . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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5 Simulation Run for the Demographic Transition in Japan . . . 5.1 Initial Settings for Standard Run . . . . . . . . . . . . . . . . . . . 5.2 Total Population, Crude Birth Rate, and Crude Death Rate 5.3 Age Structure and Dependency Ratio . . . . . . . . . . . . . . . . 5.4 Social Capital and Life Expectancy . . . . . . . . . . . . . . . . . 5.5 Fertility Development . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Timing Shift of Reproduction . . . . . . . . . . . . . . . . . . . . . 5.7 Social Capital Generation and Population Growth Rate . . . 5.8 Maximum Fertility and Population Growth Rate . . . . . . . . 5.9 Maximum Lifespan and Population Growth Rate . . . . . . . 5.10 Migration Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.11 Meaning of the Simulation Results . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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6 Conclusion: Demographic Future of Human Society 6.1 Present State of World Population . . . . . . . . . . . 6.2 Driving Force of Demographic Transition . . . . . 6.3 Recovering Replacement Fertility . . . . . . . . . . . 6.4 Limits of Expanding Lifespan . . . . . . . . . . . . . . 6.5 Role of Migration . . . . . . . . . . . . . . . . . . . . . . . 6.6 Sustainable Future of Human Population . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 System Dynamics Model of Demographic Transition 4.1 Basic Concept of Modeling . . . . . . . . . . . . . . . . 4.2 Six Model Sectors of DTMJ . . . . . . . . . . . . . . . 4.3 Population, Age Structure, and Migration . . . . . . 4.4 Fertility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.5 Marriage Timing . . . . . . . . . . . . . . . . . . . . . . . . 4.6 Social Production . . . . . . . . . . . . . . . . . . . . . . . 4.7 Life Expectancy . . . . . . . . . . . . . . . . . . . . . . . . 4.8 Population Indicators . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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7 Epilogue: Toward a Sustainable Society . . . . . . . . . . . . 7.1 Background Dependence of Sustainable Population 7.2 Sustainable Economy . . . . . . . . . . . . . . . . . . . . . . 7.3 Sustainable Ecology . . . . . . . . . . . . . . . . . . . . . . . 7.4 Sustainable Culture . . . . . . . . . . . . . . . . . . . . . . . . 7.5 Sustainable Society . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Chapter 1

Introduction: The Sustainability of the World Population

Abstract According to the UN projection 2017, the world’s population will increase by more than four billion in the next 85 years and will reach 11 billion by 2100. Quoting from Prof. Lam’s N-IUSSP essay, “The world’s next 4 billion” (Lam 2017), there is a debate on the future of humankind on the sustainability of ecological environments on the earth. However, if we take a closer look at this additional 4 billion people, most of the increase is expected in elderly (65+) and working-age adults (mostly older working ages); the increase in children and young adults is lower than ever. In the same UN projection, it indicates that Japan’s population will decrease from 0.13 billion in 2015 to 0.08 billion by 2100. Japan has entered a postdemographic transitional stage (Sato and Kaneko 2015), in which it will lead the world in population aging and decline. This chapter will analyze the world’s trends in Total Fertility Rate (TFR), Net Reproduction Rate (NRR), and Life Expectancy (LE) in comparison with Japan. The results show the world is entering the last phase of the demographic transition except in Sub-Saharan Africa and most of the world will be confronting a rapid aging and population decline. Furthermore, if the next 4 billion increase successfully by 2100, the demographic transition of Sub-Saharan Africa may also enter the final stage sooner or later. After then, the entire world’s population may be living in a “shrinking society” (Hara 2014). Keywords The sustainability of world population · UN projection 2017 · Population projection of Japan · The world’s next 4 billion · Total fertility rate (TFR) · Net reproduction rate (NRR) · Life expectancy (LE) · Sub-Saharan Africa · Post-demographic transition · Shrinking society · Malthus’ law

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 T. Hara, An Essay on the Principle of Sustainable Population, Population Studies of Japan, https://doi.org/10.1007/978-981-13-3654-6_1

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1 Introduction: The Sustainability of the World Population

1.1 World’s Increasing Population and Japan’s Decreasing Population The United Nations has stated that the world’s population in 2015 is 7.38 billion and projects that it will increase continuously and reach 11 billion by 2100 (United Nations 2017)1 (Fig. 1.1). This means that the population will increase by more than 4 billion people in the next 85 years, which is a huge increase. Some people think there is a threat that the population may eventually breakthrough 10 billion people. In fact, we have already experienced a population increase of 4.8 billion people, from 2.5 billion in 1950 to 7.3 billion in 2015. This increase happened in only 65 years. That is the so-called the “population explosion”, with the record high population growth rate of 2.05% between 1965 and 1970. In contrast, the next 4 billion will rise gradually in 85 years (Fig. 1.1), and the increasing rate will be near 0%. The age of population growth is expected to be at an end. In the same UN projection 2017, it states that Japan’s population will decrease from 0.13 billion in 2015 to 0.08 billion by 2100. According to the 2015 Population Census of Japan, Japan’s total population (including foreign residents) is 127,094,745 (about 0.13 billion)(IPSS 2017a). Based on a medium-fertility and mortality projection of the National Institute of Population and Social Security of Japan (IPSS 14 000 000

140 000 UN2017 Projection 120 000

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Fig. 1.1 Trend of world’s population and Japan’s population (United Nations 2017; IPSS 2017b)

1 The

total number of human populations currently living on the Earth is over 7.67 billion people as of December 2018 indicated in the website (www.worldometers.info/world-population/). This number is estimated and projected by certain procedure. The 2017 Revision of World Population Prospects is the 25th round of official United Nations population estimation and projection. They are prepared by the Population Division in UN DESA (Department of Economic and Social Affairs).

1.1 World’s Increasing Population and Japan’s Decreasing Population

3

2017b),2 Japan is also expected to undergo a long period of population decline to around 0.9 billion (88 million) by 2065. This projection represents a 30.8% decrease (39.19 million) compared to the population in 2015. According to auxiliary projections, Japan’s population will be less than 0.06 billion (60 million) by 2100 (Fig. 1.1). The discrepancy between UN projection and IPSS projection is because of different assumptions on fertility, mortality, and migration movement. Nevertheless, both projections show clearly that the Japanese population has entered a post-demographic transitional stage (Sato and Kaneko 2015) in which it will lead the world in population decline and aging.

1.2 World’s Next 4 Billion People “The world’s next 4 billion people will differ from the previous 4 billion” (Lam 2017). Professor David Lam pointed out the important features of the world’s next 4 billion people in his N-IUSSP essay. He compared the additional 4 billion for the next 100 years, with the 4 billion added between 1960 and 2011. The latter was explosively increased in the young population in only 50 years. If we see the additional population by 2100 by breaking them into age groups, it consists of about 19 billion elderly (65+), 18.5 billion working-age adults (15–64), and less than 0.5 billion children (0–14). This means most of the population increase is in elderly (65+) and working-age adults (15–64), and the increase in children (0–14) is very limited (Fig. 1.2). The next 4 billion people will also come from different regions. Most of the increase (about 80%) is expected in Sub-Saharan Africa (area of the continent of Africa that lies south of the Sahara Desert). In addition, as mentioned above, the future increase of working-age adults (15–64) in the world will be 18.5 billion, and the main increase is expected from 20.5 billion in Sub-Saharan Africa. This means that most of the working-age adults will belong to this area and almost 45% of the working-age population in the world will be Sub-Saharan Africans in the future (Fig. 1.2). In Asia,3 the population growth will continue. However, only the elderly (65+) will increase, while working-age adults (15–64) and children (0–14) will decrease. This situation will also happen in Latin America and the Caribbean,and even in Europe. Above all, the number of elderly (65+) will increase tremendously in Asia, and the countries will enter a post-demographic transitional stage like Japan, a Shrinking society (Hara 2014) characterized by a below replacement fertility level, and a rapid aging and decreasing population (Fig. 1.2). 2 Population Projections for Japan: 2016–2065, was released in April 2017. They are based on three

alternative assumptions about future changes in both fertility and mortality (a low, medium, and high variant of each) with a result of nine projections. There are auxiliary projections for the period from 2061 to 2110, where the survival rate-fertility rate, sex ratio at birth, and international migration rate are assumed to remain constant from 2061. 3 Asia contains Japan (Fig. 1.2).

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1 Introduction: The Sustainability of the World Population 4,000,000 3,500,000 3,000,000 2,500,000 2,000,000

                                         

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Fig. 1.2 Population Changes in the next 4 billion by age group and region (United Nations 2017). Note Asia contains Japan

In Northern America and other regions, the elderly (65+) and working-age adults (15–64), as well as children (0–14), will increase, although their growth will be on a small scale (Fig. 1.2).

1.3 Demographic Transition of World Population As described above, the world’s population will be confronting a rapid aging and decline in most regions, except Sub-Saharan Africa. A fertility rate below replacement level and an increasing life expectancy, which has long been the usual phenomena in Japan, are spreading globally and at the same time, the demographic transition of the world population will enter its last phase. The United Nations has estimated and projected the fertility trends of the world from the past to the future (Fig. 1.3). The average Total Fertility Rate (TFR) of the world declines from 5.05 at the peak period (1960–1965) to 2.57 at the present period (2010–2015). The region which stays at the world’s peak fertility is SubSaharan Africa, with a TFR 5.10. This TFR in Asia is 2.02 and 2.14 in Latin America and the Caribbean. The fertility trends of both regions show that they are nearing the replacement level. However, for the highly developed regions such as Europe, Northern America, and Japan, the TFR is far below the replacement level, 1.60, 1.85, 1.40, respectively. Among these main regions driving the world economy, their total fertility rate is below 2.1 births per woman at present (Fig. 1.3). According to the 2017 UN estimates (United Nations 2017), almost one-half of the world’s population lives in the countries in which TFR is below replacement level (Frejika 2017). The Net Reproduction Rate (NRR) indicates the level of actual fertility (TFR) in comparison with the replacement level of fertility, which is adjusted with the sex ratio at birth and the survival rate of a woman at the end of reproductive age

1.3 Demographic Transition of World Population

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8.00

Total ferlity (live births per woman)

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Net reproducon rate (surviving daughters per woman)

Fig. 1.3 Trend of total fertility rates by region: estimates (1950–2015) and projections (2016–2100) in medium variant (United Nations 2017)

Period

Fig. 1.4 Changing net reproduction rates estimates (1950–2015) and projections (2016–2100) in medium variant (United Nations 2017)

(Fig. 1.4). An NRR of one means mothers in each generation are having exactly enough daughters to replace themselves. If the NRR is less than one, the population cannot reproduce enough. For example, if the NRR is 0.70, the fertility level of the

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1 Introduction: The Sustainability of the World Population

population is only 70% of replacement fertility and the population will shrink by 30% in each generation. According to UN estimation (United Nations 2017), the NNR of the world’s population is 1.102, the one in Sub-Saharan Africa is 2.08 at present (2010–2015). Nevertheless, the NRR in Latin America and the Caribbean is 1.01, almost at a reproductive level, and in Asia is 0.997, slightly less than the reproductive level. In contrast, in highly developed regions in the world economy, such as Europe, Northern America, and Japan, NNR is far below the replacement level, they are 0.766, 0.891, and 0.680, respectively. As mentioned above, almost half of the world’s population live in countries below replacement NNR. It is predictively that more children (0–14) and working-age adults (15–64) will not be expected in the future, except Sub-Saharan Africa. UN estimations and projections (United Nations 2017) show the trend of an average life span from the past to the future. The life expectancy at birth (both sexes combined) of the world’s population has extended from 47.0 years (1950–1955) to 70.8 years (2010–2015). According to the projection in the medium variant, the average life span of the population will be 82.6 years in 2100 (Fig. 1.5). Japan’s life expectancy has increased from 62.8 years during the postwar period (1950–1955) to 75.4 years (1975–1980) and became one of the longevity countries. The life expectancy in Japan has continued to increase steadily until now, and it is expected to reach 93.9 by 2100. On the other side, Sub-Saharan Africa’s life expectancy was 36.3 years in the postwar period (1950–1955), in which most of the countries in this region were suffering from the colonial time. Nevertheless, the average life span has increased

Japan

Projections

90.0 Northern America 80.0 70.0 Europe

Asia

60.0 World

Sub-Saharan Africa

50.0 40.0 Latin America and the Caribean 30.0

1950-1955 1955-1960 1960-1965 1965-1970 1970-1975 1975-1980 1980-1985 1985-1990 1990-1995 1995-2000 2000-2005 2005-2010 2010-2015 2015-2020 2020-2025 2025-2030 2030-2035 2035-2040 2040-2045 2045-2050 2050-2055 2055-2060 2060-2065 2065-2070 2070-2075 2075-2080 2080-2085 2085-2090 2090-2095 2095-2100

Life expectancy at birth for both sexes combined

100.0

Period

Fig. 1.5 Changing life expectancy by region estimates (1950–2015) and projections (2016–2100) in medium variant (United Nations 2017)

1.3 Demographic Transition of World Population

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to 57.8 years in the period of 2010–2015. According to the UN projection, life expectancy is expected to expand to 77.8 years by 2100, which will be almost the same level as the developed countries at present.

1.4 Extinction Scenario of Human Society Toward Prof. Lam’s N-IUSSP essay, “The world’s next 4 billion” (Lam 2017), there is a debate about the future of humankind. Grossman wrote, “My concern is that the past four billion have degraded natural world upon which we depend, and that this degradation will make the world much less welcoming to the next four billion” (Grossman 2017), he criticized Lam’s optimistic view of additional world’s population increase. Besides, Martine argued that the recent expansion of economic growth has boosted the availability of goods and services for the global population. He mentioned that success is unsustainable because economic growth is based on constant increases in production and is stimulated by consumerism which produces an imminent ecological collapse (Martine 2018). Furthermore, Livi Bacci pointed out two of the several threats to sustainability. First, the environmental consequences of the struggle against poverty and backwardness; second, the increasing anthropization of land4 (Livi Bacci 2018). Essentially, the entire discussions stand from the viewpoint of increasing next 4 billion population is threatening the sustainability of ecological environments on the earth. Neither of the debater’s view is about the demographic sustainability of the world’s population. As described above, the world’s population is entering the last phase of the demographic transition. Except Sub-Saharan Africa, the world will be confronting a rapid population aging and decline. Fewer children (0–14) and working-age adults (15–64) are expected in the future. According to the United Nations’ projections, most of the total population increase (about 80%) is expected to occur in Sub-Saharan Africa. However, this expectation is based on the assumptions that Sub-Saharan Africa’s TFR will be decreasing slowly from 5.10 to a replacement level of 2.1, and the life expectancy will expand from 57.8 years (2010–2015) to 77.8 by 2100, which is almost the same level as the present developed countries. On the other side, among the main regions driving the world economy, such as Europe, Northern America, and Japan, the total fertility rate is already below 2.1 births per woman. Clearly, they have entered a post-demographic transitional stage, characterized by below replacement fertility rate and a decreasing and rapid aging population. If this demographic situation remains unchanged, they will lose their 4 He

argues that an expanding population requires more land and space in a finite world and the available space declines as population grows. The “anthropization of land” means increasing land use for human activities, more concretely saying is “13% of the earth’s land occupied by arable land, 26% by permanent pastures, 8% by managed forests, 3% by urban areas and 4% cent by infrastructures and economic activities, 54% of all land is now directly or indirectly affected by human activities” (Livi Bacci 2018: 3).

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1 Introduction: The Sustainability of the World Population

economic power and it will be unsure which region can help the economic growth of Sub-Saharan Africa. Logically thinking makes it clear that the UN projection about the world’s next 4 billion should be the scenario, in which Sub-Saharan African will realize the selfsustained economic growth and almost 45% of the working-age world population will be living in Sub-Saharan Africa. Although this scenario is not completely deniable, the possibility of another scenario is more likely, in which the highly developed countries lost their economic power together with their decreasing and rapid aging populations. In this case, the demographic transition of Sub-Saharan Africa will fall by the wayside, and the entire human society will be at high risk of collapse. Furthermore, if the next 4 billion increase successfully by 2100, the demographic transition of Sub-Saharan Africa may also enter the final stage sooner or later. After then, the entire world’s population will be living in a “shrinking society”. Livi Bacci wrote, “Malthus again?” in the last chapter of his N-IUSSP essay (Livi Bacci, 2018). However, it is not necessary simply to go “back to the Malthus”, instead we need to revise his principle of population.

1.5 About This Book This book focuses on the future of human population and proposes to revise Malthus’ Law. The United Nations projects that the world population will increase 11 billion more by 2100 and its growth will be near to an end. There will be a new equilibrium after the long demographic transition in history from high birth and death rates to low ones. But as above mentioned, the fertility developments reported in the World Population Prospects 2017 states that most regions are near or below the replacement level, except sub-Saharan Africa, and warns a possible scenario of an extinction of human society as a shrinking society. When Malthus wrote his essay on the principle of population in 1798, England was at phase two of historical demographic transition. This stage leads to a fall in death rates and an increase in population. At the same time, the world population was still at phase one, in which death rates and birth rates were both high and rapidly fluctuated according to natural and social conditions. In contrast, we are at the last stage of historical demographic transition, in which death rates and birth rates are at low level and the population increase rate is near zero. In this case, we must reexamine Malthus, his Essay on the Principle of Population should be critically reconsidered. This book constructs 7 chapters. In the following Chap. 2, “The Principle of Sustainable Population”, I begin with the consideration of the so-called extinction curve, which shows the exponential rise of the world population takes place only since the end of the seventeenth century in the past 10,000 years in human history. This curve indicates the powerful nature of exponential growth, but I demonstrate that this can be observed every moment from the past to the present, and even in the future. Moreover, I argue that human population is developing as continual waves with many demographic transitions by using the population wave model. Then I return

References

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to Malthus and reexamine what he said. Simple simulations show the exponential growth and decay is unsustainable beyond the narrow ranges of the net reproduction rate. The limits of growth are given in any case, to the extent that time and space will permit. From this perspective, teleological conditions such as instinct, passion, or even natural reproductive tendencies are irrelevant and unnecessary. When the population deviates too far from the replacement level, either shrinking or exploding will overshoot the limits of its existence. This principle of sustainable population indicates that the demographic transition must follow a logistic curve. In Chap. 3, “Japan’s Demographic Transition (JDT)”, I reconsider the Demographic Transition (DT) known as the historical process from high fertility and mortality in preindustrial society, to low fertility and mortality in postindustrial society. The Classical DT and Second Demographic Transition (SDT) are reexamined and why the causality of DT has been not successfully elucidated until today is also explained. By using historical data, I analyze the historical process of JDT by comparing it with DT and SDT and clarify the basic causalities to promote the process and postulate a causal model for JDT. In Chap. 4, “System Dynamics Model of Demographic Transition”, I explain the Demographic Transition Model of Japan (DTMJ), which I have constructed by using a System Dynamics (SD) approach referencing the World3 (Meadows et al. 1972). This model is based on the causal model of JDT in Chap. 3. It includes six major factors: population-age structure, fertility, reproduction timing, social capital accumulation, lifespan, and migration. The basic concept of modeling, the relations among six major sectors, and the structures and functions of each sector are presented in detail. The variables and equations of DTMJ are defined and discussed. Chapter 5, “Simulation Run for the Demographic Transition in Japan”, I explain initial settings of the standard run and show the results of the simulations. Using only endogenous variables, this model successfully reproduces the historical process of Japan’s demographic transition. Thereby, the timing and periods of reproduction, maximum fertility, and maximum lifespan are the keys to sustainability. Besides, migration affects basically the speed of population change. In Chap. 6, “Conclusion: Demographic Future of Human Society”, I reconsider the present stage of the world population and the driving factors of demographic transition. The United Nations’ projection 2017/2019 shows a scenario hardly to be realized but maybe only possible narrow pass to the future. In my study, I consider the measures for recovering replacement fertility, extending lifespan, the control of migration and the sustainable future of the human population. In the last Chap. 7, “Epilogue :Toward A Sustainable Society”, I point out sufficient conditions to realize sustainable population, beyond the demography. The Demographic Transition Model of Japan (DTMJ) is constructed with optimal assumptions as the background conditions which are basically depending on the historical context. Therefore, not only the sustainable population, we also need sustainable society, economy, ecology, culture, and politics. I try to imagine and sketch them in this chapter. Where were we from and where are we going? They are difficult questions to be answered but we must seek the answers.

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1 Introduction: The Sustainability of the World Population

References Frejka T (2017) Half the world’s population reaching below replacement fertility. N-IUSSP.ORG. http://www.niussp.org/article/half-the-worlds-population-reaching-below-replacement-fertility/ ?print=pdf. Accessed 4 Dec 2017 Grossman R (2017) The world in which the next 4 billion people will live. N-IUSSP.ORG. Accessed 13 Nov 2017 Hara T (2014) A Shrinking Society Post-Demographic Transition in Japan, (Series: Springer Briefs in Population Studies 2014), vol VI, 94 p 20 illus. ISBN 978-4-431-54809-6 Lam D (2017) The world’s next 4 billion people will differ from the previous 4 billion. N-IUSSP.ORG. http://www.niussp.org/article/the-worlds-next-4-billion-people-will-differfrom-the-previous-4-billion/Accessed 24 July 2017 Livi Bacci M (2018) Thinking about the future: the four billion question. N-IUSSP.ORG. http://www.niussp.org/article/thinking-about-the-future-the-four-billion-question/?print=pdf. Accessed 12 Feb 2018 Martine G (2018) Global population, development aspirations and fallacies. N-IUSSP.ORG. http:// www.niussp.org/article/global-population-development-aspirations-and-fallacies/. Accessed 5 Feb 2018 Meadows DH, Meadows DL, Randers J, Behrens WWIII, et al (1972) The limits to growth. potomac associates-universe books. donellameadows.org/wp-content/userfiles/Limits-to-Growth-digitalscan-version.pdf Accessed 23 April 2019 IPSS (2017a) Population statistics of Japan 2017. www.ipss.go.jp/p-info/e/psj2017/PSJ2017.asp. Accessed 19 Dec 2018 IPSS (2017b) Population Projections for Japan: 2016 to 2065 (Appendix: Auxiliary Projections 2066 to 2115) http://www.ipss.go.jp/pp-zenkoku/e/zenkoku_e2017/pp_zenkoku2017e.asp Accessed 19 Dec 2018 Sato R, Kaneko R (2015) Japan in the post-demographic transition period: theoretical and empirical perspectives on the long-term population dynamics (Japanese). J Popul. Prob. 71(2):65–85 http:// www.ipss.go.jp/publication/e/jinkomon/pdf/20067301_25.pdf.Accessed. Accessed 09 May 2019 United Nations Population Division (2017) World population prospects: the 2017 revision (Database). Retrieved from (Note: All projections are based on the UN’s Medium Fertility Variant Projections.) https://esa.un.org/unpd/wpp/

Chapter 2

The Principle of Sustainable Population

Abstract In the past 10,000 years of human history, the exponential rise of world population takes place only since the end of the seventeenth century. Joel E. Cohen drew a graph to show the historical change of human population from One Million B.C. up to the present. It looks like a reverse L-shaped curve with a long tail. It suggests a possible extinction of the human population. It indicates the powerful nature of exponential growth, but it can also be observed as every moment from the past to the present, and to the future. Differently, the population wave model shows that the development of human population is a continual wave with many demographic transitions. It has multifractal structure and composed of innumerable logistic waves in a short term, which are integrated into a single logistic wave at the end. Back to Malthus’ theory, what he said was reexamined. Simple simulations show the exponential growth is unsustainable beyond the narrow ranges of the population growth rate. When the growth rate deviates too far from the replacement level, either exploding or shrinking will occur and the balance between population and society will collapse. The principle of sustainable population indicates that only the society can be existed and be sustainable, if it can successfully maintain or recover its population to a stationary level. Keywords Extinction curve · Population wave model · The principle of population · Exponential growth · Logistic curve · Logistic equation · The limit of growth · A carrying capacity of the environment · The principle of sustainable population

2.1 Extinction Curve How many people can the Earth support? Mathematical biologist and demographer, Joel E. Cohen wrote a book about this question (Cohen 1998: 204–264). He reviewed eight representative estimations in the past, from Ravenstein’s1 “6 billion in the year

© The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2020 T. Hara, An Essay on the Principle of Sustainable Population, Population Studies of Japan, https://doi.org/10.1007/978-981-13-3654-6_2

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2 The Principle of Sustainable Population 8000

World Populaon (in million)

7000 6000 5000 4000 3000 2000 1000 0 -1,000,000

-800,000

-600,000

-400,000

-200,000

0

200,000

Time ( years )

Fig. 2.1 The historical change of human population from one million B.C. up to the present

2072” to De Wit’s2 “146 billion at a maximum calculated from the carbohydrate production, limited by photonic synthesis on the Earth”. Cohen criticized that the notion of “population allowance” of the Earth is unambiguous and it must be limited not only with clear physical conditions like land area, photonic synthesis, energy, etc., but also affected by various other factors, such as social and economic infrastructure, productivity, mobility, social norms, education system, political system, etc. Without regarding the quality of life, I think the upper limit of world population at any given time cannot be measured or discussed as it’s varied socially and historically. Nevertheless, there must be a certain limit, beyond which we cannot exceed. Cohen drew a graph to show the historical change of human population from one Million B.C. up to the present. It looks like a reverse L-shaped curve with a long tail. He depicted this curve as an airplane running on the long runway and take off vertically against a high wall (Fig. 2.13 ). This curve gives us an impression that the world population would reach an end of the development and distinct sooner or later. He used a bold line to express the population development, because of the uncertainty of the confidence interval of the estimated population. Above all, the blank space between the present state and 200,000 AC suggests an implicit assumption that human population would not last for 10,000 years more. If it would last until 200,000 AC, the high wall of the bold line would be a black rectangle to fill the blank space in this graph. I believe such an extinction curve must be observed commonly in evolutionary history of spices, as far as they are not immortal. The critical question is not if the world population will extinct but when. Are we going out in the next 2,000 years as this curve suggests? 1 Ernst

Georg Ravenstein (1834–1913) was a German-English geographer. De Wit (1924–1993) was a Plant, Soil, and Microbial Scientist. 3 The data in Fig. 2.1 is different to Cohen’s. Cohen’s original figure was made in 1995 and the top of the curve does not reach 6 billion. However, the data shown in Fig. 2.2 is adjusted to 2015 by Author. 2 C.T.

2.1 Extinction Curve

13

Fig. 2.2 The changing growth rate of world population

This question seems reasonable, because the exponential rise of the world population took place only since the end of the seventeenth century, since the past 2,000 years in human history. We can verify this fact by the changing growth rate of the world population (Fig. 2.2). The population growth rate from 10,000 BC to Year zero could be estimated annually by 0.04% on average, based on the assumptions that the world population increased from 5 million at 10,000 BC to 250 million at Year zero for 10,000 years (IPSS 2017a). The transition from a hunter-gatherer society to an agricultural society began in this period. Until around 1650 AC, the number of world population reached between 470 and 545 million. The annual growth rate in this period can be considered as 0.29%. With the beginning of the industrial revolution around 1750, this rate doubled from 0.51% to 0.98% until the end of the nineteenth century. The world population in 1900 was between 1,550 and 1,762 million. After World War II, the growth rate began to rise rapidly and reached 2.05% between 1965 and 1970. According to the estimation by UN in 2017, the world population in 1965 was 3,339 million (United Nations 2017). After that, the population growth rate began to decrease and dropped back to 1.19% in the period 2010–2015. According to the UN 2017 Projection (United Nations 2017), this rate is diminishing from 1.09% (in the period 2015–2020) to 0.11% (in the period 2095–2100). Yet, the world population will increase continuously. If the growth rate is near 0% and stable, the population will top 11 billion by 2,100, as already mentioned in the former chapter, and would be stabilized at that level. However, if the growth rate decreases continuously or below 0%, like −0.18% in Japan (2017), the world population will shrink sooner or later. Therefore, we cannot ignore the possibility of extinction of human society in the next 2,000 years. On the other side, we should know the same reverse L-shaped curve with a long tail (Fig. 2.1) can be drawn in every moment in human history, as far as the population

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2 The Principle of Sustainable Population 300

World Populaon (in million)

250 200 150 100 50 0 -1,000,000

-800,000

-600,000

-400,000

-200,000

0

200,000

Time ( years )

Fig. 2.3 The historical change of human population from bc one million up to year zero 500

World Populaon (in million)

450 400 350 300 250 200 150 100 50 0 -1,000,000

-800,000

-600,000

-400,000

-200,000

0

200,000

Time ( years )

Fig. 2.4 The historical change of human population from bc one million up to around 1650

development follows exponential growth for a certainly long period. Namely, we can draw an extinction curve in Year zero, where the world population was 250 million with the population growth rate as 0.04% (Fig. 2.3). We can observe a resembling extinction curve also around 1650. The world population was about 500 million with an increasing rate of 0.29% (Fig. 2.4). They have exactly the same pattern with the extinction curve up to the present (Fig. 2.1). They are different from each maximum value of the world population at a moment in human history.4 4 If

one calculates the world population with a growth rate of 0.04% from 10,000 BC to Year zero until present, we can see an exact same pattern showing in other extinction curves (Figs. 2.1, 2.3, 2.4), even though the world population would not reach 6 billion in 2100. Thus, an explosive growth

2.1 Extinction Curve

15

That means the human history in a long-time perspective is always confronting at risk of extinction with exponential growth of population until the end of days. The nature of exponential growth will be explained in the later Sect. 2.4 but this fate is common with all other creatures.

2.2 Population Wave Model Surely, the recent experience with the world population growth rate of 2.05% in the period 1965–1970 is a rare case in human history. However, a similar explosive increase must have happened after “Out of Africa5 ”, the discovery of the New World and so on, where the spatial limitation for expanding was broken out. It is also thinkable that the transition from hunter-gatherer society to agricultural society (Hara 2000) or the beginning of the Industrial Revolution could have resulted in a quantum leap of social production and shifted the threshold level of a sustainable population. In those cases, the growth rate of an excess of 2% in a relatively short period could be observed. In fact, we can find countless cases of explosive growth in the regional population, in countries, cities, small communities, where not only natural growth also the social growth (migration) affects the population. Yet, the population growth rate is basically not constant and will change steadily with a given condition of circumstances. It’s wavy. It increases from near 0 to the maximum value, then decreases to near 0 or below, eventually in possible ranges, which are allowed between the limit of growth and the limit of distinction. Furthermore, the population development should not be composed of a single cycle of a wave, rather a series of waves composed of different population groups. Thus, the history of the human population can comprehend a series of waves in multistage. Cohen presented it as “Deevy’s curve6 ” (Cohen 1998: 125). He plotted the graph by taking the number of world population in Y-axis, and the number of years from past to present, in X-axis, both in logarithmic scale.7 This graph was plotted according to Deevy’s estimations of world population development. It shows three population waves. The first wave begins one million years ago since the invention rate of over 2% is not necessary for an extinction curve, if exponential growth will not continue for a certainly long time. 5 “Out-of-Africa” means the early migration of modern humans (Homo sapiens) from northern Africa to other part of the world, possibly beginning as early as 270,000 years ago, and certainly during 130,000–115,000 ago. There were various waves and the most “recent” wave took place about 70,000 years ago, via the so-called “Southern Route”, spreading along the coast of Asia and reaching Australia by around 65,000–50,000 years ago. At the same time, Europe was populated by an early offshoot which was settled at the Near East and Europe less than 55,000 years ago (WIKI 2019a). 6 Edward S. Deevy, “The Human Population,” Scientific American, vol. 203, no. 9, September 1960, pp. 195–204 (Cohen 1998: 512–513). 7 Without log conversion of both axes, a series of waves are compressed and visually seems to be an extinction curve (Fig. 2.1).

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2 The Principle of Sustainable Population

of advanced tools in hunter-gather society. The curve is rising and turning to be flat 100,000 years ago and continues until around 10,000 years ago. The second wave begins with the emergence of agriculture around 10,000 years ago. The curve is rising and turning to be flat and lasts 2,000 years ago, at the time the world population reached one million. The third wave begins with the Industrial Revolution, less than 500 years ago. It shapes a similar curve and turning to be a flat line till now. As for Japan, Prof, Takahiko Furuta proposes “Jinko Hadou Setsu (Population Wave Theory)”; it explains the history of the Japanese population by a series of six waves. They are (1) prehistoric fore wave, (2) prehistoric after wave, (3) agricultural fore wave, (4) agricultural after wave, (5) industrial fore wave, (6) industrial after wave (Furuta 1996: 11). He argues that human being has the ability to change the natural environment by themselves. In other words, the ability to create own culture and civilization. Therefore, the history of human population can comprehend as a series of multistage waves, which are conditioned by the upper limit of population allowance mainly given by productivity and the environment. He explains each wave as a logistic curve, of which growth rate increases from near 0 to the max value, then decreases to near 0 or even below. The nature of the logistic curve will be explained later (Sect. 2.5). Using a simple population wave model (Fig. 2.5), it demonstrates human population development as a series of multistage waves. This model has one equation and contains two main variables, the amount of population (Pop) and the population change (Popchange). Pop(t) = Pop(t − dt) + (Popchange) ∗ dt

Fig. 2.5 A simple multistage wave model

2.2 Population Wave Model

17

This type of equation is a difference equation. The differential time (dt) is the calculation interval and set to be one year in this model. The above equation refers to the present Pop at time (t) as the past Pop at time (t − dt) added to Popchange by (dt). Popchange is described as multiple variables, they are the amount of population (Pop), maximum population growth rate (rMax) and the population-K ratio (KPratio), in the following equation. Popchange = Pop × rMax × KPratio The maximum population growth rate(rMax)is set to be 0.04 (4%).That means the population can increase annually with a maximum growth rate of 4%. The population growth rate at time t (rt) can be calculated through Popchange divided by Pop. rt = Popchange/Pop The population-K ratio (KPratio) indicates the proportion of the population to a carrying capacity of the environment, represented by the symbol K. K is defined as the upper limit of “population allowance” in a given environment. KPRatio =(K −Pop)/K The value of KPRatio is slightly smaller than 1 at the beginning and decreases to 0, when Pop equals K.8 The population growth rate at time t (rt) changes from near rMax to 0%. The level of K can be switched by SWT during simulation, by the following equation. K = If time< SWT1 then K1 else if time < SWT2 then K2 else if time < SWT3 then K3 else K4. The settings for simulation are; Initial population (Ipop) = 10 at start time K1 = 100 K2 = 1,000 (after SWT1 at ST: Simulation Time 1000) K3 = 10,000 (after SWT2 at ST 2000) K4 = 1,000,000 (after SWT3 at ST 3000) The simulation runs for 5000 years. These data for setting are virtual, they do not have any relation to historical data. They are used to demonstrate a series of population waves visually. Four waves occur seriously as follows. 8 If

Pop shoots K over, KPRatio takes a minus value, which is slightly smaller than 0 and decreases to −1. This simple model doesn’t include any variable to generate an overshoot of Pop. Therefore, Pop is staying at K.

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2 The Principle of Sustainable Population

Wave 1: at start time (ST 0), the total population is set to 10 persons. It increases to K1 (100 persons) at around 150 years and stagnates (Fig. 2.6). Wave 2: after SWT1 (ST1000), K1 is switched to K2 (1,000 persons). The limit of population allowance becomes ten times more as much as K1. Then, the next logistic curve begins and reaches 1,000 persons at around 1,200 years and stagnates (Fig. 2.7). Wave 3: after SWT2 (ST 2000), K2 is switched to K3 (10,000 persons). The population allowance becomes 10 times more as much as K2. Then, the wave starts and reaches 10,000 persons at around 2,200 years and stagnates (Fig. 2.8). Wave 4: after SWT3 (ST3000), K3 is switched to K4 (1,000,000 persons). The limit of population allowance becomes 100 times more as much as K3. The last wave starts and reaches one million at around 3,200 years and stagnates (Fig. 2.9).

Fig. 2.6 Wave 1 (from ST 0 to ST200)

Fig. 2.7 Wave 2 (from ST800 to ST1200)

2.2 Population Wave Model

19

Fig. 2.8 Wave 3 (from ST1800 to ST2200)

Fig. 2.9 Wave 4 (from ST2800 to ST3200)

The population growth rate at time t (rt) rises from 0 to 5% and shrinks to 0% in spike-like four times, every 1000 years (Fig. 2.10). The most interesting thing is that a series of four waves in multistage result in a single logistic curve from a long-time perspective (Fig. 2.11). This fact means a series of population waves has the multifractal structure.9 Theoretically, it can be said that population development is composed of innumerable logistic waves in a short term, which will integrate into a single logistic wave at the end. Each wave arises, grows. Most of them may shrink and goes out. In the long term, an integrated wave at the end shows a single logistic wave. If the last wave shrinks and 9 The

concept of fractal was born from mathematics. Fractals tend to appear nearly the same at different levels. Regrettably, it is beyond my reach to define this multifractal structure mathematically, but I believe it is possible.

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2 The Principle of Sustainable Population

Fig. 2.10 The changing population growth rate at time t (rt)

Fig. 2.11 A series of 4 waves in multistage as a single logistic curve

goes out, the total development shows an extinction curve (Fig. 2.1) with exponential growth, a reverse L-shaped curve with a long tail. In a long timescale, a logistic curve is to be compressed, and it cannot be distinguished with an exponential curve.

2.3 What Malthus Says The powerful nature of exponential population growth was suggested by T.R. Malthus. In 1798, he published his first edition of the Principle of Population (An Essay on the Principle of Population, as it affects the future improvement of society, with remarks on the speculations of Mr. Godwin, M. Condorcet, and other writers) (Malthus 1798). He wrote, “I think I may fairly make two postulates. First, that food is necessary to the existence of man. Secondly, that the passion between the sexes is necessary and will remain nearly in its present state (Chap. 1—para 14). Assuming then, my

2.3 What Malthus Says

21

postulates as granted, I say, that the power of population is indefinitely greater than the power in the earth to produce subsistence for man (Chap. 1—para 17).” Then, he declared his famous “principle of population”; “Population, when unchecked, increases in a geometrical ratio. Subsistence increases only in an arithmetical ratio. A slight acquaintance with numbers will show the immensity of the first power in comparison of the second (Chap. 1—para 18).” Malthus’s finding was essentially the fact that the population increases geometrically, namely, exponentially.10 Today, this fact can be described as a function of four variables in the following equation, N t = N 0 er t N t represents the number of population at time t and N 0 is the number of population at time 0. The large e is the base of natural logarithm (alias Napier’s constant, e  2.71828) and r 11 is the population growth rate (alias increase rate). The small t is the length of time. The above equation is derived from a differential equation as follows, dN = rN dt This is the so-called “exponential equation”. It shows that a small change of population N per small t is the multiple of population growth rate r with population N. The reason why population increase is geometrical is very simple. A population increases in proportion to the cumulative number of a population at a given time. That is referred to as exponential growth, which is applied not only to the human population, but also to various populations, and resembles phenomena in various disciplines. Malthus himself did not clearly explain the case, in which a population growth rate takes a negative value (r < 0). In this case, a population decreases also geometrically. Thus, Malthus’ famous phrase cited above can be more exactly rewritten as When unchecked, (1) Population increases exponentially (i.e. in a geometrical ratio) if the growth rate is positive (r > 0). (2) Population is stationary if the growth rate is zero (r = 0). (3) Population decreases exponentially (i.e. in a geometrical ratio) and reaches a minimum (0) at the infinite position, if the growth rate is negative (r < 0). Simple simulations of a population of 10,000 persons at time zero (Fig. 2.12), shows three different curves by the value of r. The curve 1) r > 0, if the value of r is 5%, then the population increases by up to 40,000 persons and more, in 30 years. 10 He has missed to recognize the simple fact that subsistence (food production) must increase also in a geometrical ratio, as far as population increases in a geometrical ratio, if food is necessary for the existence of man. And that was happened in human history at least until today. 11 This r is a decimal number not in %.

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2 The Principle of Sustainable Population 50,000

Population

45,000 40,000

1) r㸼㸮

35,000

2) r㸻㸮

30,000

3) r㸺㸮

25,000 20,000 15,000 10,000 5,000 0 0

2

4

6

8

10 12 14 16 18 20 22 24 26 28 30 time

Fig. 2.12 Three different curves by the value of r

The curve 3) r < 0, if the value of r is −5%, then the population shrinks to almost 2,000 persons, in 30 years. Only curve 2) r = 0, if the value of r is exactly 0%, then the population is stable at 10,000 persons. Malthus’s famous two postulates on the food necessity for human existence and the passion of both sexes are merely some of the various conditions for population development. Following those postulates, he recognized the power of exponential growth for population but not for the power in the earth to produce subsistence for man. He supposed that food production can increase only linearly (i.e. in an arithmetical ratio).12 The exponential increase in food production since the industrial revolution clearly denied his prediction. However, his image for a limit of population growth was still not wrong in relation to the planet Earth.

2.4 Exponential Growth and Exponential Decay The condition given by Malthus as “when unchecked,” is still very important in our age in relation to the concepts of ‘Limits to Growth (LTG)’13 (Meadows et al. 1974) or ‘Sustainable Development Goals (SDGs)’(DSDG 2017).14 However, it is 12 Maybe, he would have thought of “the low of diminishing returns” in Economics. However, as mathematically regarding, even in this case, the food production doesn’t increase linearly (i.e. in an arithmetical ratio). 13 “The limits of growth” is the title of the first report of the Club of Rome (Meadows et al. 1972). The computer simulations of this report demonstrated that economic growth at that time could not continue indefinitely because of resource and environmental limitation. After the oil crisis in 1973, this concept was widespread in the world. 14 Sustainable development (or sustainability) was initially described in three terms, the environment, the economy and the society, proposed by the economist René Passet in 1979. In 2015, the

2.4 Exponential Growth and Exponential Decay

23

difficult to predict, when it will be checked. As mentioned above, Malthus’s other principle,’subsistence increases only in an arithmetical ratio’ was defeated in following industrial development in modern history. Instead, we are now worried about global warming and biodiversity degrading as a check. I think ‘when checked’ depends on the relative relation between the population and the environment, at the same time it is affected by the social system. It would not be possible to predict the absolute limits of growth in the human population, a priori. Nevertheless, the common characteristic of exponential growth is that the speed of increase is accelerated according to the growth rate(r), if it is deviated from 0%. As a result, the social system’s adaptation to the changing environment will be difficult and cannot succeed in time. In such cases, the system faces a crisis of ‘limits of growth’ or ‘sustainability’. The above-mentioned equation of exponential growth can be transformed, and a doubling time can be calculated. Td =

70 log(2) ≈ r r × 100

T d represents a doubling time. T d is the natural logarithm of 2 divided by the population growth rate r expressed in a decimal number. Roughly, Td equals 70 divided by population growth rate expressed in %. Doubling time means the length of time in which the number of a population is doubled. It depends on the annual population growth rate. It is about 70 years at 1% (r = 0.01), 35 years at 2%, 23.4 years at 3%, 17.5 years at 4%, 14 years at 5% (Fig. 2.13). For example, a population with an annual growth rate of 1% doubles every 70 years. Thus, after 140 years, it will be 2 × 2 = 4 times. After 210 years, it will be 2 × 2 = 8 times and after 280 years, it will be 2 × 2 × 2 × 2 = 16 times. An increasing population with 2% annually will be doubled every 35 years (almost in each one generation). It can degrade socio-economic circumstances and the natural environment in a short period. What we know is the ‘population explosion’ of the world population in the 1960s was in any case unsustainable for a long time. However, it may not be ignored that doubling time is the same length for a decaying population. In this case, instead of “a doubling time”, the notion of “half-life (halving time)” is applied. The term “half-life” is rarely used in demography but very popular in archeology and atom physics to express a lifetime of the radioisotope. In other words, in a shrinking society like Japan, the population is decreasing by half every 70 years under the condition of a population growth rate is −1% per year (r = − 0.01).15 Namely, after 140 years it will be (1/2) × (1/2) = (1/4) times, after 210 years, it will be (1/2) × (1/2) × (1/2) = (1/8) times, and after 280 years, United Nations adopted ‘The 2030 Agenda for Sustainable Development’, a set of 17 Sustainable Development Goals (SDGs) (WIKI 2019b; DSDG 2017). 15 The annual population growth rate of Japan recorded −0.18% in 2016–2017. It is expected to be −1.06% in 2060–2065 (IPSS 2017).

24

2 The Principle of Sustainable Population 70.0

Doubling Time : years

60.0

Doubling Time

50.0 40.0 30.0 20.0 10.0

1% 6% 11% 16% 21% 26% 31% 36% 41% 46% 51% 56% 61% 66% 71% 76% 81% 86% 91% 96%

0.0 Anual Population Growth Rate: r

Fig. 2.13 Doubling time of exponential growth

it will be (1/2) × (1/2) × (1/2) × (1/2) = (1/16) times. In less than 300 years, the population will shrink 6.25% of the initial state. This rate of decaying population is also unsustainable and can degrade Japan’s socio-economic circumstances and natural environment.16 The present human beings, homo sapiens have been living for one hundred thousand years or more on the Earth. Then, a population growth rate near to ±1% or more must have been an extraordinarily rare case, which could be maintained only for a short period, unless they should have been diminished for long ago. Conversely thinking the fact that humans are still existing from past to present, the average annual population growth rate must have been less than 0.01%, which is known as an increasing rate of prehistoric hunter-gatherer society. It may be at a very low level, which is slightly positive, near to 0%.

2.5 Limit of Growth and Logistic Curve Malthus said, ‘Population, when unchecked, increases in a geometrical ratio’. Then, when checked, what happens to the population? In population biology, it is supposed that there is a support threshold that the environment can maintain. It is the so-called a carrying capacity of the environment, represented usually by the symbol K. Population is increasing to draw an S-shaped curve and reaching K. This S-shaped curve is called a logistic curve (Fig. 2.14). This art of population growth is described as a function with K in the following equation,

16 The

rapidly shrinking population can devastate natural environment including human activity in its balance.

2.5 Limit of Growth and Logistic Curve

25

Fig. 2.14 logistic curve and carrying capacity of the environment K

Nt =

N 0 K er t K − N 0 + N 0 er t

N t represents the population number at time t and N 0 is the population number at time 0. The large e is the base of the natural logarithm (alias Napier’s constant, e  2.71828) and r 17 is the population growth rate (alias increase rate). The small t is the length of time. K is carrying capacity of the environment. The above equation is derived from a differential equation as follows, Nt+dt = Nt + Nt r

K − Nt dt K

This is the so-called “logistic equation”. It shows a small change of population N per small t is the multiple of population growth rate r 18 , population N, and (K − N)/K. The (K − N)/K is the same as KPratio in Sect. 2.2. This indicates the difference between the population N and the carrying capacity of the environment K, in proportion to K. If N increases to K, (K − N)/K decreases from 1 to 0.19 . This means the population increases exponentially with r at the beginning, approaches to K and stagnates at K. As mentioned, it is difficult to predict the level of K in the case of human beings. It is because K is not fixed a priori but relatively changed according to the adaptation capacity of the human being. In fact, it is decided posteriori, when the growth rate reaches 0. Thus, K is the result of adaptation in the case of human society. I think that K can be decided only posteriori, also in other creatures, if we consider the complexity of ecological balance or food chain in biosphere. 17 This

r is a decimal number, not in %.

18 Maximum intrinsic rate of increase means the theorical value of intrinsic increase rate under ideal

conditions (for example enough food, space, etc.). 19 If N is nearly to Zero, (K − N) is nearly to K. Then, the value of (K − N)/K is K/K = 1. If N is nearly to K, (K − N) is nearly to Zero. Then, the value of (K − N)/K will be 0/K = 0.

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2 The Principle of Sustainable Population

The actual population growth rate at t (rt) can be also calculated from dN/dt (cf.rt = Popchange/Pop, in Sect. 2.2). In fact, the population growth rate (r) of population biology is given not as a constant value but as a difference between the birth rate (b) and the death rate (d) (without migration) in the following equation, r = b−d If this r = b − d would be constant and larger than 0 for long time, the population would increase exponentially, all the weight of the population would be the same as the Earth and this would be expanding with light speed to all the universe (Willson and Bossert 1977). Thus, in population biology, r = b − d is usually, regarded as “density dependence”. Namely, the birth rate b decreases, and the death rate d increases according to population density. In the process, in which the population growth rate (r) is reaching 0, the birth rate(b) and the death rate (d) are changing to reduce the difference between them. If the space for expanding is limited, population density is changing proportionally to the population. Therefore, we can think that the difference between the birth rate(b) and the death rate (d) is decreasing according to the number of population N. And K indicates the number of populations, where the birth rate(b) and the death rate (d) is crossing and their deference becomes 0 (Fig. 2.15). In population biology, according to the large population N (or density of N) the birth rate is to decrease and the death rate is to increase because of getting worse in conditions. It is like the intensified competition for mating, the decreasing food per capita, the deterioration of the (natural) environment, etc. That is called “density-dependent effect”.

b:Birth Rate or d:Death Rate

b d

r=b-d >0 N