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MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY

Part of: Integral equations, integral transforms General theory in ordinary differential equations Mathematical biology in general

Published online by Cambridge University Press:  18 December 2020

DINY ZULKARNAEN Open the ORCID record for DINY ZULKARNAEN [Opens in a new window]  and
MARIANITO R. RODRIGO
DINY ZULKARNAEN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; e-mail: [email protected]. Department of Mathematics, Universitas Islam Negeri Sunan Gunung Djati, Bandung, West Java, Indonesia; e-mail: [email protected].
MARIANITO R. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; e-mail: [email protected].
*
e-mail: [email protected]
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Abstract

We assume that human carrying capacity is determined by food availability. We propose three classes of human population dynamical models of logistic type, where the carrying capacity is a function of the food production index. We also employ an integration-based parameter estimation technique to derive explicit formulas for the model parameters. Using actual population and food production index data, numerical simulations of our models suggest that an increase in food availability implies an increase in carrying capacity, but the carrying capacity is “self-limiting” and does not increase indefinitely.

Keywords

logistic modelvariable carrying capacityfood production indexmathematical modelling

MSC classification

Primary: 34A12: Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions
Secondary: 65R32: Inverse problems 92B05: General biology and biomathematics
Type
Research Article
Information
The ANZIAM Journal , Volume 62 , Issue 3 , July 2020 , pp. 318 - 333
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Copyright
© Australian Mathematical Society 2020

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References

Anderson, C., Jovanoski, Z., Sidhu, H. S. and Towers, I. N., “Logistic equation with a simple stochastic carrying capacity”, ANZIAM J. 56 (2016) C431–C445; doi:10.21914/anziamj.v56i0.9386.CrossRefGoogle Scholar
Brauer, F. and Castillo-Chávez, C., Mathematical models in population biology and epidemiology, 2nd edn, (Springer, New York, 2011); doi:10.1007/978-1-4614-1686-9.Google Scholar
Cohen, J. E., “Population growth and the Earth’s human carrying capacity”, Science 269 (1995) 341–346; doi:10.1126/science.7618100.CrossRefGoogle ScholarPubMed
Encyclopaedia Britannica, 2020, Great famine, Encyclopaedia Britannica Inc., accessed 10 August 2020, available at https://www.britannica.com/event/Great-Famine-Irish-history.Google Scholar
Food and Agriculture Organization, Food production index, The World Bank, accessed 15 March 2018, available at http://api.worldbank.org/v2/en/indicator/AG.PRD.FOOD.XD?downloadformat=excel.Google Scholar
Gotelli, N., A primer of ecology, 2nd edn, (Sinauer Associates, Sunderland, MA, 1998).Google Scholar
Hatfield, L. G., What factors affect the carrying capacity of an environment? Seattlepi, accessed 6 August 2020, available at https://education.seattlepi.com/factors-affect-carrying-capacity-environment-6190.html.Google Scholar
Hopfenberg, R., “Human carrying capacity is determined by food availability”, Popul. Environ. 25 (2003) 109–117; doi:10.1023/B:POEN.0000015560.69479.c1.CrossRefGoogle Scholar
Hopfenberg, R. and Pimentel, D., “Human population growth as a function of food supply”, Environ. Dev. Sustain. 3 (2001) 1–15.CrossRefGoogle Scholar
Holder, A. B. and Rodrigo, M. R., “An integration-based method for estimating parameters in a system of differential equations”, Appl. Math. Comput. 219 (2013) 9700–9708; doi:10.1016/j.amc.2013.03.052.Google Scholar
International Institute for Sustainable Development, 2017, PRB’s 2017 world population data sheet focuses on youth, International Institute for Sustainable Development, accessed 1 September 2018, available at https://sdg.iisd.org/news/prbs-2017-world-population-data-sheet-focuses-on-youth/.Google Scholar
Kaneda, T., 2017, 2017 world population data sheet with focus on youth, Population Reference Bureau, accessed 1 September 2018, available at https://www.prb.org/2017-world-population-data-sheet/.Google Scholar
Lakshmi, B. S., “Oscillating population models”, Chaos Soliton Fract. 16 (2) (2003) 183–186; doi:10.1016/S0960-0779(02)00157-1.CrossRefGoogle Scholar
Leach, P. G. L. and Andriopoulos, K., “An oscillatory population model”, Chaos Soliton Fract. 22 (2004) 1183–1188; doi:10.1016/j.chaos.2004.03.035.CrossRefGoogle Scholar
McConnell, R. L. and Abel, D. C., Environmental issues: measuring, analyzing, evaluating, 2nd edn, (Prentice Hall, Upper Saddle River, NJ, 2001).Google Scholar
Meyer, P. S., “Bi-logistic growth”, Technol. Forecast. Soc. Change 47 (1) (1994) 89–102; doi:10.1016/0040-1625(94)90042-6.CrossRefGoogle Scholar
Meyer, P. S. and Ausubel, J. H., “Carrying capacity: A model with logistically varying limits”, Technol. Forecast. Soc. Change 61 (1999) 209–214.CrossRefGoogle Scholar
Molden, D. and Fraiture, C., “Water scarcity: The food factor”, Issues Sci. Technol. 23 (2007) 39–48.Google Scholar
Pastor, J., Mathematical ecology of populations and ecosystems, (Wiley-Blackwell, Chichester, 2008).Google Scholar
Pomeroy, R., 2012, Human carrying capacity: few answers, lots of questions, RealClear, accessed 6 August 2020, available at https://www.realclearscience.com/blog/2012/04/human-carrying-capacity.html.Google Scholar
Rogovchenko, S. P. and Rogovchenko, Y. V., “Effect of periodic environmental fluctuations on the Pearl-Verhulst model”, Chaos Soliton Fract. 39 (2009) 1169–1181.10.1016/j.chaos.2007.11.002CrossRefGoogle Scholar
Safuan, H. M., Jovanoski, Z., Towers, I. N. and Sidhu, H. S., “Coupled logistic carrying capacity”, ANZIAM J. 53 (2012) 172–184.CrossRefGoogle Scholar
Safuan, H. M., Jovanoski, Z., Towers, I. N. and Sidhu, H. S., “Exact solution of a non-autonomous logistic population model”, Ecol. Modell. 251 (2013) 99–102; doi:10.1016/j.ecolmodel.2012.12.016.CrossRefGoogle Scholar
Shepherd, J. J. and Stojkov, L., “The logistic population model with slowly varying carrying capacity”, ANZIAM J. 47 (EMAC 2007) (2007) C492–C506; doi:10.21914/anziamj.v47i0.1058.CrossRefGoogle Scholar
United Nations Population Division, World population, The World Bank, accessed 15 March 2018, available at http://api.worldbank.org/v2/en/indicator/SP.POP.TOTL?downloadformat=excel.Google Scholar
Wilson, E. O. and Bossert, W. H., A primer of population biology, (Sinauer Associates, Stamford, CT, 1971); doi:10.2307/2528987.Google Scholar
Yarrow, G., 2009, Habitat requirements of wildlife: food, water, cover and space, Clemson Extension, accessed 11 August 2020, available at https://www.academia.edu/5165242/Habitat_Requirements_of_Wildlife_Food_Water_Cover_and_Space.Google Scholar