Skip to main content Accessibility help
×
Home
Hostname: page-component-768ffcd9cc-jp8mt Total loading time: 0.247 Render date: 2022-12-03T16:17:18.856Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY

Published online by Cambridge University Press:  18 December 2020

DINY ZULKARNAEN
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; e-mail: dz862@uowmail.edu.au. Department of Mathematics, Universitas Islam Negeri Sunan Gunung Djati, Bandung, West Java, Indonesia; e-mail: dzulkarnaen@uinsgd.ac.id.
MARIANITO R. RODRIGO*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, New South Wales, Australia; e-mail: dz862@uowmail.edu.au.

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.

Type
Research Article
Copyright
© Australian Mathematical Society 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Anderson, C., Jovanoski, Z., Sidhu, H. S. and Towers, I. N., “Logistic equation with a simple stochastic carrying capacity”, ANZIAM J. 56 (2016) C431C445; 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) 341346; 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) 109117; 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) 115.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) 97009708; 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) 183186; 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) 11831188; 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) 89102; 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) 209214.CrossRefGoogle Scholar
Molden, D. and Fraiture, C., “Water scarcity: The food factor”, Issues Sci. Technol. 23 (2007) 3948.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) 11691181.10.1016/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) 172184.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) 99102; 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) C492C506; 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
3
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

MODELLING HUMAN CARRYING CAPACITY AS A FUNCTION OF FOOD AVAILABILITY
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *