Can the Earth feed 9 billion people? Predicting population growth and its impact on food availability

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Can the Earth feed 9 billion people? Predicting population growth and its impact
on food availability?
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3rd March 2020

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Can the Earth feed 9 billion people? Predicting population growth and its impact
on food availability
1. Introduction
Usually, we have seen images in the media, especially children, suffering from
hunger and poverty. More than one billion of today’s seven billion people suffer from
hunger (UNICEF, 2015). Will it be enough food to feed the increasing global
population in the future? Feeding the world will be a huge challenge for humanity.
The issues of hunger and poverty are dealt in the framework of Sustainable
Development Goals and more specifically in SDG1 and SDG2. In this context,
concepts such as exponential growth, human carrying capacity and food availability
are extremely relevant in this context. Exponential growth "only occurs when a
species lives under optimal conditions, with enough food, water and space... and
above a certain population size, the growth rate slows down gradually" (Rutherford,
2009, p. 160-161). Population sizes are usually close to the carrying capacity, defined
as the maximum of human population that, the Earth can sustainably carry or support
(ibid.). This is a complex issue for a number of reasons. Among these reasons are that
humans use much more natural resources than any other animal. Also, the use of
resources varies according to differences in economic situation, culture and lifestyles.
Consequently, the question, how many people can the Earth support, cannot be easily
answered numerically. This means, that any estimates of human carrying capacity
depend on the choices we are going to make in the future as well as natural events.
We have also to keep in mind that population is increasing at a higher rate than
agricultural production (FAO, 2007) as well as that a lot of food is wasted. Reaching a
balance between the agricultural production and the rate of population growth can
limit the risks associated with a lack of food.

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In this study, I have decided to use two formulas for predicting world
population growth: one based on an exponential growth model (Hathout, 2013) and
the other on a logistic growth model (Hillen, 2016). I will compare my projections
with the UN (2015) forecast that world population is going to grow from 7.3 billion to
more than 9.6 billion by 2050. Next, my objective is to explore if the Earth can feed
the population growth projected through these two models, using data related to food
availability. Upon finding out the rate of the population growth and the food
production levels, I will delve more in to the question whether the earth can feed a
large population. In the discussion, I will also provide suggestions and solutions to
take care of the looming food crisis due to overpopulation.
2. Predicting World Population Growth
Global population has grown exponentially. However, most of this growth will
take place in developing countries as well as in urban areas (FAO, 2016). By 2050,
66% of the world‘s population is expected to live in urban areas, especially in Africa
and Asia (UN, 2014). To my mind, predicting population growth and being able to
answer the impacts of population growth on global hunger seems to be a very
important issue to explore. There are now more than 7 billion of people on Earth and
as world population continues to grow, the need for far more water, food, land,
transport and energy will also continue to increase (Crist, Mora, & Engelman, 2017).
As a result, we are accelerating the rate at which we're using our natural resources. It
is, thus, important to understand how all this is connected. Upon attaining the
necessary understanding of how things work we will be able to find solutions to the
problem of the depletion of the available natural resources.
2.1. Applying an Exponential Growth Model
Based on the growth model of population
P=Po∙ert

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Where,
P=final population
Po=initial population
r=rate of growth
t=time (years)
I reformulated the exponential model as follows, by setting 1960 as the t=0:
P=PO∗er (t−1960)
In order to estimate the rate of growth, I substitute
Po with the population of 1960, t with 2009 and P with the population of 2009. The
reason for choosing 2009 is because it was the closest most accurate year to 2016.
Since the population in 1960 was 3.04 billion (Po) and in 2009 the population was
6.816 billion (US Census1). I use the population of years 1960, P (1960) =3.04 and the
population of 2009, P (2009) = 6.816 in order to calculate r.
6.816=3.04∗er ( 2009−1960)
6.816
3.04 =e49 r
ln (6.816)
3.04 =49 r
r =0.631
49
R=0.016
P ( t ) =3.04∗e0.016(t−1960)
T=2050-1960=90 I calculate the population of 2050
P (2050) =3.04∗e0.016(2050−1960)=13.393
Based on the exponential model the population in 2050 will reach 13.39 billion
people.
1 http://www.census.gov/population/international/data/idb/worldpoptotal.php

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Figure 1. World population growth applying an exponential mathematical model
POPULATION VS TIME
I use derivatives for further analysis of the rate of growth, I found that first derivative
of the population curve is positive and therefore, the population is an increasing
function.
P(t)=3.04∗e0.016(t−1960)
dP(t)
dt = ́P ( t )=3.04 ¿ e0.016(t −1960)∗[0.016∗(t−1960)]
=3.04*e0.016(t −1960)∗0.016
=0.05*e0.016(t −1960)

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Figure 2. Derivative result of exponential world population growth
GROWTH RATE VS TIME
By plotting the derivative of population curve (Figure 2), I conclude that it’s an
increasing function. This means, that every year the population growth increases in
relation to the previous.
2.2. Applying a Logistic Model
As an indicator of the carrying capacity M, meaning the maximum of human
population that the Earth can sustainably carry or support, I have decided to take 14.8
billion that is the population increase predicted from the census of China and to apply
in the logistic model.
P ( t ) = M∗Po
Po+ ( M −Po ) ∗e− λt
Where, λ= rate of population growth (just as I had r in the exponential model). I set
1960 as t=0 and the initial population in 1960 Po= 3.04
P ( t ) = M∗Po
Po+ ( M −Po ) ∗e− λ(t −1960)
In 2009, the population was 6.816 billion, bellow I am calculating λ using population
1960 and population 2009.