Ecology. Michael Begon

details).

      In 1679, van Leeuwenhoek estimated the inhabited area of the Earth as 13 385 times larger than his home nation of Holland, whose population then was about one million people. He assumed all this area could be populated as densely as Holland, yielding an upper limit of roughly 13.4 billion. In 1967, De Wit asked how many people could live on Earth if photosynthesis was the limiting factor (but neither water nor minerals were limiting) and suggested 1000 billion, though if people wanted to eat meat or have a reasonable amount of living space the estimate would be lower. By contrast, Hulett in 1970 assumed levels of affluence and consumption in the USA were optimal for the whole world, and he included requirements not only for food but also for renewable resources like wood and non‐renewable resources like steel and aluminium. He suggested a limit of no more than 1 billion. Kates and others made similar assumptions using global rather than US averages. They estimated a global carrying capacity of 5.9 billion people subsisting on a basic diet (principally vegetarian), 3.9 billion on an ‘improved’ diet (about 15% of calories from animal products), or 2.9 billion on a diet with 25% of calories from animal products.

      As Cohen (2005) has pointed out, most estimates have relied heavily on a single dimension – biologically productive land area, water, energy, food and so on – when in reality the impact of one factor depends on the value of others. Thus, for example, if water is scarce and energy is abundant, water can be desalinated and transported to where it is in short supply, a solution that is not available if energy is expensive. And as the examples above make clear, there is a difference between the number the Earth can support (the concept of a carrying capacity we normally apply to other organisms) and the number it can support at an acceptable standard of living. It is unlikely that many of us would choose to live crushed up against an environmental ceiling or wish it on our descendants.

      what is the ‘human population problem’?

      Our difficulties in defining a global carrying capacity raise a deeper difficulty. What is ‘the human population problem’? It may be simply that the present size of the global human population is unsustainably high – greater than the (presently unknown) carrying capacity. Or it may be not the size of the population but its distribution over the Earth that is unsustainable. Crowding as much as population size is the problem. As we have seen, the fraction of the population concentrated in urban environments has risen from around 3% in 1800 to more than 50% today. Each agricultural worker today has to feed her‐ or himself plus one city dweller. By 2050 that will have risen to each worker feeding two urbanites (Cohen, 2005). Or perhaps it is not the size but the age distribution of the global population that is unsustainable. In developed regions, the percentage of the population over 65 rose from 7.6% in 1950 to 12.1% in 1990. This proportion is now increasing faster still, as the large cohort born after World War II passes 65. Or finally it may not be that resources are limited but that their uneven distribution is unsustainable. Competition may be unbearably intense for some, while for others density‐independence prevails. In 1992, the 830 million people of the world’s richest countries enjoyed an average income equivalent to US$22 000 per annum. The 2.6 billion people in the middle‐income countries received $1600. But the two billion in the poorest countries got just $400. These averages themselves hide other enormous inequalities.

      Of course, the human population problem, just like the problem in any crowded population, is not simply one of intense intraspecific competition for limited resources. Individuals in poor condition may be more vulnerable to predation and parasitism, and the spread of parasites may itself be enhanced. We return to the ways in which the abundances of populations are determined by the combination of forces acting on them in Chapter 14.

      inescapable momentum

      Finally we can ask what would happen if it were possible to bring demographic transition to all countries of the world so birth rates equalled death rates and population growth was zero. Would the population problem be solved? The answer is no, for at least two important reasons. We saw in Chapter 4 that the net reproductive rate of a population is a reflection of age‐related patterns of survival and birth, but these patterns also give rise to different age structures within the population. If birth rates are high but survival rates low (‘pre‐transition’), there will be many young and relatively few old individuals in the population. But if birth rates are low and survival rates high – the ideal to which we might aspire post‐transition – relatively few young, productive individuals must support the many who are old, unproductive, and dependent: an aspect of the problem that we noted above.

      In addition, even if our understanding was so sophisticated and our power so complete that we could establish equal birth and death rates tomorrow, would the human population stop growing? The answer, once again, is ‘No.’ Population growth has its own momentum, and even with birth rate matched to death rate, it would take many years to establish a stable age structure, while considerable growth continued in the meantime. According to projections by the United Nations, even with low fertility the world’s population will grow from slightly more than seven billion today to more than eight billion by 2050 (Figure 5.19b). There are many more babies in the world now than 25 years ago, so even if birth rate per capita drops considerably now, there will still be many more births in 25 years’ time than now, and these children, in turn, will continue the momentum before an approximately stable age structure is eventually established. As Figure 5.19c shows, it is the populations in the developing regions of the world, dominated by young individuals, that will provide most of the momentum for further population growth.

5.5 Mathematical models: introduction

      The desire to formulate general rules in ecology often finds its expression in the construction of mathematical or graphical models. It may seem surprising that ecologists interested in the natural living world should spend time reconstructing it in an artificial mathematical form. But there are several good reasons why this should be done. The first is that models can crystallise, or at least bring together in terms of a few parameters, the important, shared properties of a wealth of unique examples. This simply makes it easier for ecologists to think about the problem or process under consideration, by forcing us to try to extract the essentials from complex systems. Thus, a model can provide a ‘common language’ in which each unique example can be expressed; and if each can be expressed in a common language, then their properties relative to one another, and relative perhaps to some ideal standard, will be more apparent.

      Even more important, models can shed light on the real world that they mimic. They can exhibit properties that the system being modelled had not previously been known to possess, and they can make it clear how the behaviour of a population, for example, depends on the properties of the individuals that comprise it. Models do this because they force us to make explicit any assumptions that we choose to make, and mathematical methods are designed precisely to allow a set of assumptions to be followed through to their natural conclusions. We can ask, for example, ‘If only juveniles migrate, what would this do to the dynamics of their populations?’. As a consequence, models often suggest what would be the most profitable experiments to carry out or observations to make – ‘Since juvenile migration rates appear to be so important, these should be measured in each of our study populations’.

      These ideas are more familiar, perhaps, in other contexts, but are equally valid in ecology. Other than in their imaginations, Newton never laid hands on a perfectly frictionless body, and Boyle never saw an ideal gas. But Newton’s Laws of Motion and Boyle’s Law have been of immeasurable value to us for centuries.

      These reasons for constructing models are also criteria by which any model should be judged. Indeed, a model is only useful (i.e. worth constructing) if it does perform one or more of these functions. Of course, in order to perform them a model must adequately describe real situations and real sets of data, and this ‘ability to describe’ or ‘ability to mimic’ is itself a further criterion by which a model can be judged. However, the crucial