The word ‘competition’ is used in everyday language, and so we all have a feeling for what it means. We tend to think of competition as an active process in which individuals are striving for a common goal, and trying to outdo each other so that there are winners and losers. In the biological world, individual organisms struggle to obtain the resources necessary for living, such as water, light and food, and we can think of this struggle as involving both intraspecific and interspecific competition. Darwin talked of these processes in terms of the ‘struggle for existence’ in the development of his theory of natural selection.

Defining competition

How do we define competition so that we can study the process in a rigorous way? Many ecologists prefer an operational definition that gives us a way of measuring whether competition is occurring or not. Following this logic, I will modify the definition of Emlen (1973) and define competition as follows: Competition occurs when two or more individuals or species experience depressed fitness (reduced r or K) attributable to their mutual presence in an area. Thus, in simple terms, competition is defined in terms of a mutual inhibition of growth. We have informally used this definition to define and measure intraspecific competition in Chapter 5 (section 5.1), and we will see that it is easy to extend the logistic growth model to include interspecific competition.

Population genetics considers how the frequencies of alternative states of genes in populations are maintained or changed from generation to generation. First, however, it is important that we understand the terms that are used; otherwise, it is easy for beginners to become confused. It is also important to know how the terms will be used in this book, because many of the terms are not used consistently in the wider literature.

Terminology

The following should clarify how the various terms introduced in this chapter are used throughout the book.

phenotype The morphological, physiological, behavioural or biochemical characteristic of an individual, or a group of individuals in a population. Typically, the term refers to a single characteristic, such as body colour or blood group type, but can also refer to more than one characteristic. Almost invariably, there is more than one phenotype for a given characteristic. For example, there may be both short and tall plants in a population.

genotype This is the genetic constitution of an individual, or a group of individuals in a population, which is related by simple Mendelian rules to the phenotype. The theory in this book mainly considers genes with just two different alleles in the population, e.g. A and B, so that there will be just three different genotypes, AA, AB and BB. These will result in three different phenotypes if there is no dominance, but only two if there is dominance. If genotypes AA and AB give rise to the same phenotype, A is considered to be dominant to B, and if AB and BB give the same phenotype, B is considered dominant to A. Theory relating to multiple genes and alleles is considered in Chapter 12.

If different phenotypes have different age-specific birth and death rates, their growth rates, and hence their fitness (see Chapter 10) will vary. Thus, natural selection shapes both the survivorship (lx) and fecundity (mx) curves, and we will look at this particular aspect of evolution in this chapter. However, the life-history characteristics of organisms also include such traits as body size, size of the offspring at birth, the degree of parental care provided to the young, and so on, and consequently our review will also consider some of these life-history traits.

A simplistic view of natural selection would suggest that all organisms should adopt an ideal life history in which they live as long as possible, start to reproduce at an early age, reproduce frequently, and produce a vast number of offspring which have a high rate of survival. However, even a cursory look at the life-history traits of different organisms shows that this is not the case in nature. Consider the following three examples of large, long-lived organisms.

Adult blue whales (Balaenoptera musculus) are about 27 metres long, weigh about 150 tonnes, and may live for about 80 years. After a gestation period of about one year, females normally produce a single, well-developed offspring that weighs as much as an adult elephant. The young calves suckle for about a year, and are provided with considerable parental care and protection during their early life. Their survival is quite high.

In addition to his theory of natural selection, Darwin also proposed a theory of sexual selection to account for certain types of sexual dimorphism (Darwin 1859). He was trying to explain the evolution of secondary sexual characteristics, like the tail of the peacock. The huge ornamental tail in this species appears to be maladaptive, in the sense that it increases the chances of the individual being eaten by a predator by making it harder for the males to fly away, and so is not readily explained by the theory of natural selection. Darwin went on to develop his theory of sexual selection more fully in one of his later books, The Descent of Man and Selection in Relation to Sex (1871).

In this chapter we will look at the basic reasons for sexual competition, go on to consider sexual selection, and finally make a brief survey of some of the different types of mating systems in animals. In a sense, we are completing a circle. We started this book by looking at Darwin's theory of natural selection, and we will end it by looking at a particular type of selection, namely sexual selection.

Sexual conflict and competition

In sexual reproduction, the interests of males and females may conflict with one another. There may also be competition within members of one sex for the reproductive services of the other. The seeds of this conflict and competition lie in the evolution of anisogamy.

Before we can apply the range of equations describing zygotic selection to natural populations, we must be able to estimate the fitness of the different genotypes. This can be difficult to do in practice.

Estimating fitness and selection

We will consider three basic methods of calculating fitness for natural populations. A more complete discussion of these and some additional methods may be found in Johnson (1976).

Direct calculation of partial-generation selection coefficients

Frequently, survival or viability is measured over part of the life cycle. If we use this information to estimate fitness for our selection model, we assume that the other components of fitness, such as number of viable offspring, are the same for the different genotypes. In other words, we are assuming that the coefficients we calculate for part of the life cycle, i.e. the partial-generation coefficients, are the same as those for the full life cycle (full-generation coefficients). It should be recognized that these estimates are only approximations.

Example 11.1A sample of newly weaned mice was marked just prior to the winter, and the following spring, when they had reached reproductive age, they were live-trapped to estimate their pre-reproductive survival. Other evidence suggested that the different genotypes did not differ in their fertility or fecundity during their brief reproductive lives. Calculate the relative fitness and selection coefficients of the different genotypes from the following data.

In randomly breeding populations, the allelic and genotypic frequencies remain constant from generation to generation and are predicted by the Hardy–Weinberg principle, provided there is no mutation, migration or selection, and the population is infinitely large (see Chapter 6). Population size is finite, however, and many species are structured into several more or less discrete populations (subpopulations or demes) which may be quite small in size. As a consequence there will be changes in allelic frequencies from generation to generation because of sampling error in the production of gametes.

What do we mean by sampling error? Consider a game of coin-tossing in which there is an equal chance of obtaining heads or tails. However, if we toss a coin repeatedly, there is not a sequence of heads, tails, heads, tails, and so on ad infinitum, but rather a random sequence in which there are groupings of heads and tails. Consequently, we would not be surprised if there were not exactly half heads and half tails in a small sample of coin tosses. We would expect the proportion of heads and tails to be distributed in some way around 50%.

Consider the results of a coin-tossing experiment (Fig. 8.1). When the coin was tossed 20 times, the percentage of heads ranged from 25% to 75% in individual trials, and the average across all trials was 49.55%. When the coin was tossed 200 times, the percentage of heads ranged from 42.5% to 57.5%, and the average across all trials was 50%.

We typically think of predators as animals that kill and eat other animals, such as lions eating zebra, or spiders eating flies. These are true predators that consume prey animals to obtain food for their own survival and reproduction. However, there are other types of predators that have some but not all of the features of true predators. These include parasitoids, which are hymenopterans or dipterans that are free-living in the adult stage, but whose larvae live in or on other arthropods (usually insects), doing little harm at first but eventually consuming and killing the host just prior to pupation. There are also plant and animal parasites that live in an obligatory relationship with another species, and harm their hosts, but usually do not kill it. Then there are animals that eat plants, the herbivores. Seed-eating herbivores act like true predators, because they consume all of their ‘prey’. Others act rather like parasites, because they live in close association with the plant and derive their nourishment from it (e.g. aphids). However, the majority of herbivores only consume a part of the plant, and their detrimental effects can be very variable. Partial or complete defoliation of a plant may have a large effect on the plant's fitness, by reducing its growth rate and seed production, and possibly leaving the plant more vulnerable to attack by plant pathogens.

Darwin noted that on average parents produce more offspring during their lifetime than are needed to replace themselves, and so populations have the potential to increase in number. This fact is one of the cornerstones of his theory of natural selection and we can ask why organisms should have this characteristic? Why should there be an overproduction of offspring? Perhaps the easiest way to answer this question is to consider the fate of populations which do not have this characteristic. Obviously, if individuals cannot fully replace themselves, the population will decline to zero and be eliminated. Populations adopting an exact replacement strategy suffer the same fate, because there is always a chance that some individuals will die before they reproduce and so these populations will decline to extinction as their reproductive base shrinks. Thus, although natural selection can select for any reproductive rate, providing that rate leaves the most descendants, only those populations where there is an overproduction of offspring survive over the long term, the others are eliminated.

We can conclude that overproduction is one of the necessary conditions for the long-term survival of populations, allowing them to compensate for pre-reproductive losses and to recover from reductions in population size. We can make similar arguments for the long-term survival of variation in the population. There must be overproduction of copies of specific variants if they are to survive and not be eliminated from the population, and we should bear these facts in mind when we consider the production of new variation by mutation in Chapter 7 and the selection of different variants in Chapters 10 to 12.

Population biology has its roots in many different areas: in taxonomy, in studies of the geographical distribution of organisms, in natural history studies of the habits and interactions between organisms and their environment, in studies of how the characteristics of organisms are inherited from one generation to the next, and in theories which consider how different types of organisms are related by descent. Charles Darwin made a synthesis of these areas in his 1859 book, The Origin of Species by Means of Natural Selection, and this provides us with a convenient starting-point for our introduction to population biology.

The theory of evolution by means of natural selection is the most important theory in biology, but with some notable exceptions one would not realize this after reading many of texts in the area of population biology. Thus, it is no accident that we begin this book with an evolutionary bias.

The purpose of the following three chapters is to provide a historical perspective, and also an understanding of the philosophical content, of Charles Darwin's theory of evolution through the process of natural selection. It is important to understand this Darwinian perspective of biology, because it provides a loose framework for the remainder of this book. In the first chapter we will examine some of the early experiences of Darwin, which may have led him to conclude that organisms evolve and are related by descent.

This part of the book provides an introduction to some simple mathematical models that describe the growth of populations, and Quattro Pro and Excel spreadsheet programs are used to simulate these populations. The emphasis is on making a quantitative assessment of the consequences of Darwin's ‘overproduction of offspring’ and some aspects of ‘the struggle for existence’.

Two basic types of population growth models are described. First, the consequences of Darwin's ‘overproduction’ of organisms are considered in Chapter 4, and described in mathematical terms using the geometric and exponential growth models. These models assume that there are no limits to the numbers of organisms and show that all populations growing in this manner will soon exhaust the earth's resources. Second, in Chapter 5 we look at one aspect of Darwin's ‘struggle for existence’, intraspecific competition, which occurs when a population grows in an environment of finite size. This form of growth is described using the logistic, or sigmoid, growth model, which has some rather restrictive assumptions. This basic model is then modified to assess the effects of time lags and environmental variation on the form of population growth. The models are applied to laboratory and field data show how they relate to reality.

In Chapters 4 and 5, we examined different models of population growth where the structure of the population, in terms of age or size, was constant or unimportant and so could be ignored. However, we are well aware that such factors as sex and age have profound effects on the chances of an individual dying, or producing offspring, and so we need to incorporate some of these factors into our growth models. These vital statistics of populations are called demographics, and the study of these statistics is called demography.

First, the pattern of mortality in relation to age is examined and quantified in Chapter 14. These age-specific death rates are combined with the age-specific birth rates in the following chapter to calculate the exponential growth rates of populations. Some populations with more complex growth characteristics cannot be modelled by the basic equations, and so matrix models of population growth are also introduced because they can be used to describe the growth of any population. Finally, Chapter 16 considers how the pattern of age-specific birth and death rates might have evolved by natural selection, followed by a brief review of the evolution of life-history traits of organisms.

Organisms have a phenomenal potential for increase in numbers when there are no limits to growth. We may enjoy calculating this potential, but don't worry that if we leave the house for a few days we will return to find bacteria many metres deep over the kitchen counters, or if we lock up our summer cabin and inadvertently enclose a female housefly that we will return next spring to find trillions of her offspring buzzing about the place. We recognize that there are insufficient resources to sustain such growth because we live in a finite world, and although we see many instances of population increase we know that there are limits to the size they may eventually reach.

This chapter will focus on developing models which describe how population growth may be influenced by population density through the effects of intraspecific competition for resources. As populations increase in density, the resources needed to sustain them become limiting. For example, barnacles may cover the entire surface of a rock until there is no more space available for further growth of the population. Similarly, cavity nesting birds may have the size of the breeding population limited by the availability of suitable holes in trees. The basic premise of our models is that the realized growth rate will decline as population density increases.

Logistic growth model

The logistic growth model modifies the exponential growth equation δN∕δt = rmN by making the growth rate per capita, r, a function of density, f(N).

Ecologists and population geneticists view migration in very different ways. To the ecologist, migration is the movement of individuals or sometimes whole populations from one area to another. The movements often occur on an annual or seasonal basis, like the birds that overwinter in tropical and subtropical areas and then migrate north to breed in Holarctic regions during the spring or summer, or the caribou (Rangifer tarandus) herds that overwinter in the northern boreal forest and migrate north to calve on the tundra during the summer months. The movements may also be part of the life cycle, like in the Pacific sockeye salmon (Oncorhynchus nerka) that hatch in the headstreams of the rivers, move to the lower reaches of the rivers to feed, and then between the ages of three and seven years move to feed in the oceans before migrating back to their place of birth where they spawn and die. Ecologists seek to understand why animals migrate. Are they moving to take advantage of food resources that become available at different times and places, or is there some other explanation? Many of these migrations are spectacular and may cover huge distances, but to the population geneticist the issue is not how far they may have moved but whether there has been a movement of genes from one population to another. In other words, they are concerned about gene flow.