Species Interactions Can Be Classified Based on Their Reciprocal Effects.

If we designate the positive effect of one species on another as +, a detrimental effect as −, and no effect as 0, we can use this qualitative description of the different ways in which populations of two species interact to develop a classification of possible interactions between two co-occurring species (Table 12.1). When neither of the two populations affects the other, the relationship is (00), or neutral. If the two populations mutually benefit, the interaction is (++), or positive, and the relationship is called mutualism (Chapter 15). When one species maintains or provides a condition that is necessary for the welfare of another but does not affect its own well-being, the relationship (+0) is called commensalism . For example, the trunk or limb of a tree provides the substrate on which an epiphytic orchid grows (Figure 12.1). The arrangement benefits the orchid, which gets nutrients from the air and moisture from aerial roots, whereas the tree is unaffected.

When the relationship is detrimental to the populations of both species (−−), the interaction is termed competition (Chapter 13). In some situations, the interaction is (−0). One species reduces or adversely affects the population of another, but the affected species has no influence in return. This relationship is amensalism . It is considered by many ecologists as a form of asymmetric competition, such as when taller plant species shade species of smaller stature.

Relationships in which one species benefits at the expense of the other (+−) include predation, parasitism, and parasitoidism (see Chapter 14 for more information on predation and Chapter 15 for more information on parasitism and parasitoidism). Predation is the process of one organism feeding on another, typically killing the prey. Predation always has a negative effect on the individual prey. In parasitism , one organism feeds on the other but rarely kills it outright. The parasite and host live together for some time. The host typically survives, although its fitness is reduced. Parasitoidism , like predation, kills the host eventually. Parasitoids, which include certain wasps and flies, lay eggs in or on the body of the host. When the eggs hatch, the larvae feed on it. By the time the larvae reach the pupal stage, the host has succumbed.

12.2 Species Interactions Influence Population Dynamics

The varieties of species interactions outlined in the previous section typically involve the interaction of individual organisms. A predator captures a prey or a bacterium infects a host organism. Yet through their beneficial or detrimental effects on the individuals involved, these interactions influence the collective properties of birth and death at the population level, and in doing so, influence the dynamics of the respective populations. For example, by capturing and killing individual prey, predators function as agents of mortality. We might therefore expect that as the number of predators (Npredator) in an area increases, the number of prey captured and killed will likewise increase. If we assume the simplest case of a linear relationship, we can represent the influence of changes in the predator population (Npredator) on the death rate of the prey population (dprey) as shown in Figure 12.2a. As the number of predators in the population (Npredator) increases, the probability of an individual in the prey population (Nprey) being captured and killed increases. Subsequently, the death rate of the prey population increases. The net effect is a decline in the growth rate of the prey population. Note the similarity in the functional relationship presented in Figure 12.2a with the example of density-dependent population control presented earlier (Chapter  11, Figure 11.1). Previously, we examined how an increase in population size can function as a negative feedback on population growth by increasing the mortality rate or decreasing the birthrate (density-dependent population regulation; Section 11.2 and Figure  11.4). The relationship shown in Figure 12.2a expands the concept of density-dependent population regulation to include the interaction between species. As the population of predators increases, there is a subsequent decline in the population of prey as a direct result of the prey’s increased rate of mortality.

A similar approach can be taken to evaluate the positive effects of species interactions. In the example of predation, whereas the net effect of predation on the prey is negative, the predator benefits from the capture and consumption of prey. Prey provides basic food resources to the predator and directly influences its ability to survive and reproduce. If we assume that the ability of a predator to capture and kill prey increases as the number of potential prey increase (Nprey), and that the reproductive fitness of a predator is directly related to its consumption of prey, then we would expect the birthrate of the predator population (bpredator) to increase as the size of the prey population increases (Figure 12.2b). The result is a direct link between the availability of prey (size of the prey population, Nprey) and the growth rate of the predator population (dNpredator/dt).

In Chapter 11, we developed a logistic model of population growth. It is a model of intraspecific competition and density-dependent population regulation using the concept of carrying capacity, K. The carrying capacity represents the maximum sustainable population size that can be supported by the available resources. The carrying capacity functions to regulate population growth in that as the population size approaches K, the population growth rate approaches zero (dN/dt = 0).

When individuals of two different species share a common limiting resource that defines the carrying capacity, there is potential for competition between individuals of the two species (interspecific competition). For example, let’s define a population of a grazing antelope inhabiting a grassland as N1, and the carrying capacity of the grassland to support that population as K1 (the subscript 1 refers to species 1). The logistic model of population growth (see Section 11.1) would then be:

dN1/dt = r1N1(1 − N1/K1)dN1/dt = r1N1(1 − N1/K1)

Now let’s assume that a second species of antelope inhabits the same grassland, and to simplify the example, we assume that individuals of the second species—whose population we define as N2—have the same body size and exactly the same rate of food consumption (grazing of grass) as do individuals of the first species. As a result, when we evaluate the role of density-dependent regulation on the population of species 1 (N1), we must now also consider the number of individuals of species 2 (N2) because individuals of both species feed on the grass that defines the carrying capacity of species 1 (K1). The new logistic model for species 1, will be:

dN1/dt = r1N1(1 − (N1 + N2)/K1)dN1/dt = r1N1(1 − (N1 + N2)/K1)

For example, if the carrying capacity of the grassland for species 1 is 1000 individuals (K1 = 1000)—because species 2 draws on the exact same resource in exactly the same manner—the combined carrying capacity of the grassland is also 1000. If there are 250 individuals of species 2 (N2 = 250) living on the grassland, it effectively reduces the carrying capacity for species 1 from 1000 to 750 (Figure  12.3a). The population growth rate of species 1 now depends on the population sizes of both species 1 and 2 relative to the carrying capacity (Figure  12.3b). Although we have defined the two antelope species as being identical in their use of the limiting resource that defines the carrying capacity, this is not always the case. In reality, it is necessary to evaluate the overlap in resource use and quantify the equivalency of one species to another (see Quantifying Ecology 12.1).

In all cases in which individuals of two species interact, the nature of the interaction can be classified qualitatively as neutral, positive, or negative, and the influence of the specific interaction can be evaluated in terms of its impact on the survival or reproduction of individuals within the populations. In the discussion that follows, we develop quantitative models to examine how the diversity of species interactions outlined in Table  12.1 influence the combined population dynamics of the species involved (Chapters 13, 14, and 15). In all cases, these models involve quantifying the per capita effect of interacting individuals on the birthrates and death rates of the respective populations.

Quantifying Ecology 12.1 Incorporating Competitive Interactions in Models of Population Growth

When individuals of two different species (represented as populations N1 and N2) share a common limiting resource that defines the carrying capacity for each population (K1 and K2), there is potential for competition between individuals of the two species (interspecific competition). Thus, the population density of both species must be considered when evaluating the role of density-dependent regulation on each population. In Section 12.2, we gave the example of two species of antelope that share the common limiting food resource of grass. We assumed that individuals of the two species were identical in their food selection and the rate at which they feed, therefore, with respect to the carrying capacity of the grassland, individuals of the two species are equivalent to each other; that is, in resource consumption one individual of species 1 is equivalent to one individual of species 2. As a result, when evaluating the growth rate of species 1 using the logistic model of population growth, it is necessary to include the population sizes of both species relative to the carrying capacity (see Figure 12.4):

dN1/dt = r1N1(1 − (N1 + N2)/K1)dN1/dt = r1N1(1 − (N1 + N2)/K1)

However, two species, even closely related species, are unlikely to be identical in their use of resources. So it is necessary to define a conversion factor that can equate individuals of species 2 to individuals of species 1 as related to the consumption of the shared limited resource. This is accomplished by using a competition coefficient, defined as a, that quantifies individuals of species 2 in terms of individuals of species 1 as related to the consumption of the shared resource. Using the example of two antelope species, let us now assume that both species still feed on the same resource (grass), however, individuals of species 2 have on average only half the body mass of individuals of species 1 and therefore consume grass at only half the rate of species 1. Now an individual of species 2 is only equivalent to one-half an individual of species 1 with respect to the use of resources. In this case, a = 0.5, and we can rewrite the logistic model for species 1 shown previously as:

dN1/dt = r1N1(1 − (N1 + αN2)/K1)dN1/dt = r1N1(1 − (N1 + αN2)/K1)

Because in Section 12.2 we defined the carrying capacity of the grassland for species 1 as K1 = 1000, we can substitute the values of a and K1 in the preceding equation:

dN1/dt = r1N1(1 − (N1 + 0.5N2)/1000)dN1/dt = r1N1(1 − (N1 + 0.5N2)/1000)

Now the growth rate of species 1 (dN1/dt) approaches zero as the combined populations of species 1 and 2, represented as N1 + 0.5N2, approach a value of 1000 (the value of K1).

We have considered how to incorporate the effects of competition from species 2 into the population dynamics of species 1 using the competition coefficient a, but what about the effects of species 1 on species 2? The competition for food resources (grass) will also function to reduce the availability of resources to species 2. We can take the same approach and define a conversion factor that can equate individuals of species 1 to individuals of species 2, defined as b. Because individuals of species 1 consume twice as much resource (grass) as individuals of species 2, it follows that an individual of species 1 is equivalent to 2 individuals of species 2; that is, b = 2.0. It also follows that if individuals of species 2 require only half the food resources as individuals of species 1, then the carrying capacity of the grassland for species 2 should be twice that for species 1; that is, K2 = 2000. The logistic growth equation for species 2 is now:

dN2/dt = r2N2(1 − (N2 + βN1)/K2)dN2/dt = r2N2(1 − (N2 + βN1)/K2)

or, substituting the values for b and K2

dN2/dt = r2N2(1 − (N2 + 2.0N1)/2000)dN2/dt = r2N2(1 − (N2 + 2.0N1)/2000)

We now have a set of equations that can be used to calculate the growth of the two competing species that considers their interaction for the limiting food resource. We explore this approach in more detail in the following chapter (Chapter 13).

In the example of the two hypothetical antelope species presented previously, the estimation of the competition coefficients (a and b) appear simple and straightforward. Both species are identical in their diet and differ only in the rate at which they consume the resource (which is defined as a simple function of their relative body masses). In reality, even closely related species drawing on a common resource (such as grazing herbivores) differ in their selection (preferring one group of grasses of herbaceous plants over another), foraging behavior, timing of foraging, and other factors that influence the nature of their relative competitive effects on each other. As such, quantifying species interactions, such as resource competition, can be a difficult task, as we shall see in the following chapter (Chapter 13, Interspecific Competition).

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