Invasive species are a major threat to global biodiversity (ESA 2000; Davis 2003; Gurevitch and Padilla 2004), second only to habitat destruction. Invasive species have rapid rates of population growth, and displace native species from the habitat. One solution to the invasive plant species problem is biological control. In plants, for instance, biological control consists of introducing enemies (e.g., herbivores) from the plant's native range. The herbivores are meant to "damage" the invasive plant species by consuming plant tissue, reducing plant resources, and therefore curbing its population growth. Sometimes biological control is successful, and sometimes it is not (Messing and Wright 2006). Thus, it is critical for ecologists to predict the likely success of biological control, and how much damage the control agent must inflict on an invasive species in order to significantly reduce its rate of population growth.
Population ecologists often use demographic matrix models to project the growth rate of a population (Horn 1975, van Groenendael et al., 1988; Akcakaya et al., 1999; Caswell 2000; Morris and Doak, 2002). Demographic matrix models are particularly useful for plants and animals that are easily classified into stage and size classes. Many organisms fit this criteria. For example, trees can be classified into seeds, seedlings, saplings and adults. Many insects can be classified based on their number of molts. Amphibians can be classified into eggs, tadpoles and adults.
Demographic matrix models use detailed information about growth, survivorship and fertility of organisms to project the growth rate of the population. These models are especially useful for invasive plants, because we can project how fast the population is growing, and examine how different management techniques will curb this growth. The input parameters of matrix models are vital rates (survivorship, growth, fertility) of individuals in each stage class (e.g., in plants, stage classes often include seedlings, juveniles and adults) in a population. The output of these models is the growth rate of the population. If the growth rate of the population (λ) is 1, then the population is expected to stay the same size through time. If λ>1, then the population will grow exponentially. If λ<1, the population will decline towards extinction.
Reducing the population growth rate of an invasive plant might be achieved through management. Once a demographic matrix model is created, this model can be used to inform managers which stage classes they should focus their management on in order to cause the most dramatic decrease in the growth rate of the population. The stage-specific vital rates contribute unequally to population growth rate; changes in some vital rates will have large effects on population growth rate, while others have relatively small effects. Elasticity analysis can be conducted to determine how changes in each vital rate will affect population growth rate. Elasticity analysis is a type of perturbation analysis that is achieved by making small changes in each vital rate and quantifying how such changes affect the population growth rate.
The goal of biocontrol is to cause a rapidly growing invasive population (i.e., λ>1) to either stabilize (λ=1) or decline towards extinction (λ<1). In order to evaluate the likely success of biological control, researchers can damage (remove leaf tissue manually) invasive species in a manner similar to that of a biocontrol agent, and measure the effects of that damage on vital rates. Matrix models in the presence and absence of damage can be compared to see if the damage inflicted will curb the population growth rate of the invasive species.
Further, even if biological control is predicted to be a feasible option, it is still considered a risky management strategy, as the control agents may have unexpected and negative effects on native species (Louda et al 2003). Typically, such negative effects are instances of host-switching, where the introduced control agent not only damages the invasive target species, but also native species (Messing and Wright 2006). A moth, Cactoblastis cactorum, for example, was introduced to the United States to control an invasive prickly pear cactus, but resulted in attack on many native cacti (Louda et al 2003). Furthermore, plants and herbivores are not the only members of an ecological community; there are also predators of herbivores, carnivores, parasites, etc. Therefore, it is essential to examine all trophic interactions, including those beyond the species of interest, to fully understand which interactions might produce unexpected effects following an introduction of an herbivorous biocontrol agent into a community (Pearson and Callaway 2006).
In this issue students can build on interpreting graphs and teaching each other, to exploring how matrix models are used to predict potential effectiveness of biological control using an example from the literature. This exercise allows them to integrate research data into a computer program (R, which is freely available on the internet, http://cran.r-project.org/bin/windows/base/), hypothesize about and interpret their results, teach other students, and understand the application of the research. Further, they will learn about how trophic cascades can result in unintended consequences when scientists and communities decide to go forward with introducing biological control agents.