Ecology lab – Wolf conservation Predators and Prey on Isle Royale Introduction Isle Royale is an island about 15 miles from the northern shore of Lake Superior, which is one of the Great Lakes on the border of Canada and the U.S. Lake Superior is the largest freshwater lake in the world, stretching 160 miles from north to south and well over 300 miles from east to west. Not many large animals have made it from the shores of Lake Superior to Isle Royale. About 100 years ago, however, a few moose found their way across from mainland Canada to the island, probably walking most of the way across surface ice during an especially cold winter. The moose found a veritable paradise, with lots of grass, bushes, and low-lying trees to eat and no predators. The moose population exploded, reaching several thousand individuals at its peak. In 1949, the area around Lake Superior had another cold winter and large parts of the lake's surface froze solid. A small pack of wolves found a stretch of ice that extended all the way to Isle Royale. There they found a huge population of moose that had eaten most of the available food, and many of whom were severely undernourished. These starving moose were easy prey for the wolves. The wolves and moose on Isle Royale became a kind of natural experiment for studying population ecology, and in particular, predator-prey dynamics. There are four key factors that affect population size: birth, death, immigration, and emigration. Immigration and emigration are usually very difficult to quantify in most natural populations, but because Isle Royale is isolated, these factors can basically be ignored, making this an especially practical place to study population ecology. In fact, several biologists have spent their careers studying the wolf and moose populations on Isle Royale, tracking individuals and recording how many of each species are born each year and how many die, causes of death, food availability, and so on. Using these data, they try to understand what factors cause the moose and wolf populations to fluctuate over time. The Isle Royale Model in EcoBeaker In this lab, you will explore populations of predators and prey using a simplified simulation model of the Isle Royale system. The Isle Royale model involves three species: plants, moose, and wolves. The "plants" in the model represent moose food. You can change the rate at which the plant population grows, simulating, for example, particularly wet or dry years which would result in larger or smaller plant populations. Although real-world moose eat a variety of plants, in this simulation, all plant individuals are identical. The animals in the Isle Royale model are somewhat more complex than the plants. However, like the plants, the actions of each individual are determined by thesame set of rules. For example, there are rules that dictate the maximum number of squares a moose or wolf can move at a time (i.e., in one time-step) or what to do if another species is encountered. Rules dictate how much energy an individual gains if they encounter and eat their prey species, and how much energy is used up in each time-step while searching for prey. Death occurs when an individual's energy level drops below a set point. To keep things simple, there are no babies, no elderly, and no sick individuals – only middle-aged adults. You'll also see the wolves hunting alone, whereas real wolves tend to hunt in packs. These simplifications help your experiments, but still retain the basic nature of the interactions between the species. Some Important Terms and Concepts Population Ecology The study of changes in the size and composition of populations and the factors that cause those changes. Population Growth and Carrying Capacity Models of population growth can provide a helpful framework for understanding that complexity, and also, if the models are accurate, for predicting how population size will change in the future. The simplest model of population growth considers the "ideal world" case in which there are no limitations on a population's growth (i.e., all of the necessary resources to survive and reproduce are in excess). If this is the case, the larger the population becomes, the faster it will grow because in each generation, more individuals will reproduce. This type of population growth is modeled with the exponential growth model. This model assumes that the population is increasing at its maximum per capita rate of growth (also referred to as the intrinsic rate of increase), which is denoted "rmax". Using the "dN/dt" notation of differential calculus to represent the change in population size per unit time (in this case, the change in population size N over time t), if population size is N, and time is t, then: dN/dt = rmax N The following graph depicts an example of exponential population growth (notice how it starts out shallow and then becomes sharply steeper): Exponential Population Growth POPULATION SIZE (N) TIMEIn the real world, conditions are typically not quite so ideal, so population growth is often limited by the availability of important resources such as nutrients or space. Carrying capacity (symbolized as K) is the maximum number of individuals of a species that the local environment can support at a particular time. When a population is small, for example during the early stages of colonization, it may grow exponentially (or nearly so), but as resources start to run out, population growth typically slows down and eventually the population size stabilizes at the level of carrying capacity. To incorporate the influence of carrying capacity in projections of population growth rate, ecologists use the logistic growth model. In this model, the per capita growth rate (r) decreases as the population density increases. When the population is at its carrying capacity (N=K) the population will no longer grow. dN/dt = rmax N((K-N)/K) Try plugging a few numbers into this equation. For example, if N=K, then K-N in the right hand side part of the equation equals zero. Zero divided by any number equals zero. Thus,