SEE-U 2000: Biosphere 2 - Module 4

## Module 4: Growth and Competition: Population and Metapopulation Dynamics

How do the colonists that begin populations first become established? How and why do populations grow in the manner that they do? What slows or stops population growth? Why do populations die off? How can this information be used to conserve species? These important questions are some of the most vital ones within conservation biology and comprise much of the field of Population Ecology.

As we discussed in Module 3, Darwin observed that populations tend to outstrip their resources. This was one of the important observations with which he formulated the idea of natural selection. If two individuals of a species are allowed to grow and reproduce without impediments, within a few years they would completely cover the Earth, suffocating all other species. The time length to this largest of possible population explosions varies depending on the reproductive and life history biology of each species.

Population Ecology is important in conservation biology (e.g., to estimate population sizes of endangered species, to project population sizes in the future), in agriculture (e.g., to estimate and predict the degree of infestation of pest species), in ranching (e.g., to project the sizes of herds, and estimating degree of pest infestation), in epidemiology (e.g., to estimate current population size and future growth rates of illnesses in human population), and in demography (e.g., estimating human and plant and animal population size), among other fields. All of these applications involve estimating population size and future growth. With this set of ideas in mind, let us discuss the main ways of characterizing population growth.

### Population Growth

There are two main ways of characterizing population growth, one is a simple model and one is slightly more complex and realistic.

The simplest model is exponential population growth, and is commonly referred to as unregulated growth. Populations growing in this fashion consistently exponentially increase in population size. Their growth rate therefore never slows down. When these curves are plotted out, they grow slow initially due to the small number of individuals added. Eventually a rapid explosion occurs and the population steeply increases in size.

Although exponential growth curves are relatively simple, they do occur in nature when populations invade novel habitats or when available resources suddenly outstrip population size. Both of these occur naturally, frequently due to sudden environmental changes like fires or floods. However, they are more frequently due to human action, for example when there is a massive influx of fertilizers into a lake leading to rapid increase in one species of algae which then chokes out other native species. One of the most important human-caused exponential growth curves is due to the introduction of species that become pests due to either human action or natural dispersal. Introduced species are usually introduced without their naturally occurring predators, parasites, and competitors and can frequently explode in population size, as we will discuss further in Module 14.

All organisms have the inherent capability to grow exponentially. Keep this in mind as you work through the activities today and in the rest of the class. What are the factors that are limiting the growth of the species with which you working? What is an example of a species that is growing exponentially right now and causing environmental degradation world-wide?

Although exponentially growing species are apparently growing unrestrained, there are forces that are at least slowing this process. Factors such as catastrophes, extreme weather, and droughts are contributing to slowing even the most steeply exponentially growing populations. These factors are collectively referred to as density independent factors because they have the same proportionate effect irrespective of the population density. They also tend to be catastrophic events.

The slightly more complicated growth curve is called logistic growth. The curve of a population growing logistically has three phases—initially a slow increase, then a rapidly increasing phase, and then a phase wherein the population stabilizes. The first two resemble exponential growth, with the population sizes slightly reduced.

The third phase is the one that is unique to logistic growth curves. This period of stability happens because population regulatory mechanisms begin to work. These mechanisms are called density dependent factors in that they increasingly affect populations as density increases. Examples of density dependent factors are starvation, competition, available resources, cannibalism, and parasite load.

The stability phase in the curve is called the carrying capacity, because it is the maximum number of organisms of that species that that habitat can sustain at that time. Because of the limitations placed upon this definition, carrying capacities are explicitly situationally dependent. If more resources are found in that area, the carrying capacity can increase. If the habitat or resource requirements change for that species because of either demographic shifts or rapid evolutionary change, then the carrying capacity will also change.

Logistic curves are much more commonly encountered in nature than are exponential growth curves. The equations behind the logistic curves incorporate all of the density dependent factors into a single variable that modifies the exponential growth model equation.

There are other types of growth curves—e.g., those that cycle and those that fluctuate erratically. However, they are all based on these two growth curves and their underlying equations.

### Metapopulation Dynamics

Recently, some theorists have formulated a novel subset of population ecology called metapopulation dynamics. This novel branch of population ecology is concerned with determining how migration of individuals between populations affects the longevity of each population.

When individuals migrate between populations, they help to diversify the overall gene pool and to bolster the population size of their new population. This kind of exchange of individuals occurs between open populations. In contrast, closed populations are like the flour beetles living in a closed flour jar on your counter at home.

Open populations tend to have a lesser chance of local extinction than do closed populations and the reason is the exchange of individuals. If a population is declining because of a pathogen, there is a chance that a novel arrival could be resistant to the pathogen. As a consequence, that population would continue to persist if that individual mated with the residents and passed on the pathogen resistance. As more individuals arrive to a declining population, the probability of local extinction declines due to the rescue effect, which comes about as a consequence of the addition of the new arrivals rescuing the population from local extinction.

Under metapopulation models, the network of linked local populations (the metapopulation) substitutes for what was the population in the exponential and logistic growth models, and populations take the place of individuals. Models have demonstrated that as more populations are added to the metapopulation, the probability of at least one of the local populations persisting (probability of regional persistence) increases rapidly. The increase in persistence does not continue linearly as more populations are added. Once around 16 populations are added to the metapopulation, not much more increase in the probability of regional persistence is possible.

### Estimating Population Size

The numbers on all of these models assume that we actually know the population sizes at each time slice. This is often not a tenable assumption, particularly with cryptic or secretive species.

How do we know the population size that exists at any given time? The most obvious way to do so would be to count every individual that exists in the population. However, this would be exceedingly time consuming and would be possible only for some organisms, chiefly, plants and only for animals living in a single closed container (e.g., grain beetles in a bag of flour).

For most animal species therefore, how do you know that you’ve surveyed EVERY individual in a population? You cannot, as they are constantly moving in and out of an area, they are often cryptically colored, and / or they are often very small and difficult to spot. Because counting every individual in a population is usually intractable for most animals, what are some other options for estimating population size?

Most of the population estimation methods involve first capturing, marking, releasing, and then recapturing some of the population again at some time in the future (mark, release, recapture, or MRR). Marking the animals usually involves affixing some permanent mark to each individual that has been captured—usually using paint markings, clipping non-vital parts of the animal, or radio-collaring.

The ratio of the number of individuals in the next recapturing event who are marked over the number of individuals who have not been marked provides some degree of estimate of population size. The Jolly-Seber and Lincoln-Peterson methods are the two most commonly used ways to analyze these data. You will go over the methods of calculation for these in most of the activities for this module, so we won’t go into greater depth on them now. Suffice it to say that the Lincoln-Peterson method is better for relatively closed populations, such as turtles in a pond. In contrast, the Jolly-Seber method is better for more open populations, such as deer in a forest.

### Population Viability Analyses

Small populations are much more likely to go extinct than are larger populations. Small populations have reduced genetic diversity, which is the raw material of natural selection. If a population has less genetic diversity, they are less likely to by chance have the most desired form of a key trait of selective value. Additionally, small populations are strongly affected by years with adverse weather, decreased breeding sites, or inadequate resources. Larger populations are more likely to have at least a few individuals that will be able to cope with these situations. In short, larger populations are almost always more desirable than are smaller ones from a conservation perspective.

Population viability analysis (PVA) is applied population estimation on a local scale. This branch of population ecology is concerned with determining the minimum population size that would be necessary to enable a currently existing population to continue to exist. These analyses are critical for determining whether a species should be justifiably placed on the endangered species list, or what types of intervention are necessary when to prevent that occurrence. PVA studies can be used to determine the extinction likelihood for a species, given what is known about their basic biology and their current population size.

Many variables interact to determine the size of a population and its persistence. Often the only way to gain insight is to develop a mathematical model of the population and use it to perform a PVA. PVA models relate a dependent variable to the independent variables that influence it (e.g., mortality, harvesting, and weather). A PVA estimates the probability of a population persisting in any given environment. It is a form of risk analysis in which one is interested not only in the average size of a population at some time in the future, but perhaps more importantly in the range of possible future values. A robust PVA incorporates density dependent and density independent events, as well as the role of random fluctuations.

We will explore all of the above issues during the activities of Module 4—Population Dynamics.