Course: BIS 105 Environmental Biology

Unit 4 Learning Module

Limits to Growth

How Do Populations Grow in Nature?

You learned above that populations can grow exponentially if conditions are ideal. While exponential growth occurs when populations move into new or unfilled environments or rebound after catastrophes, most organisms do not live in ideal conditions very long, if at all. Let’s look at some data for populations growing under more realistic conditions.

Biologist Georgyi Gause studied the population growth of two species of Paramecium in laboratory cultures. Both species grew exponentially at first, as Malthus predicted. However, as each population increased, rates of growth slowed and eventually leveled off. Each species reached a different maximum, due to differences in size of individuals and space and nutrient needs, but both showed the same, S-shaped growth pattern. The figure below shows this growth pattern graphically as an S-shaped curve.

Two species of Paramecium illustrate logistic growth, with different plateaus due to differences in size and space and nutrient requirements. The growth pattern resembles and is often called an S-curve. Slow but exponential growth at low densities is followed by faster growth and then leveling.

Perhaps even more realistic is the growth of a sheep population, observed after the introduction of fourteen sheep to the island of Tasmania in 1800. Like the lab Paramecia, the sheep population at first grew exponentially. However, over the next 20 years, the population sharply declined by 1/3. Finally, the number of sheep increased slowly to a plateau. The general shape of the growth curve matched the S-shape of Paramecium growth, except that the sheep “overshot” their plateau at first.

As Malthus realized, no population can maintain exponential growth indefinitely. Inevitably, limiting factors such as reduced food supply or space lower birth rates, increase death rates, or lead to emigration, and lower the population growth rate. After reading Malthus’ work in 1938, Pierre Verhulst derived a mathematical model of population growth which closely matches the S-curves observed under realistic conditions. In this logistic (S-curve) model, growth rate is proportional to the size of the population but also to the amount of available resources. At higher population densities, limited resources lead to competition and lower growth rates. Eventually, the growth rate declines to zero and the population becomes stable.

Growth of populations according to Malthus’ exponential model (A) and Verhulst’s logistic model (B). Both models assume that population growth is proportional to population size, but the logistic model also assumes that growth depends on available resources. A models growth under ideal conditions and shows that all populations have a capacity to grow infinitely large. B limits exponential growth to low densities; at higher densities, competition for resources or other limiting factors inevitably cause growth rate to slow to zero. At that point, the population reaches a stable plateau, the carrying capacity (K).

The logistic model describes population growth for many populations in nature. Some, like the sheep in Tasmania, “overshoot” the plateau before stabilizing, and some fluctuate wildly above and below a plateau average. A few may crash and disappear. However, the plateau itself has become a foundational concept in population biology known as carrying capacity (K). Carrying capacity is the maximum population size that a particular environment can support without habitat degradation. Limiting factors determine carrying capacity, and often these interact. In the next section, we will explore in more detail the kinds of factors which restrict populations to specific carrying capacities and some adaptations that limit growth.

Limits to Population Growth

A limiting factor is a property of a population’s environment – living or nonliving – which controls the process of population growth. Biologists have identified two major types of limiting factors: Density-dependent factors and Density-independent factors.

Density-dependent factors promote intraspecific competition – competition between members of the same population for the same resource – as the population grows and becomes more crowded. Density-dependent limiting factors have the potential to control population size. Consider food supply as an example. When population density is low, amount of food per individual is high, and birth rates are high. As density increases, food supply per individual decline and birth rates drop, causing growth rate to decline. Eventually, food shortages may lead to increased death rates and a negative growth rate, lowering population size. Lower population size means more food per individual, and the population begins to grow again, reaching or temporarily overshooting the carrying capacity. Food supply in this instance is a regulatory limiting factor, because it keeps the population at equilibrium. Density-dependent limiting factors may include:

- Light

- Water, nutrients/minerals, or oxygen

- Waste, or the ability of an ecosystem to recycle nutrients and/or waste

- Predation by predators which feed preferentially on more abundant prey

- Disease and/or parasites

- Space, with or without territorial behaviors, or nesting sites

- Temperature

- Aggressive behaviors, often combined with stress and effects on immune systems

Let’s look at two examples in detail, to emphasize the importance of density-dependent regulation of growth. First, waste products build up with increasing population density. Most environments have some capacity for recycling of wastes, but sometimes rapid population growth means that natural environmental systems can’t keep up. An interesting - if not completely natural - example is the growth of yeast populations through fermentation in the making of wine. Alcohol is a waste product for the yeast, even though it is the point of the process as far as we’re concerned. As the yeast population grows, alcohol builds up; but alcohol is toxic – to yeast as well as to humans – and after the concentration reaches 13%, increased death rates doom the yeast population. Therefore, no naturally fermented wine contains more than 13% alcohol.

A second density-dependent limiting factor is predation. Predators kill and eat their prey, of course, so predation increases prey death rate and can cause negative growth rates – population decline. If predators have multiple types of prey, and switch their feeding to specific prey only when they are abundant, predators may regulate prey population size. However, especially in northern climates, predators often specialize on a single prey species. Goshawks, for example, feed primarily on ruffed grouse, and Canada Lynx depend on snowshoe hares. If predation causes a significant decline in the prey population, starving predators may experience their own (delayed) decrease in population as a result of lower birth rates or increased death rates. The result is a predator-prey cycle; both populations rise and fall, with predator populations trailing prey.

All of these factors have the potential to lower birth rates or increase death/emigration rates via increased intraspecific competition at higher population densities. Many natural populations are kept at or below carrying capacity by one or a complex interaction among several of the above limiting factors.

Density-independent factors can also limit populations, but they seldom regulate populations because they act irregularly, regardless of the population’s density. Populations limited by density-independent factors seldom reach carrying capacity. Weather is a good example. Agaves (Century Plants) reproduce once at the end of a long lifespan. The average lifespan is about 25 years rather than a full century, but an individual’s lifespan depends at least in part on erratic rainfall. Agaves will reproduce only after rainfall allows sufficient growth – however long that takes. Eventually, a wet season will bring about a single episode of flowering and the production of a huge number of seeds. Their growth and eventual reproduction will, in turn, depend on erratic rainfall. The density-independent factor rainfall limits birth rate, which in turn limits growth rate, but because of its unpredictability, it cannot regulate Agave populations.

Each Century Plant reproduces only once during its long lifespan. This strategy allows it to gather sufficient water over a number of years in an environment where rainfall is scarce and unpredictable. Then, during an especially wet season, the plant produces a huge number of seeds and dies. Does the Century Plant’s pattern remind you of the salmon’s life cycle?

Other density-independent limiting factors include human activities:

- Pesticides and herbicides: For example, DDT thinned the eggshells of Peregrine Falcons, reducing their birthrates and leading to their extirpation from the eastern half of North America.

- Habitat destruction: Conversion of prairies and grasslands worldwide drastically reduced populations of Burrowing Owls in North America and Giant Pandas in China.

To conclude our discussion of population dynamics, let’s look at two sets of adaptations related to the logistic growth curve which describe the growth of most populations. These should remind you of the survival patterns we discussed earlier in this lesson. Recall that for logistic growth, r is the growth rate of the population, and K is the carrying capacity.

Scientists have found that species adapted to unstable or unpredictable environments are usually limited by density-independent factors to population densities considerably lower than carrying capacity. Such environments favor adaptations which maximize growth rates: early maturity, small size, high numbers of small offspring, single episodes of reproduction, short life expectancy, and the ability to disperse widely. Because populations are usually far below carrying capacity, crowding is minimal, so these species invest little energy in competitive adaptations. Survivorship curves described above are Type III, with high early death rates. Such species are said to be r-selected – that is, selected for rapid growth. Weed species are often r-selected for colonization and rapid population of disturbed or newly created habitats such as roadsides, abandoned fields, mudslides, or lava flows. Jack pine trees are r-selected species which “pioneer” clear areas immediately after forest fires. They grow quickly in hot, dry soils and release seeds from cones which are opened only by fire – reproducing and dispersing seeds at just the right, if unpredictable, time.

Whereas density-independent factors limit r-selected species in unpredictable environments, K-selected species are adapted to stable environments and regulated by density-dependent factors. Stable environments support K-selected populations at or near carrying capacity, at which point crowding leads to significant intraspecific competition. Such environments favor adaptations for efficient resource utilization which confer competitive ability. K-selected individuals often grow slowly to large size, live long, and delay but repeat reproduction of fewer offspring. They may provide extensive parental care because they can count on environmental stability and survival of these relatively few offspring. Survivorship curves resemble the Type I pattern: long life expectancy and relatively low death rates in the stable environment. Maple trees are K-selected “climax” species which grow slowly in their own shade and reproduce relatively large seeds over a number of years throughout their relatively long lifespan.

Characteristics of r-selected and K-selected species are compared below.

 | r-Selected Species | K-Selected Species
Environment | Unstable | Stable
Type of Regulating Factors | Density-independent | Density-dependent
Organism Size | Small | Large
Maturity | Early | Late
Number of Offspring | Many | Few
Energy used to make each Individual | Low | High
Average Life Expectancy | Short | Long
Number of Reproductive Events per Individual | Once | Many
Survivorship | Type III | Type I

In conclusion, all populations eventually reach limits, at or below carrying capacities for the ecosystems in which they live. Some have adaptations for rapid growth, but the unpredictable environments in which they live inflict high death rates. Others live in stable environments where death rates are relatively low, but their populations are high, so individuals must spend energy on costly competitive strategies in order to gather scarce sunlight, nutrients, or water - or fight disease or predation. Many species live between these extremes, but all populations have limits.