In logistic growth, population expansion decreases as resources become scarce. It levels off when the carrying capacity of the environment is reached, resulting in an S-shaped curve. The bacteria example is not representative of the real world where resources are limited. Furthermore, some bacteria will die during the experiment and, thus, not reproduce, lowering the growth rate.
Therefore, when calculating the growth rate of a population, the death rate D; the number organisms that die during a particular time interval is subtracted from the birth rate B; the number organisms that are born during that interval.
This is shown in the following formula:. The birth rate is usually expressed on a per capita for each individual basis. Additionally, ecologists are interested in the population at a particular point in time: an infinitely small time interval. A further refinement of the formula recognizes that different species have inherent differences in their intrinsic rate of increase often thought of as the potential for reproduction , even under ideal conditions.
Obviously, a bacterium can reproduce more rapidly and have a higher intrinsic rate of growth than a human. The maximal growth rate for a species is its biotic potential, or r max , thus changing the equation to:. Logistic growth of a population size occurs when resources are limited, thereby setting a maximum number an environment can support.
Exponential growth is possible only when infinite natural resources are available; this is not the case in the real world. The successful ones will survive to pass on their own characteristics and traits which we know now are transferred by genes to the next generation at a greater rate: a process known as natural selection. To model the reality of limited resources, population ecologists developed the logistic growth model.
In the real world, with its limited resources, exponential growth cannot continue indefinitely. Exponential growth may occur in environments where there are few individuals and plentiful resources, but when the number of individuals becomes large enough, resources will be depleted, slowing the growth rate.
Eventually, the growth rate will plateau or level off. This population size, which represents the maximum population size that a particular environment can support, is called the carrying capacity, or K.
The formula we use to calculate logistic growth adds the carrying capacity as a moderating force in the growth rate. Thus, the exponential growth model is restricted by this factor to generate the logistic growth equation:. Thus, population growth is greatly slowed in large populations by the carrying capacity K. This model also allows for negative population growth or a population decline.
A graph of this equation yields an S-shaped curve; it is a more-realistic model of population growth than exponential growth.
There are three different sections to an S-shaped curve. Population growth is regulated in a variety of ways. These are grouped into density-dependent factors, in which the density of the population affects growth rate and mortality, and density-independent factors, which cause mortality in a population regardless of population density.
Wildlife biologists, in particular, want to understand both types because this helps them manage populations and prevent extinction or overpopulation. Most density-dependent factors are biological in nature and include predation, inter- and intraspecific competition, and parasites.
Usually, the denser a population is, the greater its mortality rate. In addition, low prey density increases the mortality of its predator because it has more difficulty locating its food source. Also, when the population is denser, diseases spread more rapidly among the members of the population, which affect the mortality rate.
Density dependent regulation was studied in a natural experiment with wild donkey populations on two sites in Australia. The high-density plot was twice as dense as the low-density plot. From to the high-density plot saw no change in donkey density, while the low-density plot saw an increase in donkey density. The difference in the growth rates of the two populations was caused by mortality, not by a difference in birth rates.
The researchers found that numbers of offspring birthed by each mother was unaffected by density. Many factors that are typically physical in nature cause mortality of a population regardless of its density. These factors include weather, natural disasters, and pollution. An individual deer will be killed in a forest fire regardless of how many deer happen to be in that area.
Its chances of survival are the same whether the population density is high or low. The same holds true for cold winter weather. In real-life situations, population regulation is very complicated and density-dependent and independent factors can interact. A dense population that suffers mortality from a density-independent cause will be able to recover differently than a sparse population.
For example, a population of deer affected by a harsh winter will recover faster if there are more deer remaining to reproduce. Woolly mammoths began to go extinct about 10, years ago, soon after paleontologists believe humans able to hunt them began to colonize North America and northern Eurasia [Figure 4]. A mammoth population survived on Wrangel Island, in the East Siberian Sea, and was isolated from human contact until as recently as BC. We know a lot about these animals from carcasses found frozen in the ice of Siberia and other northern regions.
It is commonly thought that climate change and human hunting led to their extinction. A study concluded that no single factor was exclusively responsible for the extinction of these magnificent creatures. The maintenance of stable populations was and is very complex, with many interacting factors determining the outcome. It is important to remember that humans are also part of nature. Population ecologists have hypothesized that suites of characteristics may evolve in species that lead to particular adaptations to their environments.
These adaptations impact the kind of population growth their species experience. Life history characteristics such as birth rates, age at first reproduction, the numbers of offspring, and even death rates evolve just like anatomy or behavior, leading to adaptations that affect population growth.
K -selected species are adapted to stable, predictable environments. Populations of K -selected species tend to exist close to their carrying capacity. A dense population that is reduced in a density-independent manner by some environmental factor s will be able to recover differently than would a sparse population.
For example, a population of deer affected by a harsh winter will recover faster if there are more deer remaining to reproduce. Learning Objectives Differentiate between density-dependent and density-independent population regulation. Key Points The density of a population can be regulated by various factors, including biotic and abiotic factors and population size.
Density-dependent regulation can be affected by factors that affect birth and death rates such as competition and predation. Density-independent regulation can be affected by factors that affect birth and death rates such as abiotic factors and environmental factors, i. New models of life history incorporate ecological concepts that are typically included in r- and K-selection theory in combination with population age structures and mortality factors. Key Terms interspecific : existing or occurring between different species intraspecific : occurring among members of the same species fecundity : number, rate, or capacity of offspring production.
Limitations to population growth are either density-dependant or density-independent. Density-dependent factors include disease, competition, and predation. Density-dependant factors can have either a positive or a negative correlation to population size. With a positive relationship, these limiting factors increase with the size of the population and limit growth as population size increases. With a negative relationship, population growth is limited at low densities and becomes less limited as it grows.
Density-dependant factors may influence the size of the population by changes in reproduction or survival. The red squirrel Sciurus vulgaris is a small rodent inhabiting forests in Europe and Asia. They studied squirrels in both coniferous and deciduous woodlands and investigated how limitations in food resulted in limitations in reproduction as population densities increased. They found that when squirrel densities were high, territoriality relegated some females to poor quality territory, which in turn reduced their reproductive success.
When squirrel densities were low, no females occupied the low-quality territory. Thus, it was not all individuals suffering from reduced ability to reproduce e.
Instead, a greater proportion of the population was living in poor-quality habitat, while those still living in good habitat continued to have success. This in turn led to a decrease in per capita birth rate, a limitation in population growth as a function of population density.
Density dependant factors may also affect population mortality and migration. Clutton-Brock et al. Both juvenile and adult mortality was significantly affected by population density, with juvenile mortality more strongly influenced than adult mortality Figure 2. Furthermore, they found that these differences were stronger among males than females, so that increasing population density caused a shift in the sex ratio of females to males.
This effect was enhanced by decreased male immigration and increased male emigration. Thus, density-dependant controls on population growth not only increased with increasing density, but also differentially affected males and females within the population.
However, many sources of environmental stress affect population growth, irrespective of the density of the population. Density-independent factors, such as environmental stressors and catastrophe, are not influenced by population density change. While the previously mentioned density-dependant factors are often biotic, density-independent factors are often abiotic. These density-independent factors include food or nutrient limitation, pollutants in the environment, and climate extremes, including seasonal cycles such as monsoons.
In addition, catastrophic factors can also impact population growth, such as fires and hurricanes. The quality of nutrients e. The lower the quality of the nutrients, the higher the environmental stress.
In the freshwater Laurentian Great Lakes, particularly in Lake Erie, the factor limiting algal growth was found to be phosphorus. David Schindler and his colleagues at the Experimental Lakes Area Ontario, Canada demonstrated that phosphorus was the growth-limiting factor in temperate North American lakes using whole-lake treatment and controls Schindler This work encouraged the passage of the Great Lakes Water Quality Agreement of GLWQA — a reduction in phosphorus load from municipal sources was predicted to lead to a corresponding reduction in the total algal biomass and harmful cyanobacterial blue-green algae blooms McGuken ; Figure 3.
As annual phosphorus loads decreased in the mid s Dolan , there was some indication that Lake Erie was improving in terms of decreased total phytoplankton photosynthetic algae and cyanobacteria biomass Makarewicz Further improvement continued until the mid s, until an introduced species, the zebra mussel, began altering the internal phosphorus dynamics of the lake by mineralization excretion of digested algae Figure 3; Conroy et al. C Change in Lake Erie seasonal average phytoplankton biomass in the central.
Pollutants also contribute to environmental stress, limiting the growth rates of populations. Although each species has specific tolerances for environmental toxins, amphibians in general are particularly susceptible to pollutants in the environment.
For example, pesticides and other endocrine disrupting toxins can strongly control the growth of amphibians Blaustein et al. These chemicals are used to control agricultural pests but also run into freshwater streams and ponds where amphibians live and breed. They affect the amphibians both with direct increases in mortality and indirect limitation in growth, development, and reduction in fecundity. Rohr et al. These effects limit population growth irrespective of the size of the amphibian population and are not limited to pesticides but also include pH and thermal pollution, herbicides, fungicides, heavy metal contaminations, etc.
Environmental catastrophes such as fires, earthquakes, volcanoes and floods can strongly affect population growth rates via direct mortality and habitat destruction. A large-scale natural catastrophe occurred in when hurricane Katrina impacted the coastal regions of the Gulf of Mexico in the southern United States. Katrina altered habitat for coastal vegetation by depositing more than 5 cm of sediment over the entire coastal wetland zone.
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