# if an ecosystem has a carrying capacity of 1,000 individuals for a given species and 2,000 individuals of that species are present, we can predict that the population

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## CH 36: Population Ecology Flashcards

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Flashcards » CH 36: Population Ecology

## Ch 36: Population Ecology

by jordal, Mar. 2010

Subjects: biology Favorite Add to folder Flag Flashcards Tweet

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### 49 Cards in this Set

What is the age structure of a population?

the proportion of individuals in different age groups

If an ecosystem has a carrying capacity of 1,000 individuals for a given species, and 2,000 individuals of that species are present, we can predict that the population

size will decrease.

Assume that there are five alligators per acre in a swamp in northern Florida. This is a measure of the alligator population's

density.

A tidal wave wipes out the entire population of mice living on an island. This is an example of

the effects of abiotic factors on a population (density independent limiting factor).

In a population of rabbits, which is the best example of a density dependent facto

competition with other rabbits for shelter

You drive through Iowa in the spring and notice that along a stretch of several kilometers, every third fence post has a male redwing blackbird perched on it defending its nesting territory. This is an example of

uniform dispersion.

Which of the following statements best describes features of a logistic growth curve

The population grows exponentially at first (when resources are plentiful) but population growth levels off at the carrying capacity due density dependent factors, such intraspecific competition

You have been studying a population of 200 shrews for one month. You record 50 shrew births and 10 shrew deaths in this time interval. What is the per capita rate of increase (r)?

.2

Which of the following refers to individuals of a single species that live in the same general area and can potentially interbreed

Population

A population that has a high level of parental care and high survivorship through the reproductive years likely has what type of survivorship curve?

Type I

Population Ecology is concerned with what?

changes in population size and the factors that regulate populations over time.

Population

a group of individuals of a single species that occupy the same general area.

Population Density

The number of individuals of a species per unit area or volume

Dispersion Pattern

Dispersion Pattern of a population refers to the way individuals are spaced in their areas.

Clumped Dispersion Pattern

Grouped, most common in nature, results from unequal distribution of resources in environment, mating, or social behavior. Reduces predation and increases feeding efficiency.

Uniform Dispersion Pattern

evenly disbursed, often results from interactions between individuals of a population. Animals may exhibit uniform dispersion as a result of territorial behavior.

Random Dispersion Pattern

unpredictably spaced, without pattern. Varying habitat and social interactions make random dispersion rare.

survivorship curves

plot survivorships as the proportion of individuals from an initial population that are alive at each age.

life tables track survivorship

Describe the general type of work performed by population

ecologists.

1. develop sustainable foods

2. assess the impact of human activities.

3. balance human needs with the conservation of bio-diversity and resources.

The larger the number of sample plots...

the more accurate the estimates.

Three characteristics of Individuals in a population are?

– Rely on the same resources

– Are influenced by the same environmental factors

– Are likely to interact and breed with one another

A population increases through...

birth and immigration

a population is decreased by...

death and

emigration out of an area

Type I curve

humans and other large mammals.

usually produce few offspring, give them good care, increasing the likelihood they will survive to adulthood. (Starts high and curves down)

Type II curve

Intermediate, survivorship constant over the life span--no more vulnerable than any other point in life. Seen in invertebrates, lizards, rodents.(a straight line decreasing from left to right)

Type III curve

low survivorship for young, followed by a period when survivorship is high for individuals who live to a certain age. produce large number of offspring.

little to no care.

Seen in invertebrates, oysters, perch. (a sloped L looking curve)

exponential population growth model

{ G=rN } The rate of population increase under ideal conditions.

J-curve

logistic population growth model.

{ G = rN * (K- N)/K }

a description of idealized population growth that is slowed by limiting factors as the population size increases.

r

per-capita rate of increase (the average contribution of of each individual to population growth)

G

growth rate of the population ( # of individuals added per time interval)

N

the population size (number on individuals in population at a particular time)

## Carrying Capacity

## Carrying Capacity

K is the carrying capacity and represents the number of individuals at the high-density equilibrium.

From: Conceptual Breakthroughs in Evolutionary Ecology, 2020

## Related terms:

HematocritEcosystemsBiomassHabitatsBlood CellsPopulation GrowthHemoglobin

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## Carrying Capacity

M.A. Hixon, in Encyclopedia of Ecology, 2008

### Basic Ecology

Carrying capacity is most often presented in ecology textbooks as the constant K in the logistic population growth equation, derived and named by Pierre Verhulst in 1838, and rediscovered and published independently by Raymond Pearl and Lowell Reed in 1920:

Nt=K1+ea−rtintegral form

dNdt=rNK−NKdifferential form

where N is the population size or density, r is the intrinsic rate of natural increase (i.e., the maximum per capita growth rate in the absence of competition), t is time, and a is a constant of integration defining the position of the curve relative to the origin. The expression in brackets in the differential form is the density-dependent unused growth potential, which approaches 1 at low values of N, where logistic growth approaches exponential growth, and equals 0 when N = K, where population growth ceases. That is, the unused growth potential lowers the effective value of r (i.e., the per capita birth rate minus the per capita death rate) until the per capita growth rate equals zero (i.e., births = deaths) at K. The result is a sigmoid population growth curve (**Figure 1**). Despite its use in ecological models, including basic fisheries and wildlife yield models, the logistic equation is highly simplistic and much more of heuristic than practical value; very few populations undergo logistic growth. Nonetheless, ecological models often include K to impose an upper limit on the size of hypothetical populations, thereby enhancing mathematical stability.

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Figure 1. The definition of carrying capacity most frequently used in basic ecology textbooks. (a) Logistic population growth model, showing how population size (N) eventually levels off at a fixed carrying capacity (K) through time (t). (b) Logistic population growth rate (dN/dt) as a function of population size. Note that the growth rate peaks at 0.5 K and equals zero at K.

Of historical interest is that neither Verhulst nor Pearl and Reed used ‘carrying capacity’ to describe what they called the maximum population, upper limit, or asymptote of the logistic curve. In reality, the term ‘carrying capacity’ first appeared in range management literature of the late 1890s, quite independent of the development of theoretical ecology (see below). Carrying capacity was not explicitly associated with K of the logistic model until Eugene Odum published his classic textbook Fundamentals of Ecology in 1953.

The second use in basic ecology is broader than the logistic model and simply defines carrying capacity as the equilibrial population size or density where the birth rate equals the death rate due to directly density-dependent processes.

The third and even more general definition is that of a long-term average population size that is stable through time. In this case, the birth and death rates are not always equal, and there may be both immigration and emigration (unlike the logistic equation), yet despite population fluctuations, the long-term population trajectory through time has a slope of zero.

The fourth use is to define carrying capacity in terms of Justus Liebig’s 1855 law of the minimum that population size is constrained by whatever resource is in the shortest supply. This concept is particularly difficult to apply to natural populations due to its simplifying assumptions of independent limiting factors and population size being directly proportional to whatever factor is most limiting. Moreover, unlike the other three definitions, the law of the minimum does not necessarily imply population regulation.

Note that none of these definitions from basic ecology explicitly acknowledges the fact that the population size of any species is affected by interactions with other species, including predators, parasites, diseases, competitors, mutualists, etc. Given that the biotic environment afforded by all other species in the ecosystem typically varies, as does the abiotic environment, the notion of carrying capacity as a fixed population size or density is highly unrealistic. Additionally, these definitions of carrying capacity ignore evolutionary change in species that may also affect population size within any particular environment.

View chapter Purchase book

## Human–Environment Relationship: Carrying Capacity

M.E. Geores, in International Encyclopedia of the Social & Behavioral Sciences, 2001

Carrying capacity is the margin of the habitat's or environment's ability to provide the resources necessary to sustain human life. The earth is the habitat for human life. Estimates of the number of people who can be supported by the earth have ranged widely, with some scholars maintaining that the carrying capacity has been reached, and others certain that the earth can support more people. Human appropriation of the earth's resources can both expand the carrying capacity and diminish it, depending on how the resources are used. Some scholars believe that human innovation will continue to expand the carrying capacity, while others believe that the carrying capacity is finite. These two views fuel the debate about the need for population control.

Source : **www.sciencedirect.com**

## Exponential growth & logistic growth (article)

How populations grow when they have unlimited resources (and how resource limits change that pattern).

## Key points:

In **exponential growth**, a population's per capita (per individual) growth rate stays the same regardless of population size, making the population grow faster and faster as it gets larger.

In nature, populations may grow exponentially for some period, but they will ultimately be limited by resource availability.

In **logistic growth**, a population's per capita growth rate gets smaller and smaller as population size approaches a maximum imposed by limited resources in the environment, known as the **carrying capacity** (

K K K ).

Exponential growth produces a **J-shaped curve**, while logistic growth produces an **S-shaped curve**.

## Introduction

In theory, any kind of organism could take over the Earth just by reproducing. For instance, imagine that we started with a single pair of male and female rabbits. If these rabbits and their descendants reproduced at top speed ("like bunnies") for

7 7 7

years, without any deaths, we would have enough rabbits to cover the entire state of Rhode Island

^{1,2,3} 1,2,3

start superscript, 1, comma, 2, comma, 3, end superscript

. And that's not even so impressive – if we used E. coli bacteria instead, we could start with just one bacterium and have enough bacteria to cover the Earth with a

1 1 1 -foot layer in just 36 36 36 hours ^4 4

start superscript, 4, end superscript

!

As you've probably noticed, there isn't a

1 1 1

-foot layer of bacteria covering the entire Earth (at least, not at my house), nor have bunnies taken possession of Rhode Island. Why, then, don't we see these populations getting as big as they theoretically could? E. coli, rabbits, and all living organisms need specific resources, such as nutrients and suitable environments, in order to survive and reproduce. These resources aren’t unlimited, and a population can only reach a size that match the availability of resources in its local environment.

Population ecologists use a variety of mathematical methods to model **population dynamics** (how populations change in size and composition over time). Some of these models represent growth without environmental constraints, while others include "ceilings" determined by limited resources. Mathematical models of populations can be used to accurately describe changes occurring in a population and, importantly, to predict future changes.

## Modeling population growth rates

To understand the different models that are used to represent population dynamics, let's start by looking at a general equation for the **population growth rate** (change in number of individuals in a population over time):

\quad \quad\quad\quad\quad\quad\quad\quad \quad\quad\quad\dfrac{dN}{dT} = rN

dT dN =rN

start fraction, d, N, divided by, d, T, end fraction, equals, r, N

In this equation, dN/dT dN/dT d, N, slash, d, T

is the growth rate of the population in a given instant,

N N N is population size, T T T is time, and r r r

is the per capita rate of increase –that is, how quickly the population grows per individual already in the population. (Check out the differential calculus topic for more about the

dN/dT dN/dT d, N, slash, d, T notation.)

If we assume no movement of individuals into or out of the population,

r r r

is just a function of birth and death rates. You can learn more about the meaning and derivation of the equation here: [How we get to the population growth rate equation]

The equation above is very general, and we can make more specific forms of it to describe two different kinds of growth models: exponential and logistic.

When the per capita rate of increase (

r r r

) takes the same positive value regardless of the population size, then we get **exponential growth**.

When the per capita rate of increase (

r r r

) decreases as the population increases towards a maximum limit, then we get **logistic growth**.

Here's a sneak preview – don't worry if you don't understand all of it yet:

We'll explore exponential growth and logistic growth in more detail below.

## Exponential growth

Bacteria grown in the lab provide an excellent example of exponential growth. In **exponential** growth, the population’s growth rate increases over time, in proportion to the size of the population.

Let’s take a look at how this works. Bacteria reproduce by binary fission (splitting in half), and the time between divisions is about an hour for many bacterial species. To see how this exponential growth, let's start by placing

1000 1000 1000

bacteria in a flask with an unlimited supply of nutrients.

After 1 1 1

hour: Each bacterium will divide, yielding

2000 2000 2000

bacteria (an increase of

1000 1000 1000

Guys, does anyone know the answer?