**Human Population Growth: A Case Study**

Humans have a large impact on the global environment: Our population has grown explosively, along with our use of energy and resources.

Human population reached 6.8 billion in 2010, more than double the number of people in 1960.

Our use of energy and resources has grown even more rapidly.

From 1860 to 1991, human population quadrupled in size, and energy consumption increased 93-fold.

**Predicted Decrease in Growth of Population **

**Ecological footprint: **Total area of productive ecosystems required to support a population. Uses data on agricultural productivity, production of goods, resource use, population size, and pollution. The area required to support these activities is then estimated.

****Population: 6.6 billion, a 40% overshoot of carrying capacity.

One of the ecological maxims is:* “No population can increase in size forever.”*

The limits imposed by a finite planet restrict a feature of all species: A capacity for rapid population growth.

Ecologists try to understand the **factors that limit** or promote population growth

A **life table **is a summary of how survival and reproductive rates vary with age.

Information about births and deaths is essential to predict future population size.

*Sx* = **survival rate**: Chance that an individual of age *x* will survive to age *x* + 1.

*lx* = **survivorship**: Proportion of individuals that survive from birth to age *x*.

*Fx* = **fecundity**: Average number of offspring a female will have at age *x*.

**Birth and death rates can vary greatly** between individuals of different ages.

In some species, age is not important, e.g., in many plants, reproduction is more dependent on size (related to growth conditions) than age.

Life tables can also be based on size or life cycle stage.

**Survivorship curve**: Plot of the number of individuals from a hypothetical cohort that will survive to reach different ages.

Survivorship curves can be classified into three general types.

**Type I**: Most individuals survive to old age (Dall sheep, humans).

**Type II**: The chance of surviving remains constant throughout the lifetime (some birds).

**Type III**: High death rates for young, those that reach adulthood survive well (species that produce a lot of offspring).

A population can be characterized by its **age structure**—the proportion of the population in each age class.

Age structure influences how fast a population will grow.

If there are many people of reproductive age (15 to 30), it will grow rapidly.

A population with many people older than 55 will grow more slowly.

Third world countries exhibit **rapid growth; **Modern economies are showing stabilization in growth (**zero growth**) or even **negative growth**

*Growth rate* (λ): Ratio of population size in year *t *+ 1 (*N _{t}*

_{+1}) to population size in year

*t*(

*N*).

_{t}If survival or fecundity rates change, population growth rate will change.

Example: If *F*_{1} changes from 2 to 5.07 (and other values stay the same), λ increases to 2.0.

Age distribution would also change.

But life table data indicated that the best way to increase growth rates was to increase survival rates of juveniles and adults.

*Sudden change in environmental factors can change birth or death rates:*

Geometric growth and exponential growth can lead to rapid increases in population size.

**Geometric growth (A)**: If a population reproduces in synchrony (same time) at discrete time periods and the growth rate doesn’t change.

The population increases by a *constant proportion*: The number of individuals added is larger with each time period.

λ = **geometric growth rate** or per capita **finite rate of increase**. It has a double factor (2,4,8,16,32 etc.)

**Exponential growth (B)**: When individuals reproduce *continuously*, and generations can overlap. (**r species) **

**Exponential growth is described by:**

** = rate of change in population size at each instant in time.**

*r *= exponential population growth rate or per capita intrinsic rate of increase. Intrinsic rate of increase

If a population is growing geometrically or exponentially, a plot of the natural logarithm of population size versus time will result in a straight line.

For the human population, current growth rate is 1.18%, so *r* = 0.0117.

If 2010 is time *t* = 0 and N(0) = 6.8 billion,

population size in one year N(1) = 6.8 × e^{0.0117}, or 6.88 billion.

If *r *remained constant, population would be over 80 billion in 215 years.

**Effects of Density**

**Population size can be determined by density-dependent and density-independent factors.**

Under ideal conditions, λ > 1 for all populations.

But conditions rarely remain ideal and λ fluctuates over time.

**Density-independent factors**

Effects on birth and death rates are independent of the number of individuals in the population:

Temperature and precipitation, catastrophes such as floods or hurricanes.

**Density-dependent factors**: Birth, death, and dispersal rates change as the density of the population changes.

As density increases, birth rates often decrease, death rates increase, and dispersal (emigration) increases, all of which tend to decrease population size.

**Density-independent factors**: Effects on birth and death rates are independent of the number of individuals in the population: Temperature and precipitation, catastrophes such as floods or hurricanes.

**Population regulation**: Density-dependent factors cause a population to increase when density is low and decrease when density is high.

Ultimately, food, space, or other resources are in short supply and population size decreases.

Density-independent factors can have large effects on population size, but do not regulate population size.

**Logistic growth: **Population increases rapidly, then stabilizes at the **carrying capacity** (maximum population size that can be supported indefinitely by the environment).

The growth rate decreases as population nears carrying capacity because resources begin to run short.

At carrying capacity, the growth rate is zero, so population size does not change.

The *logistic equation* assumes that *r* declines as *N* increases:

*N* = population density

*r* = per capita growth rate

*K *= carrying capacity

When densities are low, logistic growth is similar to exponential growth.

When *N *is small, (1 – *N*/*K*) is close to 1, and the population increases at a rate close to *r*.

As density increases, growth rate approaches zero as population nears *K*.