## Learning Objectives:

- Define population, population size, population density, geographic range, exponential growth, carrying capacity, logistic growth, and metapopulation.
- Compare and distinguish between geometric and logistic population growth equations and the resulting growth curves
- Recognize that population growth rate is constant with exponential growth, but that population growth rate slows with logistic growth with a carrying capacity.
- Compare and contrast factors that regulate population size, and, looking at a graph, be able to analyze it and determine if regulation is influenced by density
- Identify key features of an organism’s life history and how they respond to environment/natural selection regimes
- Calculate population (net) reproductive rate from life tables to determine if a population is growing or shrinking
~~Predict population growth trajectories from life history tables and population demographic structure~~

## Population ecology

A **population** is a group of interacting organisms of the same species, and contains stages: pre-reproductive juveniles and reproductive adults. Most populations have a mix of young and old individuals, and characterizing the numbers of individuals of each age or stage indicates the **demographic structure** of the population. In addition to demographic structure, populations vary in the number of individuals in the group, called **population size**, and how densely packed together those individuals are, called **population density**. A population’s **geographic range** has limits, or bounds, established by the encroachment of other species, by the physical limits that the organisms can tolerated, such as temperature or aridity. A key characteristic of a population is the dynamics of whether its growing in size, shrinking, or remaining static over time.

## Exponential (or Geometric) Population Growth

The most basic approach to population growth is to begin with the assumption that every individual produces two offspring in its lifetime, then dies, which would double the population size each generation. This population doubling at each generation is how an ideal bacterium in unlimited resources would reproduce.

The **growth rate** of the population in this image is constant. Mathematically, the growth rate is **the intrinsic rate of natural increase**, a constant called **r**, for this population of size N. *r* is the birth rate *b* minus the death rate *d* of the population. The exponential growth equation

helps us understand the growth pattern over time t: the population size times the growth rate gives the change in population size with time. Considering population growth in discrete generations can clarify this for us even more. If the population size at the next generation is the current population size times the growth rate in that time interval, or *N*[t+1] = *N*[t]exp[*r*], then we see stepwise population growth. We define exp[*r*] as the **discrete growth rate, lambda**.

The values of lambda and r are fixed with time, but the population doesn’t grow linearly; instead every individual that was born in that generation reproduces. The population explodes in size very quickly. In nature, a population growing at this dramatic rate would quickly consume all available habitat and resources. Natural populations have size limits created by the environment.

## Logistic Population Growth levels off at a carrying capacity

A natural population at the maximum population size that the environment can sustain is said to be at **carrying capacity**. Any individuals born into this population would increase the population size, so individuals must also be dying at a similar rate if the population size remains the same from one generation to the next. With exponential growth, population growth rate was constant, but with the addition of a carrying capacity imposed by the environment, population growth rate slows as the population size increases, and stops when the population reaches carrying capacity.

Mathematically, we can achieve this by incorporating a density-dependent term into the population growth equation, where *K* represents carrying capacity:

What happens to population growth when *N* is small relative to *K*? When *N* is near *K*? And when is the population adding the most individuals in each generation?

## Population size is regulated by factors that are dependent or independent of population density

Biological and non-biological factors can influence population size. Biological factors include interspecific interactions like predation, competition, parasitism, and mutualism, as well as disease. Non-biological factors are environmental variables like temperature, precipitation, disturbance, pollution, salinity, and pH. All of these factors can *change* population size, but only the biological factors (except mutualism) can “*regulate*” a population, meaning they push the population to an equilibrium density, or carrying capacity. Of the biological factors, mutualism does not regulate population size because mutualisms promote population growth through beneficial interactions with another species.

The biological factors regulate population growth by affecting dense versus sparse populations differently. For instance, communicable disease doesn’t spread quickly in a sparsely packed population, but in a dense population, like a college dormitory, disease can spread quickly through contact between individuals. Density plays a key role in population regulation:

- Territoriality: Maintaining a territory will enable an individual to capture enough food to reproduce, where space is a limiting resource.
- Disease: Transmission rate often depends on population density
- Predation: Predators may concentrate on the most abundant prey
- Toxic Wastes: Metabolic by-products accumulate as populations grow

## Metapopulations are populations of the same species linked together by migration (excerpted from OpenStax CNX)

A species that is ecologically linked to a specialized, patchy habitat may likely assume the patchy distribution of the habitat itself, with several different populations distributed at different distances from each other. This is the case, for example, for species that live in wetlands, alpine zones on mountaintops, particular soil types or forest types, springs, and many other comparable situations. Individual organisms may periodically disperse from one population to another, facilitating genetic exchange between the populations. This group of different but interlinked populations, with each different population located in its own, discrete patch of habitat, is called a **metapopulation**.

There may be quite different levels of dispersal between the constituent populations of a metapopulation. For example, a large or overcrowded population patch is unlikely to be able to support much immigration from neighboring populations; it can, however, act as a source of dispersing individuals that will move away to join other populations or create new ones. In contrast, a small population is unlikely to have a high degree of emigration; instead, it can receive a high degree of immigration. A population that requires net immigration in order to sustain itself acts as a sink. The extent of genetic exchange between source and sink populations depends, therefore, on the size of the populations, the carrying capacity of the habitats where the populations are found, and the ability of individuals to move between habitats. Consequently, understanding how the patches and their constituent populations are arranged within the metapopulation, and the ease with which individuals are able to move among them is key to describing the population diversity and conserving the species.

## Life history traits and their evolution

Individuals in a population experience a life cycle of birth, growth and development, maturity to adulthood, and then decline into reproductive senescence. Questions that address an organism’s **life history traits** include: how big and fast should I grow, when should I reach sexual maturity, how many babies should I have each time I reproduce, how many times should I reproduce, and when should I die. Life History Theory explains how evolution optimizes the survival and reproductive characteristics of each population of organisms.

Notice that survival and reproduction are “optimized” not maximized. This is because when evolution increases one of these traits, say survival of the parent, the result is usually a decrease in some aspect of reproduction, and vice versa.

This observation is called a life-history trade-off. The leading hypothesis for trade-offs in survival and reproduction is that energy is the limiting factor. Organisms have finite energy, so if they allocate energy toward survival, then they don’t have as much available to reproduce. As a result, some organisms like the Chinook salmon reproduce only once in their lifetime (semelparous organisms), while others such as Atlantic Cod…and humans…reproduce many times (iteroparous organisms).

## Life tables are a valuable tool to examine how age structure can change a population’s growth trajectory

Population demography is the study of numbers and rates in a population and how they change over time. The basic tool of demography is the **life table**. Life tables are an analytical tool that population ecologists use to study age-specific population characteristics such as survival, fecundity, and mortality. These data can be critical in conservation efforts (such as reintroductions or pest reductions) where ecologists would like to know how well an endangered or transplanted population is doing.

Life tables determine the number of individuals that survive from one age group to the next. Cohort life tables follow one group of individuals born at the same time, called a cohort, until the death of all individuals. This technique of demographic assessment requires key assumptions:

1) The population sample of each age class is proportional to its numbers in the population

2) Age-specific mortality rates remain constant during the time period, meaning that subsequent cohorts will exhibit similar pattern of birth and death.

Life Table:

The first row represents the birth year of the cohort, and each subsequent row of the life table shows that same group one year older. Assuming that the unit of age (x) is years, the number alive (nx) column indicates that not all individuals survive from year to year. **Survivorship** converts that mortality into a proportion alive of of the original cohort (lx = nx/n0). The average number of offspring born to individuals of each age is **age-specific fecundity**, and it cannot be calculated from other information provided in the table but instead must be estimated from data.

Here’s the best bit…the reason we bother to gather all the age-specific survivorship and fecundity information: if the assumptions (1 and 2 above) are met, then the sum of the product of survivorship and fecundity at each age gives a population growth parameter called R0 (pronounced R-nought). When R0 exceeds 1, the population is producing more offspring than its losing from deaths. In other words, the population is growing.

- Is the population above growing, shrinking, or stable?
- At what age is fecundity maximized? Survivorship?

Because of life history trade-offs, patterns of age-specific survival are predictive of the general life history of a population. While a life table shows the survivorship in a numerical form, assessing pattern from columns of data is difficult. Instead, ecologists create** survivorship curves** by plotting lx versus time.

Population biologists look for three types of patterns in survivorship curves (note that the y-axis is a log scale):

Type I curves are observed in populations with low mortality in young age classes but very high mortality as an individual ages. Type II curves represent populations where the mortality rate is constant, regardless of age. Type III curves occur in populations with high mortality in early age classes and very low mortality in older individuals. Populations displaying a Type III survivorship curve generally need to have high birth rates in order for the population size to remain constant. High birth rates ensure that enough offspring survive to reproduce, ensuring the population sustains itself. In contrast, populations characterized by a Type I survivorship curve often have low birth rates because most offspring survive to reproduce, and very high birth rates result in exponential population growth.

Here’s Hank Green’s take on Population Growth to help you review these ideas:

Video was unnecessarily long, but at least he’s interesting to listen to.