UNM Biology Undergraduate Labs

Population Growth and Regulation


Important Vocabulary

Population - any group of organisms coexisting at the same time and place that are capable of interbreeding with one another.

Community - any ecologically integrated group of species of microorganisms, plants, and animals inhabiting a given area.

Density - the number of individuals per unity area

Natality (b) - the birth rate
                                                                        **When natality > mortality, the population will grow
Mortality (d) - the death rate

Exponential growth - growth that is a simple function of the size of the growing entity:  the larger the entity, the faster it grows.  If we assume that births and deaths occur continuously and at constant rates, while ignoring immigration and emigration, such a growth pattern forms a continuous curve.

Carrying capacity (K) - the largest number of organisms of a particular species that can be maintained indefinitely in a given part of the environment.

Logistic growth - growth that slows steadily as the entity approaches its maximum size, or carrying capacity.

Density-independent - factors that eliminate a proportion of a population regardless of population density.

Density-dependent - factors that act on a population such that the proportion eliminated depends on the population density.

Abiotic factors - usually regulate a population independently of its density.
                        Ex. temperature, precipitation

Biotic factors - usually regulate a population in a density-dependent manner.
                        Ex. predation, disease, competition

Organisms do not usually exist as isolated individuals in nature but are parts of larger biological units called populations.  These reproductive and evolutionary units consist of the members of a single species occupying a specific geographical region.  Organisms within each population are linked through gene overflow in reproduction, and natural selection operates on the individuals to shape a population’s adaptation to their environment over several generations.  Populations are the fundamental building blocks of species affected by evolution.  There are 2 major reasons for studying populations – 1) gene flow, selection and adaptation, and 2) population management.  The latter focuses on the interaction between humans and the environment (ex. reduce pests, increase beneficials). 

Population studies always begin with basic questions like “How many individuals in this pop?”, “Is pop increasing or decreasing?”, or “How is the pop distributed in the study area?”  We answer this question by taking samples and estimating the number of individuals in the pop distributed in a certain space – population density.  To get the most accurate results, random sampling must occur.

Populations vary in size over time due to a number of factors – some natural, some created.   Births, deaths, and environmental conditions are examples of natural factors that can affect a population.  A few examples of created size variation include hunting an organism to endangerment or extinction, or man made disasters like the atom bomb.  When conditions are good, birth exceeds death resulting in exponential growth.  A population that shows exponential growth never stops growing.  Click here to see a graph of an exponential growth curve.    This curve can be described by the exponential growth equation:


Where:        ∆N – the change in number of individuals
                   ∆t – the change in time
                   r – the rate of increase in number of individuals
                   b – natality; the average per capita birth rate
                   d – mortality; the average per capita death rate
                   N – the number of individuals

Exponential growth assumes an infinite growing space and an infinite growth time period for the species of interest.  However sometimes the allotted space is just not big enough or there are not enough resources to support a larger population, and the species growth levels off resulting in a logistic growth.  Click here to see a graph of a logistic growth curve.  This curve can be described by the logistic growth equation: 


Where:        ∆N, ∆t, r, and N have all the same values as for exponential growth
                   K – carrying capacity        

Here the population can just plateau or we could begin to see a decline.  The biological assumption in this equation is that each individual added to the population makes things slightly worse for the others because it competes for available resources. 

  Population growth stops when N = K because then (K-N) = 0, so (K-N)N = 0, and .

As (K-N) approaches 0, the population is near carrying capacity and the growth rate of the population slows down considerably.

For both equations, the growth rate of the population can be determined by calculating the slope of the curve at the point in interest. 

An excellent organism for studying Population growth and regulation is Lemna, commonly known as duckweed.  Duckweed is the smallest flowering plant; it floats on the surface of still or slow-moving water and can often appear to be an algal bloom to the casual observer.  There are over 40 species of duckweed (family Lemnaceae) worldwide, with 20 species found in the United States.  One Lemna plant consists of one frond. The fronds look like little leaves but actually are a combination of leaf and stem, attached to rootlets that dangle down in the water.  Although duckweed is a flowering plant, it rarely flowers. Usually it reproduces through budding (vegetative reproduction) — new fronds grow from buds on the parent plant. Eventually each new frond grows its own roots and breaks off to become an independent plant.


Factors Regulating Population Size:

There are a number of different factors that affect population size.  These factors are divided into 2 groups – density-independent and density-dependent.  Biotic factors are usually density-dependent factors while abiotic factors are density-independent factors.      

Review Questions

- Define population.
- Provide 2 emergent properties of populations.
- What is the equation for exponential growth?  Draw the graph.
- What is the equation of logistic growth?  Draw the graph.
- Fill in the blanks.  ______________ population growth assumes constraints are acting upon the population; whereas ____________ population growth assumes unlimited resources.
- Define carrying capacity.
- Do biotic factors operate density-dependently or density-independently?  Explain.
- Give an example of a biotic factor.
- Do abiotic factors operate density-dependently or density-independently?  Explain.
- Give an example of an abiotic factor.
- When would natality exceed mortality?
- Draw and explain the Exponential Growth Rate Curve.
- Draw and explain the Logistic Growth Rate Curve.
- Predation, disease, and competition are biotic factores, which usually regulate a population in a ___________ manner.
- In the equation, r=b-d, what do each of the letters represent?