Population Dynamics The Growth and Decline of Populations

Populations What is a population?

Population Dynamics • Populations grow when birth rate + immigration rate > death rate + emigration rate • Populations decline when birth rate + immigration rate < death rate + emigration rate

Population Dynamics Resources determine how a given population will grow. In general, any population of organisms with plenty of resources and ideal conditions tends to grow fast. This is called exponential growth

Exponential Growth

Exponential Growth “…give me one grain of wheat for the first square, two for the second and so on, doubling the grains for each of the 64 squares of the chess board.” How much wheat? A pyramid with a base of 28 miles and a height of 4.5 miles…. More wheat than exists on the planet!

Exponential Growth

Exponential Growth EXPONENTIAL GROWTH Occurs when resources are plentiful relative to population size Usually occurs early in population’s growth Characterized by constant growth rate and doubling time

Logistic Growth Logistic growth curves demonstrate the natural (logical) phases of population growth: slow; moderate; fast; steady state or collapse. EVENTUALLY THE GROWTH WILL LEVEL OFF OR COLLAPSE. THIS ENTIRE PROGRESSION IS KNOWN AS LOGISTIC GROWTH.

Stable Population – Steady State As resources run low population growth may level off, reaching a steady state. This is also sometimes referred to as an S–Curve.

Population Decline - Collapse As resources run low, the other possibility is that the population will collapse, sometimes referred to as a J–curve.

Carrying Capacity Theoretical point beyond which a population can no longer be sustained is known as the carrying capacity. Normal part of population logistics because resources are finite. Do populations undergo steady state growth or collapse when they reach carrying capacity?

Limiting Factors Resources – nutrients and energy – in short supply, limit population growth These resources are considered limiting factors

Limiting Factors Density-dependent limiting factors Limit population size when a population is large and crowded Examples include: food, predation, disease, stress Density-independent limiting factors Limit population size regardless of whether a population is large or small Examples include: geothermal activity, extreme weather

Mathematics of Population Growth Populations grow when there are more births than deaths Populations decline when there are more deaths than births The growth rate (r) is the difference between the death rate and the birth rate.

Mathematics of Population Growth Growth rate (r) is always calculated as an average for a specific time period, i.e. average yearly growth rate or average daily growth rate If a population of 100 added 4 people in a year, the average yearly growth rate would be r = 0.04 or 4%. This means that 0.04 new people were added for every person in the original population. It also means that 0.4 were added for every 10 or 4 people were added for every 100!

Mathematics of Population Growth Practice Using the fruit fly data from the textbook: What is the growth rate for the fruit fly population between day 15 and day 20? Using the rabbit data from the textbook: What is the growth rate for the rabbit population between generation 2 and generation 25?

Mathematics of Population Growth Once a population’s average growth rate is known, we can make predictions - both future population and doubling time. These predictions make the assumption that the old growth rate will be the growth rate in the future!

Mathematics of Population Growth Practice Using the fruit fly data from the textbook: What is the average daily growth rate for the fruit fly population between day 15 and day 20? Based on the average daily growth rate between day 15 and day 20, what do you predict the population will be on day 60? Based on the average daily growth rate between day 30 and day 35, what do you predict the population will be on day 60?

Mathematics of Population Growth Practice Using the rabbit data from the textbook: What is the average generational growth rate for the rabbit population between generation 2 and generation 25? Based on the average generational growth rate between generation 2 and generation 25, what do you predict the population will be on generation 125? Based on the average generational growth rate between generation 86 and generation 100, what do you predict the population will be on generation 125?