eco Ch 11 (still need info from book this is just slides)

planktonic populations of diatoms

“bloom” each spring.

zooplankton populations

increase as they feed on diatoms.

COVID has had different rates of increase

initially having exponential growth

later periods of slower rates of growth

eventually having periods of decline

Geometric growth

When generations do not overlap, growth can be modeled geometrically.

• Successive generations differ in size by a constant ratio.

N_t = N₀𝜆^t

•N_t = Number of individuals at time t

•N₀ = Initial number of individuals

•𝜆 = Geometric rate of increase

•t = Number of time intervals or generations

Phlox Drummondii (I think case study cuz it’s a graph of a flower)

The population grows from 0 at year zero to 100,000 by year five, 200,000 by year six, roughly 500,000 by year seven, and almost 1.2 million by year eight.

Exponential growth

Continuous population growth in an unlimited environment can be modeled exponentially.

dN/dt=rN

Appropriate for populations with overlapping generations.

As population size (N) increases, rate of population increase (dN/dt) gets larger

Population size with exponential growth

•For an exponentially growing population, size at any time can be calculated as: N_t= N_0 er^t

•N_t = Number individuals at time t.

•N₀ = Initial number of individuals.

•e = Base of natural logarithms.

•r = Per capita rate of increase.

•t = Number of time intervals.

Exponential growth in nature

Assumption of constant rate of per capita increase may seem unrealistic.

•Natural populations may grow exponentially for short periods of time if abundant resources are present.

Exponential growth by tree populations.

•Pollen records document growth of postglacial tree populations in Britain.

•Exponential growth for 400 to 500 years.

Scots Pine

Following colonization, the Scots pine population grew exponentially for nearly 500 years, reaching concentrations of 50,000 grains of pollen per square centimeter per year.

Conditions for exponential growth

Populations growing exponentially share similar circumstances.

Begin growth in favorable environments at low densities.

Example: planktonic diatoms, whooping cranes.

Whooping cranes reduced to 22 in 1940.

•Grew exponentially to 220 in 2005.

Exponential growth may be important during establishment in new environments, during temporary favorable conditions, during recovery from exploitation.

Whooping Cranes

Since their protection in 1940, the whooping crane population grew exponentially from 22 to over 500 by 2020.

Slowing of exponential growth

Eurasian collared dove expanded into western Europe in 20^th century.

Population grew exponentially for decade or more.

Then rate of population growth began to slow.

•Suggests that population was approaching environmental limits.

•Environmental limitation is incorporated into model of logistic population growth.

Eurasian Collared Dove

•After colonizing Great Britain, the population grew exponentially from 1955 to 1965.

•Note the population size in 1970 and 1975 show that the population size was less by then than what was predicted by the exponential model, suggesting that population growth had slowed.

Logistic population growth

As resources are depleted, population growth rate slows and eventually stops. Exponential growth cannot continue. Growth rate slows then population size levels off.

•Sigmoidal population growth curve

Carrying capacity (K) – population size that a particular environment can support.

Finite amount of resources can only support a finite number of individuals.

•Sigmoidal population growth curve

population grows rapidly

growth slows

growth stops; population size stabilizes at carrying capacity

(like the saturation graphs in bio, goes up a lot until all the protein pumps are full then you just get a constant rate)

Logistic model of population growth

dN/dt=r(1- N/K) max

r_max = maximum per capita rate of increase under ideal conditions (intrinsic rate of increase). WhenN nearsK, the right side of the equation nears zero.

•As population size increases, logistic growth rate becomes a small fraction of growth rate. When N =K, population growth ceases. Logistic growth is highest when N=k/2

Limits to population growth

Environment influences population growth by affecting birth and death rates.

Density-dependent factors.

•Affected by population density.

•Often are biotic factors.

•Disease, competition, predation.

Density-independent factors.

•Not affected by population density.

•Often are abiotic factors.

•Floods, extreme temperatures.

Environment, birth and death among Darwin’s finches

Boag & Grant studied finches on Daphne Major. Geospiza fortis numerically dominant (1,200). After drought of 1977, population fell to 180.

•Food plants failed to produce seed crop.

In 1983, 10x normal rainfall caused population to grow (1,100).

•Abundance of seeds and caterpillars.

Rainfall, cactus finches and a cactus population

Grant and Grant documented several ways cactus finches use cacti.

•open flower buds in dry season to eat pollen

•consume nectar and pollen from mature flowers

•eat seed coating (aril)

•eat seeds

•eat insects from rotting cactus pads and under bark

Cactus finches and cactus reproduction

Finches tend to damage cactus flowers, thus preventing fertilization.

This activity may reduce seeds available to finches during the dry season.

Opuntia helleri main food source for cactus finches.

•Negatively impacted by El Niño in 1983.

•During following drought years, finch damage to flower further impacted cactus reproduction.

Interplay of biotic and abiotic factors.

Cactus abundance and damage

When cactus flowers are abundant, damage by finches is low

Applications: The human population

Most significant environmental problems today can be traced to effects of human population on environment.

Important to be familiar with aspects of human population.

•History

•Projected growth

Current state

Distribution and abundance

Human species is virtually everywhere.

•On all continents, most oceanic islands.

Except for Antarctica, current distribution did not require modern technology. Highly clumped at large scales.

•60% of humans in Asia as of 2011; most of these in two countries.

•Highest densities in coastal areas and along major river valleys.

Variation at small scales

Human population density is more variable at small scales.

•Within Asia, Singapore has density of 6,900 persons/km² while Mongolia has density of 2/km²

•United States has average density of 30/km²

-Most of this is east of the Mississippi and on the West Coast.

Population dynamics

Human population dynamics vary spatially Sweden has a stable age distribution

•Birth rate and death rate are equal

Hungary has a declining population

•Birth rate is lower than death rate

Rwanda has a growing population

•Birth rate is higher than death rate

Population growth

Rwanda’s population projected to outgrow that of Sweden and Hungary by 2020.

Sweden’s population expected to stabilize, then decline.

•Currently growing slowly due to immigration.

Hungary’s population expected to decline faster than Sweden.

Global population growth

Many developed nations have stable or declining populations

Most developing nations are growing

Global population growth has been rapid in last 500 years, at times more than exponential

•Currently showing signs of slowing

•Rate of population growth has declined

•Population size projected to level off

Perspectives on global population growth

during the past few centuries global population growth has at times exceeded exponential rates

However if plotted for more modern times, our population shows actual and reduced growth rates, which peaked in 1968