Exponentinal Population Growth

Population Regulation – Anatomy of the logistic growth curve.

Exponential vs. logistic growth model.

Relationship between N, K and r.

Relationship between N, K and r based on data.

Population growth of equilibrium vs. opportunistic species.

Logistic growth based on data.

The Allee effect

The Allee effect

The Allee effect – Vancouver Island Marmots

As the population size of Vancouver Island marmots decreases, so after a certain point, so does their reproductive rate, demonstrating an Allee effect. Figure from Brashares et al. 2010 (Journal of Animal Ecology)

Restricted to Vancouver IslandPopulation dropped 300 in 1980s -> 25 in 2001.

This Allee effect is so evident from these data that I may as well have copied this figure from a population ecology textbook. - Hannah Waters

The Allee effect – Vancouver Island Marmots

Vancouver Island marmots have a home range ten times larger than any of the closely related social marmot species in order to search for scarce mates. Figure from Brashares et al. 2010 (Journal of Animal Ecology)

Impact on finding mates• Fossorial and colonial species – only

leave their burrow to forage.• Males will leave burrow to mate, but at

high population density, they didn’t have to travel far.

• Current home range is comparatively large, increasing exposure to predators.

• Or they get lost.

Change in social behavior• Predator numbers have increased since

1970• More time spent on watch.• But fewer alarm calls are heard. – not

enough animals to stand watch for the colony.

• Time is lost for feeding, risking starvation, reduced fecundity, altering hibernatin patterns.

Logistic growth of fur seals on St. Paul Island, Alaska.

Logistic growth of introduced sheep populations

Logistic growth of reindeer

Lichen = fungus + algae

Fred fungus took a lichen to alice algae.

Lichen

Lichen growth

Lush lichen growth on Hall Island, St. Matthews group. Dry tundra. 1985. Photo: D.R. Klein.

The thick mats of fruticose lichens that dominated much of the landscape in the southern portion of St. Matthew Island prior to the introduction of reindeer had been greatly depleted by reindeer grazing when vegetation plots were established there (Station #2) in early August 1957. Only fragments of fractured lichens and moss remained on the ground surface in the depressions between the dark green willow hummocks. Photo: 1957. D.R. Klein.

Lichen growth

The thick mats of fruticose lichens that dominated much of the landscape in the southern portion of St. Matthew Island prior to the introduction of reindeer had been greatly depleted by reindeer grazing when vegetation plots were established there (Station #2) in early August 1957. Only fragments of fractured lichens and moss remained on the ground surface in the depressions between the dark green willow hummocks. Photo: 1957. D.R. Klein.

This lichen-dominated plant community with scattered hummocks of willow is on Hall Island that was never reached by the reindeer. It serves as a control for assessing the grazing impact of reindeer on similar communities on St. Matthew Island. Photo: D.R. Klein

Human population growth revisited.

Population Clocks

Density dependent regulation of the human population?

Happy Thoughts

Factors regulation population growth.

Factors regulation population growth.

Factors regulation population growth – self-thinning rule.

Density independent population growth.

Density independent population growth.

Regression parameters for Andrewartha & Birch’s model of thrip abundance

Y= average of the logarithm of the number of thrips/flower over the 30 days prior to the population peak.

X1 = the effective degree days from the 1st rains of the winter season to Aug. 31st,which might determine the growth of the annual plants on whose pollen the thrips would feed later in the season.

X2 = the rainfall during September/October – the rain that sustains the flowers that the thrips feed on.X3 = the effective degree-days during September/October, the time when temperatures are becoming

marginally adequate for thrips reproduction.X4 = the same X1, but for the previous year, to take into account any carryover of thrips or seeds from

the next near.

a. From this regression equation, they were able to account for 78% of the variation in thrips abundance.

b. X1, warmth of fall and winter most important, followed by X2, spring rainfall, and then the warmth of the previous winter X4.

Density independent population growth.

Weather Can Influence Population Size Davidson and Andrewartha accurately predicted the mean number of thrips per rose observed in Adelaide, Australia, using an equation based on four weather-related variables. (After Davidson and Andrewartha 1948.)

Density independent population growth.

Density Dependence in Thrips imaginis Smith’s reexamination of Davidson and Andrewartha’s thrips data showed that the number of individuals added to the population decreased as the density of the population increased, as would be expected if density-dependent factors were important. (After Smith 1961.)