2/21 MM 2/23 MM 2/26 DI 2/28 DI 3/1 HW1 3/2 DI 3/5 DI, HW2 3/7 DI 3/9 DI 3/12 MM 3/14 Mid-Term 3/16 MM 3/19 Spring Break

Reading Assignments BSCI363 Chapter 11: CONS670 Chapter 7:

Calculating Growth Rates Question: If there are 2 rabbits today, but 200 rabbits tomorrow, calculate r and lambda. Answer: lambda = 100 rabbits per rabbit per day. r = ln(100) = 4.61 rabbits per rabbit per day.

“Big-Bang” Reproduction (λ) Time (hrs) Population Size N=100N=1

Continuous Growth Time (hrs) Population Size N=3 N=10 N=31 N=100

Frequency Variation and The Mean Class Size Mean = 30, SD = 12.5Mean = 30, SD = 2.5

Stochastic Factors Revisited Intrinsic genetic stochasticity demographic stochasticity Extrinsic environmental variation (EV) catastrophe

Demographic Stochasticity Variability in population growth rates arising from random differences among individuals in survival and reproduction. Random fluctuation in growth rate. Random fluctuation in population structure (e.g., sex ratio, distribution of age classes)

Demographic Stochasticity BDBDBDBDBDBDBDBDBDBDBDBD BBDDBDDBBBDDDBBDDDBBBBDD DBDBDDDDBBDBDBBBDDBDBDBB BBBBBDDDDDDBBBBDBDDDBDBD

Demographic Stochasticity: Density Population Size Proportional Effect

Grizzly Bears Mean r = ±95% CI = to B. Dennis, P. L. Munholland, J. L. Scott, Ecological Monographs 61, (1991).

Whooping Cranes Mean r = 0.06 ±95% CI = 0.03 to 0.09 B. Dennis, P. L. Munholland, J. L. Scott, Ecological Monographs 61, (1991).

“First Law of Ecology” Time Population Size

Population Regulation Consider a bacterium with a rate of increase, r = 50/day. Starting with only a few individuals, these bacteria would cover the earth to a depth of 1 foot in 36 hours!!!! Second law of ecology: A population’s growth rate can’t be constant.

Density-Independent Growth Growth Rate Density r 0

Density-Dependent Growth Growth Rate Density max r K 0

Density-Dependent Growth Population Size Time (NOT Density) 0 K

Mechanisms of DD Anything that decreases growth rate as population size increases. Intra-specific competition Predation or disease DD limits the size of your population. If you understand the mechanism of DD, you may be able to increase the size of your population.

Where Are We Measuring “r” Growth Rate Density “Intrinsic” r K 0 “Realized” r

Positive Mean r B. Dennis, P. L. Munholland, J. L. Scott, Ecological Monographs 61, (1991).

Zero Mean r B. Dennis, P. L. Munholland, J. L. Scott, Ecological Monographs 61, (1991).

Negative Mean r Time / Generations N K r<0 N>K

Habitat Fragmentation

Negative mean r B. Dennis, P. L. Munholland, J. L. Scott, Ecological Monographs 61, (1991).

Estimating K Song sparrows of Mandarte Island

Estimating K for Maned Wolves Pack size: 2 adults + mean litter size (3) = 5 1 pack per territory mean territory size = 20 km 2 Reserve = 730 km 2

Estimating K for Maned Wolves

K in Conservation Biology Identifies limits to population density. Can we manipulate these limits Can we increase population density Reveals DD nature of population growth rates Implications for determining population persistence

Regulation of populations at low population densities “Inverse” density-dependence and the Allee effect

The Allee Effect In DD growth, population growth rate declines at high density. The Allee Effect is defined by a decrease in population growth rate at low density, or inverse DD. The Allee Effect is one of those repeating themes in conservation biology

The Allee Effect Growth Rate Density r K 0 DD Inverse DD Threshold Density DI