BACKGROUND • Populations are interbreeding groups; members of the same species in a geographic area • Populations are dynamic; change in size due to: births (natality) deaths (mortality) immigration (moving in) emigration (moving out) • Pattern of change can be linear, exponential or logistic, as evidenced by growth rate

S’math: Growth rate d*N dT r = B-D N 1. As change in population size change in time 2. As per capita growth rate = Births - Deaths Number in population * delta, Δ r = B-D N

30 days dN dT r = r = B - D N 5 - 2 10 = 3 = 0.3 per capita 10 Ex: In a population of 10 ducks, 5 are born and 2 die in the month of April. 13 – 10 = 3/mo = 0.3/day 30 days dN dT r = r = B - D N 5 - 2 10 = 3 = 0.3 per capita 10 On the formula sheet it’s a single equation

Linear growth • Change is constant, regardless of population size • Population is increasing but # offspring produced is not # of otters 2500 2000 1500 1000 500 +500 +500 +500 1995 2000 2005 2010 year

Exponential growth • Growth is proportionate to population size • Populations growth in the absence of limits; biotic potential • J shape to curve Large population rapid growth +20,000 gen population size Fun fact: doubling time is the rate divided by 69. EX: 3% growth rate /69 = 23 years to double Small population size, slow growth + 500 /generation generation

Exponential growth dN dT rmax N = • Amount of growth depends on the population size population size dN dT change in population size rmax N = growth rate per capita Ex: duck population’s growth rate of 0.3 per capita Fun fact: doubling time is the rate divided by 69. EX: 3% growth rate /69 = 23 years to double N Math Population change New population size 1000 0.3(1000) +300 1300 0.3(1300) +390 1690 0.3(1690) +510 2200 increasing

BIOTIC POTENTIAL UNLEASHED Staphylococcus Aureus Cells would cover the Earth 7 feet deep in 48 hours. Audesirk & Audesirk, 1993

r-selected species opt for exponential growth Small in size Short life span fast maturity One reproductive event many offspring little energy invested in offspring Organisms have two choices - maximize your chances in the short term in an unpredictable environment ‘(go with the flow’) or ‘cut and run’ to a more stable environment. Suppose you stayed. Then, one thing you could do would be to increase the number of offspring. Make lots of cheap (requiring little energy investment) offspring instead of a few expensive, complicated ones (requiring a lot of energy investment). If you lose a lot of offspring to the unpredictable forces of nature, you still have some left to live to reproductive age and pass on your genes to future generations. Many invertebrates follow this strategy - lots of eggs are produced and larvae are formed but only a few survive to produce mature, reproductive adults. Insects and spiders also follow this strategy. Alternatively, you could adapt to a more stable environment. If you could do that, you would find that it would be worthwhile to make fewer, more expensive offspring. These offspring would have all the bells and whistles necessary to ensure a comfortable, maximally productive life. Since the environment is relatively stable, your risk of losing offspring to random environmental factors is small. Large animals, such as ourselves, follow this strategy. ex: insects weeds

Reality: Limiting Factors • checks on population size • both biotic and abiotic • both density dependent and density independent ‘disasters’ symbiotic relationships space predation

r-selected species/populations are limited by density independent factors temperature change fire rapid growth rapid decline temperature change

K-selected species experience logistic growth • Large size • Long life span slow to mature • Reproduce multiple times few offspring dependent offspring Organisms have two choices - maximize your chances in the short term in an unpredictable environment ‘(go with the flow’) or ‘cut and run’ to a more stable environment. Suppose you stayed. Then, one thing you could do would be to increase the number of offspring. Make lots of cheap (requiring little energy investment) offspring instead of a few expensive, complicated ones (requiring a lot of energy investment). If you lose a lot of offspring to the unpredictable forces of nature, you still have some left to live to reproductive age and pass on your genes to future generations. Many invertebrates follow this strategy - lots of eggs are produced and larvae are formed but only a few survive to produce mature, reproductive adults. Insects and spiders also follow this strategy. Alternatively, you could adapt to a more stable environment. If you could do that, you would find that it would be worthwhile to make fewer, more expensive offspring. These offspring would have all the bells and whistles necessary to ensure a comfortable, maximally productive life. Since the environment is relatively stable, your risk of losing offspring to random environmental factors is small. Large animals, such as ourselves, follow this strategy. ex: trees whales

In K populations limiting factors establish the ecosystems carrying capacity • Sets the max population, size based on available resources • Density dependent limiting factors • Growth is logistic, creating an S-shaped curve

dN dT Calculations factor in the carrying capacity (K) K – N rmax N = Ex: duck population’s growth rate of 0.3 per capita, and a carrying capacity of 2500 ducks N Math Change to population Percent change 250 0.3(250)(2500-250/2500) 68 27 1000 0.3(1000)(2500-1000/2500) 180 18 2000 0/3(2000)(2500-2000/2500) 120 6

B>D B = births (and immigration) D = deaths (and emigration) no growth B=D logistic growth slow growth, linear even B>D time exponential growth B>D

Natural selection has produced a continuum of strategies • extreme r-selection at one end of the spectrum • extreme K-selection at the other end 1 offspring 5 years of care 500m eggs No parental care

Survivorship curve of r vs K selected species High survival probability in early and middle life, rapid decline in survival in later life. Typical of K – selected species High mortality in early life – a bottleneck – typical of r – selected species

Population Case Study • Galapagos finches, 1976 drought as limiting factor • drought: abiotic, density independent • change in food source: biotic, density dependent Population decreases in size Seed abundance decreases number of birds Seed hardness increases Beak depth increases

Population Case Study • Predator and prey as limiting factors on one another • biotic, density dependent Lag time