Population Dynamics 1950

Estimating Patterns of Survival Three main methods of estimation: Cohort life table Identify individuals born at same time and keep records from birth. Static life table Record age at death of individuals. Age distribution Calculate difference in proportion of individuals in each age class. Assumes differences from mortality.

Survivorship Curves Type I: Majority of mortality occurs among older individuals. Dall Sheep Type II: Constant rate of survival throughout lifetime. American Robins Type III: High mortality among young, followed by high survivorship. Sea Turtles

Age Distribution Age distribution of a population reflects its history of survival, reproduction, and growth potential.

Age Distribution Rio Grande Cottonwood populations (Populus deltoides wislizenii) are ….

Dynamic Population in a Variable Climate Grant and Grant studied Galapagos Finches. Responsiveness of population age structure to environmental variation.

Blacknose dace (Rhinichthys atratulus) s South Branch Codorus Creek

Africanized Honeybees Dispersal Africanized Honeybees Honeybees (Apis melifera) evolved in Africa and Europe and have since differentiated into many locally adapted subspecies. Africanized honeybees disperse much faster than European honeybees. Within 30 years they occupied most of South America, Mexico, and all of Central America.

Africanized Honeybees

Collared Doves Collared Doves, Streptopelia decaocto, spread from Turkey into Europe after 1900. Dispersal began suddenly. Not influenced by humans. Took place in small jumps. 45 km/yr

Collared Doves

Rapid Changes in Response to Climate Change Tree species began to spread northward about 16,000 years ago following retreat of glaciers and warming climate. Evidence found in preserved pollen in lake sediments. Movement rate 100 - 400 m/yr.

Rapid Changes in Response to Climate Change

Dispersal in Response to Changing Food Supply Holling observed numerical responses to increased prey availability. Increased prey density led to increased density of predators. Birds moved.

Population Growth Geometric Growth Exponential Growth Logistic Population Growth Limits to Population Growth Density Dependent Density Independent Intrinsic Rates of Increase Our Future

Geometric Growth When generations do not overlap, growth can be modeled geometrically. Nt = Noλt Nt = Number of individuals at time t. No = Initial number of individuals. λ = Geometric rate of increase. t = Number of time intervals or generations.

Appropriate for populations with overlapping generations. Exponential Growth Continuous population growth in an unlimited environment can be modeled exponentially. dN / dt = rmax N Appropriate for populations with overlapping generations. As population size (N) increases, rate of population increase (dN/dt) gets larger.

Exponential Growth For an exponentially growing population, size at any time can be calculated as: Nt = Noert Nt = Number individuals at time t. N0 = Initial number of individuals. e = Base of natural logarithms. rmax = Per capita rate of increase. t = Number of time intervals.

Exponential Growth of Human Population The Black Death! www.globalchange.umich.edu/.../human_pop.html

Logistic Population Growth As resources are depleted, population growth rate slows and eventually stops, this is called logistic population growth. Sigmoid (S-shaped) pop. growth curve. Carrying capacity (K) is the number of individuals of a population the environment can support. A finite amount of resources can only support a finite number of individuals.

Logistic Population Growth

Logistic Population Growth dN/dt = rmaxN(1-N/K) rmax = Maximum per capita rate of increase under ideal conditions. rmax occurs at extremely low population size. Growth rate (dN/dt) is greatest when N=K/2. When N nears K, the both (1-N/K) and r approach zero. N/K = Environmental resistance; defines when resources limit further growth. If N>K, then dN/dt is negative; population declines.

Limits to Population Growth Environment limits population growth by altering birth and death rates. Density-dependent factors Disease, Resource competition Density-independent factors Natural disasters

Galapagos Finch Population Growth Boag and Grant - Geospiza fortis was numerically dominant finch (1,200). After drought of 1977, population fell to (180). Food plants failed to produce seed crop. 1983 - 10x normal rainfall caused population to grow (1,100) due to abundance of seeds for adults and caterpillars nestlings.

Galapagos Finch Population Growth

Cactus Finches and Cactus Reproduction Grant and Grant documented several ways finches utilized 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

Cactus Finches and Cactus Reproduction Finches tend to destroy stigmas, thus flowers cannot be fertilized. Wet season activity may reduce seeds available to finches during the dry season. Opuntia helleri main source for cactus finches. Negatively impacted by El Nino (1983). Stigma snapping delayed recovery. Interplay of biotic and abiotic factors.

Our Future?

Life Histories Adaptation of an organism that influence its biology over its life span; e.g. offspring #; survival, size and age of reproduction, maturation transformations.

Offspring Number Versus Size Principle of Allocation: If organisms use energy for one function such as growth, the amount of energy available for other functions is reduced. Leads to trade-offs between functions such as number and size of offspring.

12_04.jpg

12_07.jpg

Seed Size and Number in Plants Small plants producing large number of small seeds appear to have an advantage in areas of high disturbance. Plants producing large seeds are constrained to producing fewer seedlings more capable of surviving environmental hazards.

12_06.jpg

Seed Size and Number in Plants Many families produce small number of larger seeds. Dispersal mode might influence seed size.

12_03.jpg

Life History Classification MacArthur and Wilson r selection (per capita rate of increase) Characteristic high population growth rate. K selection (carrying capacity) Characteristic efficient resource use. Pianka : r and K are ends of a continuum, while most organisms are in-between. r selection: Unpredictable environments. K selection: Predictable environments.

r K

Plant Life Histories Grime proposed two most important variables exerting selective pressures in plants: Intensity of disturbance: Any process limiting plants by destroying biomass. Intensity of stress: External constraints limiting rate of biomass production.

Plant Life Histories Four Environmental Extremes: Low Disturbance : Low Stress Low Disturbance : High Stress High Disturbance : Low Stress High Disturbance : High Stress

Plant Life Histories Ruderals (highly disturbed habitats) Grow rapidly and produce seeds quickly. Stress-Tolerant (high stress - no disturbance) Grow slowly - conserve resources. Competitive (low disturbance low stress) Grow well, but eventually compete with others for resources.

end

Grime’s Plant Life History Triangle

Opportunistic, Equilibrium, and Periodic Life Histories Winemiller and Rose proposed new classification scheme based on: juvenile survivorship (lx), fecundity (mx), and age of reproductive maturity (α) Opportunistic: low lx - low mx - early α Equilibrium: high lx - low mx - late α Periodic: low lx - high mx - late α

Opportunistic, Equilibrium, and Periodic Life Histories

12_22.jpg

End

Rates of Population Change Birth Rate: Number of young born per female; seeds per individual plant. Fecundity Schedule: Tabulation of birth rates for females of different ages. “Life Table” of survivorship per age grouping (see above) combined with fecundity schedule can be used to calculate net reproductive rates.

Estimating Rates for an Annual Plant Phlox drummondii (phlox) Ro = Net reproductive rate; Average number of seeds produced by an individual in a population over lifetime (“birth rate”). Ro=∑ lxmx X= Age interval in days. lx = % pop. surviving to each age (x). mx= Average number seeds produced by each individual in each age category.

Estimating Rates for an Annual Plant Because P. drummondii has non-overlapping generations, we can estimate growth rate. Geometric Rate of Increase (λ): λ=N t+1 / Nt N t+1 = Size of population at future time. Nt = Size of population at some earlier time.

Estimating Rates when Generations Overlap Common Mud Turtle (K. subrubrum) About half turtles nest each year. Average generation time: T = ∑ xlxmx / Ro X= Age in years Per Capita Rate of Increase: r = ln Ro / T ln = Base natural logarithms fwie.fw.vt.edu/VHS/Kinosternon_subrubrum.htm

10_02.jpg