Presentation on theme: "Population ecology readings: Ch 9 – population structure Ch 10 – Life Tables, pp. 239-249 Ch 11- Exponential and Logistic Growth DEF: Populations are individuals."— Presentation transcript:
Population ecology readings: Ch 9 – population structure Ch 10 – Life Tables, pp Ch 11- Exponential and Logistic Growth DEF: Populations are individuals of the same species that live together in time and space
POPULATION ECOLOGY Why here and why now? (1) Populations have emergent structures…. - Wolf packs; cooperative hunting, deferred reproduction individualspopulations Are born and diebirth rates and mortality rates Disperseimmigration and emigration rates Extinction population structures (e.g., clumping) Evolve
POPULATION ECOLOGY Why here and why now? (2) Many important processes related to, in particular, mortality and reproduction are Density Dependent as opposed to being Density Independent. Abiotic forces are density independent : - Fire kills irrespective of the number of trees - Saguaros: Frost kills irrespective of the number of cacti - Cold weather kills irrespective of the number of squirrels Biotic forces are density dependent : - Competition: your food availability depends on how many mouths there are - Predation: predators seek food patches containing many prey - Escaping predation depends on group defense - Mutualisms: seed production depends on the number of pollinators Are these statements always true?
Hence, we want to characterize the number of individuals
Populations: Abundance or Density ( # individuals) (# individuals/area) Survival of indivs: Reproduction of indivs: } Project abundance/density into the future Growth Rate Building Life Tables: (1)Follow a population (or given group of indivs – a cohort) from birth to death (2) Follow a population of known-age indivs for a shorter period of time and record deaths and births as a function of age
Terms: X = Age (days, weeks, years) of individuals N X = Number of individuals alive at the start of age X l X = Proportion of the initial population that is alive at the BEGINNING of age X. ****l 0 = 1.0 m X = The number of daughters born to an average female during the interval X to X+1. Because only females contribute to population growth, life tables only track female individuals
XN X l X m X What do we have? (1)Maximum lifespan is 4 years Age # survivor maternity
XN X l X m X (2) We can plot the natural logarithm of N X (or l X ) versus age to examine survivorship: (book plots Nx on a Log scale) age X ln(N X ) Population experiences constant survivorship with age: ~ ½ the population dies at each interval Age # survivor maternity
This is in contrast with populations that senesce: age X ln(N X ) E.g., Humans, whales or, experience greatest mortality early in life age X ln(N X ) E.g., Most insects, many plants
XN X l X m X (3) Reproductive effort (per individual) is greatest at midlife Age # survivor maternity
But even better, we can calculate a population growth rate and determine whether the population is increasing or declining XN X l X m X Age # survivor maternity l X m X l X m X = the number of daughters each initial female can expect to give birth to during the interval X to X+1.
XN X l X m X Age # survivor maternity l X m X The difference between l X m X and m X is the former accounts for mortality. E.g., m 2 = 3 and L 3 m 3 = < 3 because 75% of females die before the age of 2
l X m X Expected # daughters between ages 0 – 1 Expected # daughters between ages 1 – 2 Expected # daughters between ages 2 – 3 Expected # daughters between ages If we add all these up, we get the expected number of daughters over a females lifetime That sounds Useful !!! And IT IS
The sum of l X m X is called the Net Reproductive Rate, R 0 R 0 = (l X m X ) is the expected number of daughters born to each female during her lifetime. It is true that many females do not reproduce, those that do have many daughters in their lifetime – what we are examining is the reproductive output of the average female. Given that each female dies in her lifetime (-1 female) if R 0 = 1 daughter, then she exactly replaces herself in her lifetime Has the population therefore grown or declined??
If R 0 = 1 the population is neither growing or declining, rather population size is stable. If, however, R 0 > 1 the population is growing And, if R 0 < 1 the population is declining R 0 = 1.25 = 25% population increase/generation ** R 0 = 0.67 = 33% population decrease/generation ** ** True in special circumstances (e.g., annual plants)
Why are Life Tables Useful?? We can tell at a glance: (1) patterns of survivorship, (2) at what age reproductive potential is stored, (3) The direction and magnitude of population change Furthermore, we can understand the effects of changes in age-specific death or maternity whether by accidental or by design.
Peter and Rosemary Grants study of Darwins Finches
Life Tables – the COHORT approach
Age in years Percentage of finches droughts La Niña drought 1977 See Fig in your text Bottom-heavy Increasing populations Top-heavy declining populations The STATIC approach
XN X l X m X R 0 = R 0 = 1.38 XN X l X m X Hunters target young adults XN X l X m X Hunters target old adults Constant mortality rate with age and reproductive senescence R 0 = 1.41
XN X l X m X XN X l X m X XN X l X m X Increase survival of hatchlingsIncrease survival of adults R 0 = 0.96R 0 = 1.07 Constant mortality (50%) rate with age and increasing reproductive output with age R 0 = 0.465
Fundamental Niche Realized Niche R 0 > 1.0 R 0 < 1.0 The Niche concept place in a Population Framework predation competition Factor One Factor Two