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Finish Population Dynamics (Ch. 10) Fecundity Schedule for Phlox drummondii Age (days) nx lx 0-299 996 1.00 299-306 158 0.16 306-313 154 0.15 313-320 151 0.15 320-327 147 0.14 nx= number survivors mx lxmx xlxmx lx = survivorship mx = Age-specific fecundity: Average number seeds produced by individual in age category. Fecundity Schedule for Phlox drummondii Age (days) nx lx mx 0-299 996 1.00 0.0000 299-306 158 0.16 0.3394 306-313 154 0.15 0.7963 313-320 151 0.15 2.3995 320-327 147 0.14 3.1589 lxmx mx = Age-specific fecundity: Average number seeds produced by individual in age category. i.e. plants 300 days old produce on average 0.3394 seeds xlxmx Fecundity Schedule for Phlox drummondii Age (days) nx lx mx lxmx 0-299 996 1.00 0.0000 0.0000 299-306 158 0.16 0.3394 0.0532 306-313 154 0.15 0.7963 0.1231 313-320 151 0.15 2.3995 0.3638 320-327 147 0.14 3.1589 0.4589 Ro= lxmx Sum these! xlxmx x = age interval lx = proportion pop. surviving to age x mx = Age-specific fecundity: Average number seeds produced by individual in age category. Annual Plant • Phlox drummondii (hermaphrodite) – Ro = Net reproductive rate; Average number seeds produced by individual during life – If > 1, population increasing – If = 1, population stable – If < 1, population declining Annual Plant Is pop. stable, increasing, decreasing? Annual Plant • Non-overlapping generations: can estimate growth rate (per unit time). • Geometric Rate of Increase, lambda (): Annual Plant • Non-overlapping generations: can estimate growth rate. • Geometric Rate of Increase, lambda (): – = Nt+1 / Nt – Nt+1 = Size population future time – Nt = Size population earlier time Annual Plant • Geometric Rate of Increase, lambda (): – Start 996 plants: 2.4177 seeds/individual (Table 10.1) – 996 x 2.4177 = 2,408 seeds start next year – = Nt+1 / Nt – = 2,408 / 996 – = 2.41 – = Ro for annual plant (generations do not overlap & reproduction not continuous) Estimating Rates when Generations Overlap Who am I? Hermaphrodite? Estimating Rates when Generations Overlap • Common Mud Turtle (Kinosternon subrubrum) • Data: – survivorship in age class (years) – reproductive info for each age class How can a turtle reproduce? • Need Females! Population mix males & females • Not all reproduce • Clutch Size: # eggs laid by female/nest • How many nests/year (or time period)? mx= (% fem) x (% reproducing) x (clutch size) x (# nests) • Table 10.2 – Trick: Pop. has males & females, so calculate production females by females • Sum col. 4 in Table 10.2 (lxmx), R0 = 0.601 • Stable, increasing, decreasing? Other population parameters • Common Mud Turtle – Average generation time (T): Average time from egg to egg between generations Fecundity Schedule for Kinosternon subrubrum Age (yrs) nx lx mx lxmx xlxmx 1 996 1.00 0.0000 0.0000 = 1 x 0.00 2 158 0.16 0.3394 0.0532 = 2 x 0.05 3 154 0.15 0.7963 0.1231 4 151 0.15 2.3995 0.3638 5 147 0.14 3.1589 0.4589 T= xlxmx /Ro Sum these! x = age interval lx = proportion pop. surviving to age x mx = Age-specific fecundity: Average number eggs/seeds produced by individual in age category. Table 10.2: • T = 6.4 / 0.601 = 10.6 years T = xlxmx / Ro Other population parameters • Common Mud Turtle • Per Capita Rate of Increase (r) • r = rate population change per individual per unit time r = (ln Ro) / T – ln = natural log • Also: • r is births per individual per unit time (b) minus deaths per individual per unit time (d) •r=b-d Estimating Rates when Generations Overlap • Common Mud Turtle r = (ln Ro) / T r = ln (0.601) / 10.6 r = -0.05 – rate population change per individual per unit time If r > 0, population increasing If r = 0, population stable If r < 0, population declining Makes sense: r=b-d Organism Size and Population Density • A search for patterns………….(recall size vs. density) hi population density (log) lo lo body size (log) hi Organism Size and Population Density • A search for patterns………….(recall size vs. density) • Generation time vs. size? Size – Also log-log scale Gen time (T) Generation time vs. size • Positive slope • Log-log scale Use of population dynamics info • Control invasive species (who am I?) 2008 map Use of population dynamics info • Prevent extinction rare species (who are we?) 200 or fewer individuals in wild Use of population dynamics info • Managing harvested species • Ex, orange roughy Slimehead family! New Zealand Fishery areas Use of population dynamics info • Long lived (150 years) – Breed when 25-30 yr old • Harvest only large fish (allow some to breed)? Population Density Immigration Emigration Dispersal • Important to population dynamics • Immigration: add individuals • Emigration: lose individuals Dispersal • Hard to study: • 1) tracking movements adults • 2) dispersal phase may be small wolf Bee! Dispersal • Africanized Honeybees – Killer bees... • Africanized Honeybees Dispersal – Honeybees (Apis mellifera) • subspecies • Africanized disperse faster than European honeybees. • Africanized Honeybees Dispersal They are Here!! • First in Mobile AL, Aug 2004! • 28 US fatalities 2010 near Albany GA Aug 2004, first • Most species don’t disperse fast.... When Do Organisms Disperse? • Eggs/ Sperm/ Seed (e.g. pollen, soft corals, burrs) • Larvae/Juveniles (e.g. Corals, Fish, spiders) • Adults (e.g. Cats, Butterflies, birds) Immobile adults must disperse as Juveniles, Zygotes or Gametes! Dispersal & Climate Change • Organisms spread northward 16,000 years ago (retreat of glaciers) – Evidence: preserved pollen in sediments. Changes in Response to Climate Change – Tree species: Movement slow 100 - 400 m/yr. Fig. 10.6 – Climate envelope: area with appropriate climate conditions American Pika (Ochotona princeps) Climate Change – Climate envelope: area with appropriate climate conditions Torreya taxifolia – Will envelopes move too fast? – Assisted migration: human help to prevent extinctions Dispersal in Response to Changing Food Supply • Holling: numerical responses to increased prey – Increased prey density led to increased predator density This figure from Ch. 7 showed functional responses Dispersal in Response to Changing Food Supply • Numerical response: dispersal + increased reproduction Kestrel Vole Owl Dispersal in Response to Changing Food Supply • Predators moved to areas of more dense prey Fig. 10.7 Dispersal in Rivers and Streams Dispersal in Rivers and Streams • Current (flow of water) causes drift (movement downstream) • Adaptations to maintain position: – 1) Streamlined bodies/strong swimmers Jumping salmon Dispersal in Rivers and Streams • Adaptations to maintain position: – 2) Bottom-dwelling: avoid current – 3) Adhesion: hang on! Etowah darter Alabama hogsucker Dispersal in Rivers and Streams • Still get washed downstream in flash floods (spates). James River VA, 1985 Dispersal in Rivers and Streams • Colonization cycle: interplay downstream & upstream dispersal Dispersal in Rivers and Streams • Cool story: Costa Rican river snail moves upstream in migratory wave (to 1/2 million snails!)