Unformatted text preview: Lecture 6 Lecture
Population Ecology II. Population Recap, lecture 5 Recap, Assessing population status
1. Cohort life tables
a. Calculate probability of survival and fecundity of each age a. class class b. Multiply them and then sum to obtain net reproductive rate b. QUESTION about marmots: why only females used? = common convention in pop. bio of animals. Females make young. Males do not. young. Model females to project future growth. ASSUME 50:50 sex ratio among offspring. ratio Cohort analysis…points to remember…. Cohort All species are different. Must design analysis to fit life stages relevant for Must that species (for example…how would a life table of an annual (for poppy compare to one of an oak tree ?) 2. Static age structure (what is proportion of total population in each age class ?) Today: Assessing population status continued continued 2. Static age structurefinish up. 3. Transition matrix projections – NOT 3. covered in text book. most accurate, detailed way of projecting population growth population mathematically more challenging mathematically probably why it is not covered. probably AGE Structure….. Hypothetical….. Rapidly gr owing Fr act ion of populat ion Not r eplacing i t self populat ion i s likely in decline Age Acacia burkittii, Australia Fig. 5.12, Townsend Age structure of two different populations of a tree that can be reliably aged tree Young Old Young Old NO recruitment since 1925 (rabbits probably causing this) Population in decline Lots of younger individuals Fencing out rabbits improves recruitment Population increasing ? What don’t we know about these populations ? Are old individuals still reproducing ? Could population increase if we got rid of rabbits ? Mortality > recruitment, can this be reversed ? Will recruitment continue or decline as habitat gets ‘full’ ? Are young individuals starting to compete with eachother ? 3. Transition matrices 3. (Matrix modeling) (Matrix Age based models are called Leslie Matrix Age models models (if age is chronological, must always move to (if another ‘age’ or die. If you lump ages into classes, then you are doing a Lefkovich model.) model.) Stage based models are called Lefkovich Stage matrices or models matrices (can stay in a stage) “Transition matrix” term = not Transition synonymous with “Population viability analyses” (PVAs) BUT viability Most PVAs are matrix projection models of Most matrix some sort some = THE tool of choice for evaluating rare THE species survival (came into vogue in early 1990s) 1990s) My challenge My Introduce the tool of matrix projection Introduce because it IS tool of choice for conservation and is very useful BUT conservation Keep it simple YOU DO NOT NEED TO KNOW how to YOU do matrix algebra. But must understand basic structure of models, what can be done with these matrices, and what data are needed to create them. are Transition matrices Transition
1. 2. 2. 3. 3. Like life tables, they are life stage or age based. Like MUST IDENTIFY CRITICAL STAGES or AGES. Very similar to life table analyses but you Very calculate probability of transitioning between stages/ages. Do not need to follow cohorts. Must know number in each stage at multiple Must time points to get transition probabilities. time
 For animals, frequently rely on mark/recapture data For 1. 1. 2. 2. 3. 3. 4. 5. Transitions depend on GROWTH as well as Transitions SURVIVORSHIP. You calculate probability of staying in stage or moving to another stage in staying each interval. Measure per stage fecundity. (presented as a Measure transition to egg or seed stage) Need known # starting individuals in each Need stage. stage. Can project as many time intervals as you Can chose into future chose Has more flexibility than cohort analysis to Has explore sensitivity of vital rates for population growth growth Simplistic plant life history: basic stages THREE stages Seed XX Rosette XX
Flowering XX S=seed R=Rosette F=flowering plant From: o: S S R F
A SS R
0 F
AFS NS A SR A RR 0 x NR NF 0 A RF AFF TRANSITION MATRIX (probabilities) (probabilities) COLUMN MATRIX From: S S R Fl
A SS A SR R
0 A RR F
AFS 0 NS NSASS x NR NF = NSASR 0 A RF AFF 0 TRANSITION MATRIX COLUMN MATRIX MATRIX From: S S R Fl
A SS A SR R
0 A RR F
AFS 0 NS NSASS 0 NRARR x NR NF = NSASR 0 A RF AFF 0 NRARF TRANSITION MATRIX COLUMN MATRIX MATRIX From: S S R Fl
A SS A SR R
0 A RR F
AFS 0 NS NSASS 0 NRARR NFAFS 0 x NR NF = NSASR 0 A RF AFF 0 NRARF NFAFF TRANSITION MATRIX COLUMN MATRIX MATRIX TO GET NEW COLUMN MATRIX FOR YEAR 2 NSASS NSASR 0 NRARR NFAFS 0 add across = NS t+1 add across = NR t+1
= NS t+1 NR t+1 0 NRARF NFAFF add across = NF t+1 NF t+1 NEW COLUMN MATRIX Assumption = transition probabilities are Assumption Repeat process using new column matrix each year (reflects changing population size), BUT keep same transition matrix transition relatively constant over time….this may not be true…you can play around with this. this. Have computer calculate finite rate of Have population increase (λ) after you’ve run population after the model over many time steps the [λ (lambda) = dominant eigenvalue of matrix] What happens to population over time ? What Does it go to zero ? (λ < 1) Does Does it increase ? (λ >1) Does it reach a stable age distribution ? Does (ratio of S:R:F =same for all generations thereafter). What does that look like ? thereafter). Evaluate which transitions contribute most Evaluate to population change ? Once established whole matrix on Once computer and run for generations –what if you change one vital rate by small or large amount ? How sensitive is the model to a change in this one rate ? change Desert tortoise: Gopherus agassizi Gopherus
Federally listed ‘threatened” species THREATS:
•Raven & crow predation (on younger stages) •Off road vehicles (crushing burrows and animals)—affects all stages •Highways (kill adults because they move around more) •Disease (from captive turtles)ages affected? •Low reproduction due to poor food (fecundity) Is there an obvious transition that is source of population decline (including low fecundity) ? Populations are declining dramatically... What are most sensitive stages of life cycle ? life Are there management actions that can Are help with this ? help
Modeling Population Viability for the Desert Tortoise in the Western Mojave Desert Daniel Doak, Peter Kareiva, and Brad Klepetka Ecological Applications Summarized data taken over 15 years in several different studies 8 stages in life based on carapace size size Yearling Yearling Juvenile 1 & 2 Immatures 1 & 2 Adults (3 size classes) Transition probabilities Transition GROWTH = SLOW. Animals tend to stay in same size class. •Reproduction widely variable across populations •Can run model with any of the 4 reproductive rates Desert Tortoise conclusions Desert Animals tend to stay in size class (growth Animals = slow) slow) Survival probability in stages 6 and 7, Survival when reproduction is highest is important when Reproduction widely variable among Reproduction populations populations Can run models with different fecundity values Can ALL MODELS SHOW POP. DECLINE even ALL with best reproductive values with D.T. conclusions…cont…. D.T.
AT current growth, survivorship and AT fecundity—very hard to reverse population decline decline Only those models where transitions in Only LARGEST SIZE CLASSES WERE INCREASED showed stable or increasing INCREASED population sizes ! population REDUCE ADULT MORTALITY SOURCES EXAMPLE 2: What controls rate of spread of invasive shrub Cytisus scoparius Cytisus (Scotch broom) ? (Scotch Ingrid Parker (UCSC): Ingrid •Shrub introduced to western USA from British Isles & N. Europe •Fixes nitrogen, changes whole ecosystem •Outcompetes native species •12 m tall shrub •Lives 10+ years 7 STAGES IN LIFE CYCLE In field measured In Seed production rates including success Seed of pollinators of Germination rates from soil seedbank Mortality rates of different age classes Growth rates among classes
USED MATRIX MODELS TO CALCULATE RATE OF INCREASE FOR DIFFERENT POPULATIONS (Compared urban versus wildland populations) Findings: Findings:
1. 2. 3. NO one transition dominated population NO dynamics. She decreased transitions between dynamics She different stages (one by one) and reran models. NO ONE transition would cause big reduction in pop. growth. reduction Population growth (λ) higher in natural prairies higher versus in city. versus City populations were more crowded and City habitat getting filled up. Rate of increase =lower. =lower. Interesting aside…. Interesting Pollinators limit seed set (a low proportion of the plant’s ovules (a get fertilized) get
If there were more, or better pollinators, spread of this species could increase much faster—particularly true in the natural prairies! true To reduce this species…. To Tweeked fecundity for average models… Must reduce seed production and by 99% to reduce population growth !! to Tortoise study: goal Tortoise was to enhance tortoise populations. tortoise Broom study: goal Broom was to control pest population. population. used transition matrix used to see where to increase survival to increase create positive pop. growth growth Used transition matrix Used to identify where to decrease survival or decrease decrease fecundity to decrease broom lambda lambda ...
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 Fall '08
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 Demography, Population Ecology, Matrix modeling

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