SLIDE 1 Structured PVA
Final Essay: possible topics
Historical essay: for example history of protection of Everglades Concern: Run-off of oil-products from streets/roads Management plan: how to manage the Wakulla river Protection of an endangered species
Each essay needs at least 5 citations from the peer-reviewed literature (no websites!). The essay will use these citations to show facts, etc. In the reference list, these 5 used papers need to have a short summary of the paper (about half a page).
Example titles from last semester
Coral reef resilience and susceptibility due to human interference The ripple effect: the consequences of biological control Overfishing: without immediate reform the problems of yesterday will be here to stay Grizzly bear population management and Grizzly bear-human conflict Conservation efforts towards proper medical waste disposal Endangered species protection and HIV research Each essay needs at least 5 citations from the peer-reviewed literature (no websites!). The essay will use these citations to show facts, etc. In the reference list, these 5 used papers need to have a short summary of the paper (about half a page). Birth and death rates Growth rate Fecundity
Vital rates
(Processes that contribute to change in population size)
Vital rates often depend on age and size
Survival rate depends on age
Hydra
Plant fecundity depends on size
Ln(number of seeds) Plant size
SLIDE 2 Types of PVA’s
Count based: simple -- all individuals are the same (age, size, etc.) Structured (demographic): different vital rates for different classes of individuals
Structured (demographic) models
Age-structured - use data on each age group
Structured (demographic) models
Age-structured - use data on each age group Stage structured - used data on size or stage groups
Tadpoles Juveniles Adults 25 50 75 100
Individuals
< 20 cm 20 < x < 40 cm > 40 cm 12.5 25.0 37.5 50.0
Individuals
Building a stage structured model
Understand your species Decide how many stages to include
Building a stage structured model (for loggerhead sea turtles)
Building a stage structured model (for loggerhead sea turtles)
SLIDE 3 nesting on beaches mating near shore foraging
How many stages to include?
Biological Intuition - stages should differ in vital rates from
What the data will allow - balance accuracy of more stages with amount of available data
For turtle PVA we use 5 stages
Hatchlings (and eggs): first year Small juveniles: 1-7 years Large juveniles: 8-15 years Subadults 16-21 years (mostly non-breeding) Mature adults 22-55 years, breeding
Nestlings Small juveniles
Life-cycle diagram
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
Stage Transition rate
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
SLIDE 4 Building a stage structured model
Understand your species Decide how many stages to include Gather data Nestlings Small juveniles Large juveniles Subadults Mature adults Marked in year 1 1000 1000 1000 1000 1000 Recaptured in same class 703 657 682 809 Recaptured in next larger class 675 47 19 61
4.665 61.896
Turtle data
Building a stage structured model
Understand your species Decide how many stages to include Gather data Calculate transition rates Fractions surviving but not growing Fractions surviving and growing Number of female offspring per year and female
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
SLIDE 5 Nestlings Small juveniles Large juveniles Subadults Mature adults Marked in year 1 1000 1000 1000 1000 1000 Recaptured in same class 703 657 682 809 Recaptured in next larger class 675 47 19 61
4.665 61.896
Turtle data
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
0.675
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
0.675
Nestlings Small juveniles Large juveniles Subadults Mature adults Marked in year 1 1000 1000 1000 1000 1000 Recaptured in same class 703 657 682 809 Recaptured in next larger class 675 47 19 61
4.665 61.896
Turtle data
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
0.703
Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
0.703 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.809 4.665 61.896
SLIDE 6
Building a stage structured model
Understand your species Decide how many stages to include Gather data Calculate transition rates Make model
Population (Projection) matrix
The projection matrix is the summary of all transition probabilities (all vital rates)
Fi
Number of new turtles (size class 1) produces by an average individual of size i per year
Si
Fraction of size i turtles surviving and STAYING in the same size class per year
Gi
Fraction of size i turtles surviving and GROWING to size class i+1 per year
Population (Projection) matrix A generic projection matrix
S1 F2 F3 F4 F5 G1 S2 G2 S3 G3 S4 G4 S5
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
Fi new Si surviving Gi advancing Fi
Number of new turtles (size class 1) produces by an average individual of size i per year
Si
Fraction of size i turtles surviving and STAYING in the same size class per year
Gi
Fraction of size i turtles surviving and GROWING to size class i+1 per year
Population (Projection) matrix
Note that since S and G are fractions surviving. They are between 0 and 1.
Projection matrix for loggerhead sea turtles
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091
SLIDE 7 Nestlings Small juveniles Large juveniles Subadults Adults
Life-cycle diagram
0.703 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.809 4.665 61.896
recall count based method
Nt = λNt−1
Structured model
Nt = PNt−1
Stage distribution vector
a column showing the number (or density)
- f individuals in each stage
23.85 64.78 10.33 0.73 0.31 Nestlings Small juveniles Large juveniles Subadults Adults
100.00 Total density
Stable stage (or age or size) distribution
distribution of individuals among stages that won’t change over time (if population size changes at a constant rate) Example: 100% of individuals in stage 1 is not stable – the next year there will be individuals in
Stable stage (or age or size) distribution
distribution of individuals among stages that won’t change over time (if population size changes at a constant rate) Example: 100% of individuals in stage 1 is not stable – the next year there will be individuals in
Stage distribution will converge to the stable stage distribution over time
SLIDE 8 Nt = PNt−1
? = 4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091 23.85 64.78 10.33 0.73 0.31
Nt P Nt−1
Use matrix algebra.....
Nt P Nt−1
22.59 61.64 9.83 0.69 0.30 = 4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091 23.85 64.78 10.33 0.73 0.31
Time # Eggs Juveniles Large juveniles Subadults Adults Eggs Juveniles Large juveniles Subadults Adults Same graph as last slide, but changing scale on y-axis Time # Eggs Juveniles Large juveniles Subadults Adults Stable stage distribution Time Freq
SLIDE 9 Nt P Nt−1
How do we know if population is growing or shrinking?
22.59 61.64 9.83 0.69 0.30 = 4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091 23.85 64.78 10.33 0.73 0.31
Recall that:
λ = Nt Nt−1 Nt P Nt−1
22.59 61.64 9.83 0.69 0.30 = 4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091 23.85 64.78 10.33 0.73 0.31
95.05 100.0 95.05/100 = 0.9505 = Time lambda again
Nt = λNt−1 Nt = PNt−1
In a count based model In a structured model P is playing the same role as the count based . again
Nt = λNt−1 Nt = PNt−1
In a count based model In a structured model P is playing the same role as the count based . The information in P can be summarized by a matrix (dominant eigenvalue)
SLIDE 10
In structured models, change in N is still called but can be
Summarize the information P as a single number, the dominant eigenvalue .
Nt/Nt−1
In structured models, change in N is still called but can be
Summarize the information P as a single number, the dominant eigenvalue .
Nt/Nt−1
This only will be constant if the population is at the stable stage distribution, variable until then
In structured models, change in N is still called but can be
Summarize the information P as a single number, the dominant eigenvalue .
Nt/Nt−1
This only will be constant if the population is at the stable stage distribution, variable until then This will be constant as long as P doesn’t change
AX = λX
(right) eigenvector eigenvalues
Using the turtle model for PVA
Beaches (nestlings) Ocean (juveniles, subadults, adults)
Sources of turtle mortality:
Predation of eggs by racoons, dogs, and lizards, among others Hatchlings emerging at night (fish, crabs) Hatchlings emerging at day (sea birds)
Beach lights affects hatchlings
SLIDE 11 Threats to juveniles and adults Using the turtle model for PVA
Beaches (nestlings) Ocean (juveniles, subadults, adults)
Sources of turtle mortality: Status: population is declining (=0.951)
Decline of loggerhead turtle
5 10 15 20 50 60 70 80 90
Years Total density of loggerhead
Using the PVA
Can we stop this decline of loggerhead turtle populations? What if we protect all turtles on the beach?
What element would protecting nestlings
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091 What element would protecting nestlings
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091
1.00
SLIDE 12
Using the turtle model for PVA
What if we protect turtles on the beach Change nestling survival to 100% (so G1=1) and turns to =0.974
5 10 15 20 50 60 70 80 90 100
Decline of loggerhead turtles
Years Total density of loggerhead Protected beach No protection
Using the turtle model for PVA
What if we protect turtles on the beach? Change nestling survival to 100% (so G1=1) and turns to =0.974 What happens if we protect larger turtles in the ocean?
Turtle excluder device (TED)
What element change would protecting large juveniles ?
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091
SLIDE 13
What element change would protecting large juveniles ?
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091
25% 25%
What element change would protecting large juveniles ?
Size this year 1 2 3 4 5 1 2 3 4 5 Size next year
4.665 61.896 0.675 0.703 0.047 0.657 0.019 0.682 0.061 0.8091
0.821 0.024
Using the turtle model for PVA
What if we protect turtles on the beach? Change nestling survival to 100% (so G1=1) and the growth rate =0.974 What happens if we protect larger turtles in the ocean? Change mortality of large juvenile mortality by 25% and the growth rate =1.006
INCREASE of loggerhead turtles
Years Total density of loggerhead Protected beach No protection
5 10 15 20 60 80 100 120 140 160
TED and beach
