Final Essay: possible topics Structured PVA 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 Vital rates (Processes that contribute to change in population size) Coral reef resilience and susceptibility due to human interference Birth and death rates The ripple effect: the consequences of biological control Overfishing: without immediate reform the problems of yesterday will be here to stay Growth rate Fecundity Grizzly bear population management and Grizzly bear-human conflict Conservation efforts towards proper medical waste disposal Vital rates often depend on age and size 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). Hydra Plant fecundity depends on size Ln(number of seeds) Survival rate depends on age Plant size
Types of PVA s Structured (demographic) models Age-structured - use data on each age group 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 Building a stage structured model Stage structured - used data on size or stage groups Juveniles > 4 cm < x < 4 cm Understand your species Decide how many stages to include Tadpoles < cm 5 5 75 1 Individuals 1.5 5. 7.5 5. Individuals Building a stage structured model (for loggerhead sea turtles) Building a stage structured model (for loggerhead sea turtles)
How many stages to include? mating near shore foraging Biological Intuition - stages should differ in vital rates from other stages What the data will allow - balance accuracy of more stages with amount of available data open ocean nesting on beaches For turtle PVA we use 5 stages Hatchlings (and eggs): first year : 1-7 years : 8-15 years 16-1 years (mostly non-breeding) Mature adults -55 years, breeding Stage Transition rate
Building a stage structured model Understand your species Decide how many stages to include Gather data Turtle data Marked in year 1 1 1 1 1 1 Recaptured in same class 7 657 68 89 Recaptured in next larger class 675 47 19 61 - Eggs/female/year 4.665 61.896 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 Mature adults
Turtle data Mature adults Marked in year 1 1 1 1 1 1 Recaptured in same class Recaptured in next larger class 7 657 68 89 675 47 19 61 - Eggs/female/year 4.665 61.896.675 Turtle data Mature adults Marked in year 1 1 1 1 1 1.675 Recaptured in same class Recaptured in next larger class 7 657 68 89 675 47 19 61 - Eggs/female/year 4.665 61.896.657.7.7.47.19.68.675 4.665.61 61.896.89.7
Building a stage structured model Population (Projection) matrix Understand your species Decide how many stages to include Gather data Calculate transition rates The projection matrix is the summary of all transition probabilities (all vital rates) Make model Population (Projection) matrix F i S i G i Number of new turtles (size class 1) produces by an average individual of size i per year Fraction of size i turtles surviving and STAYING in the same size class per year Fraction of size i turtles surviving and GROWING to size class i+1 per year F i S i A generic projection matrix Size next year new surviving G advancing i 1 4 5 1 S 1 F F F 4 F 5 G 1 S G S 4 G S 4 5 G 4 S 5 Population (Projection) matrix F i S i G i Number of new turtles (size class 1) produces by an average individual of size i per year Fraction of size i turtles surviving and STAYING in the same size class per year Fraction of size i turtles surviving and GROWING to size class i+1 per year Size next year Projection matrix for loggerhead sea turtles 1 4 5 1 4.665 61.896.675.7.47.657 4.19.68 5.61.891 Note that since S and G are fractions surviving. They are between and 1.
.657 recall count based method.7.47.19.68 N t = λn t 1.675 4.665.61 61.896.89.7 Structured model N t = P N t 1 Stage distribution vector a column showing the number (or density) of individuals in each stage.85 64.78 1..7.1 1. Total density Stable stage (or age or size) distribution 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: 1% of individuals in stage 1 is not stable the next year there will be individuals in other stages distribution of individuals among stages that won t change over time (if population size changes at a constant rate) Example: 1% of individuals in stage 1 is not stable the next year there will be individuals in other stages Stage distribution will converge to the stable stage distribution over time
N t = P N t 1 N t P N t 1 4.665 61.896.85? =.675.7 64.78.47.657 1..19.68.7.61.891.1 Use matrix algebra... N t P N t 1.59 4.665 61.896.85 61.64 9.8.69 =.675.7 64.78.47.657 1..19.68.7..61.891.1 # Eggs Juveniles Time Same graph as last slide, but changing scale on y-axis # Eggs Juveniles Freq Stable stage distribution Eggs Juveniles Time Time
N t P N t 1.59 4.665 61.896.85 61.64 9.8.69 =.675.7 64.78.47.657 1..19.68.7..61.891.1 Recall that: λ = N t N t 1 How do we know if population is growing or shrinking? N t P N t 1.59 4.665 61.896.85 61.64 9.8.69 =.675.7 64.78.47.657 1..19.68.7..61.891.1 lambda 95.5 1. 95.5/1 =.955 =! Time! again In a count based model N t = λn t 1 In a structured model! again In a count based model N t = λn t 1 In a structured model N t = P N t 1 P is playing the same role as the count based!. N t = P N t 1 P is playing the same role as the count based!. The information in P can be summarized by a matrix! (dominant eigenvalue)
In structured models, change in N is still called! but can be In structured models, change in N is still called! but can be N t /N t 1 Summarize the information P as a single number, the dominant eigenvalue!. N t /N t 1 This only will be constant if the population is at the stable stage distribution, variable until then Summarize the information P as a single number, the dominant eigenvalue!. In structured models, change in N is still called! but can be Using the turtle model for PVA N t /N t 1 This only will be constant if the population is at the stable stage distribution, variable until then Summarize the information P as a single number, the dominant eigenvalue!. This! will be constant as long as P doesn t change AX = λx Sources of turtle mortality: Beaches (nestlings) Ocean (, subadults, adults) eigenvalues (right) eigenvector Predation of eggs by racoons, dogs, and lizards, among others Beach lights affects hatchlings Hatchlings emerging at night (fish, crabs) Hatchlings emerging at day (sea birds)
Threats to and adults Using the turtle model for PVA Sources of turtle mortality: Beaches (nestlings) Ocean (, subadults, adults) Status: population is declining (!=.951) Decline of loggerhead turtle Using the PVA Total density of loggerhead 9 8 7 6 5 Can we stop this decline of loggerhead turtle populations? What if we protect all turtles on the beach? 5 1 15 Years What element would protecting nestlings on the beach change? What element would protecting nestlings on the beach change? Size next year 1 4 5 1 4.665 61.896.675.7.47.657 4.19.68 5.61.891 Size next year 1 4 5 1 4.665 61.896.675 1..7.47.657 4.19.68 5.61.891
Using the turtle model for PVA Decline of loggerhead turtles What if we protect turtles on the beach Change nestling survival to 1% (so G1=1) and turns to!=.974 Total density of loggerhead 1 Protected beach 9 8 7 6 5 No protection 5 1 15 Years Using the turtle model for PVA Turtle excluder device (TED) What if we protect turtles on the beach? Change nestling survival to 1% (so G1=1) and turns to!=.974 What happens if we protect larger turtles in the ocean? What element change would protecting large? 1 1 Size.675 next year 4 5 4 5 4.665 61.896.7.47.657.19.68.61.891
What element change would protecting large? What element change would protecting large? Size next year 1 4 5 1 4.665 61.896.675.7.47.657 5% 4.19.68 5% 5.61.891 Size next year 1 4 5 1 4.665 61.896.675.7.47.657.81 4.19.4.68 5.61.891 Using the turtle model for PVA INCREASE of loggerhead turtles What if we protect turtles on the beach? Change nestling survival to 1% (so G 1 =1) and the growth rate!=.974 What happens if we protect larger turtles in the ocean? Change mortality of large juvenile mortality by 5% and the growth rate!=1.6 Total density of loggerhead 16 14 1 1 8 6 TED and beach Protected beach No protection 5 1 15 Years