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Loggerhead Sea Turtle Demography

Loggerhead turtles (Caretta caretta) spend their lives in the ocean, but females come ashore to lay eggs on sandy beaches. After the eggs hatch, hatchlings make their way to the ocean.

Tonight we will explore the demography of loggerhead turtles. We will explore a stage-based model in which turtles are classified as hatchlings, small juveniles, large juveniles, sub-adults, and adults. The first row of the matrix gives the fertilities F(i) of each stage class. Recall from Ecology that F(i)=b(i)P_i where P_i is the probability of becoming or surviving as an adult and b(i) is the fecundity of a stage. The fecundity in this case is the probability of nesting x the number of eggs laid x the survivorship of eggs to hatching.

Download the spreadsheet seaturtle-551.xls. The transition matrix is given in cells C6-G10, and the initial population vector is given in cells I6-I10. The values for the initial population vector are also given in C14-G14 (this will make graphing easier).

1. Draw a transition diagram for loggerhead turtles. Label all the transition arrows with their appropriate values.
2. What is b(sub-adult)? What is b(adult)?

We will project the population for 75 years into the future. Recall from Ecology the mechanics of matrix multiplication; C15 gives you an example of the calculation necessary. Enter the appropriate formulae in cells D15-G15. Copy the formula for λ (the ratio N_t+1 / N_t) from cell H14 to H15. Once C15-H15 are complete, you can copy the cells down to row 89 to complete the population projection.

Make a graph of number of individuals in each stage vs. year (there will be 5 lines on the graph) using a semi-log scale (y-axis should be logarithmic, x-axis should be regular). Where the lines become parallel, the stable stage distribution has been reached; even though the number of individuals is changing each time unit, the proportion in each stage is not. λ will also stabilize at this point at its asymptotic value.

3. Which stage is most abundant once the stable stage distribution is reached?
4. What is the asymptotic value of λ? Is the population increasing, decreasing, or stable?
5. Change the initial population vector in I6-I 10. Does the initial population vector affect the asymptotic value of λ?

6. A major source of mortality for larger turtles in drowning in shrimp trawls. Turtle exclusion devises (TEDs) reduce the by-catch of turtles. Use the transition matrix expected if TEDs are widely used (from the transition matrices sheet) and determine the asymptotic value of λ. With TEDs, is the population increasing, decreasing, or stable?
7. Another strategy for sea turtle conservation is protecting egg-laying beaches by curbing or eliminating human access to beaches from egg-laying until hatchlings go to sea. Which values in the transition matrix would change with this strategy? By how much would they have to change to have the same effect on λ as TEDs?
8. Also used is head-starting turtles-- collecting eggs, raising turtles until their shells are about 30-cm diameter, and releasing them into the ocean. Which values in the transition matrix would change with this strategy? By how much would they have to change to have the same effect on λ as TEDs?