Reference no: EM133019734
1. Characteristics of single population
Open RAMAS Metapop, and then the file 'Betts_single_pop.mp'
(a) Vary reproductive rate (r) (0.7, 1.0, 1.2), holding population size at 100 and environmental stochasticity at 0.5. Do this by going to the 'Model' tab > Stage Matrix and typing new values into the "Fecundity coeff' and "Survival coef boxes (ensure that the same value is in the "Stage I" box). Environmental stochasticity is set in the Standard Deviation Matrix tab. To run a model go to Simulation > Run. Results are found in Results> Metapopulation Occupancy or Time to Extinction. Click on the Text tab for exact values. What is the effect of r on `metapopulation occupancy' and median time to extinction? (Show this in a table). Why is this?
(b) Vary population size (5, 10, 50, 100), holding rat 1.0 and stochasticity at 0.5. You can vary population size by choosing Model > Populations and changing the Initial Abundance dialogue box. What is the effect of initial population size on `metapopulation occupancy' the cumulative probability of extinction (i.e., the value at 30 years in the Time to Quasi-Extinction result)? (Plot the results). Give an explanation for the pattern you see.
(c) Vary stochasticity (environmental) (0, 0.2, 0.5, 1.0), holding rat 1.0 and population size at 10. Again, change environmental stochasticity by altering the value in Model > Standard Deviation Matrix. What is the effect of initial population size on cumulative probability of extinction and metapopulation occupancy? (Show this in a table). Explain.
(d) Holding all other parameters constant (r=1.0, SDO.5, population size = 10), try models with and without demographic stochasticity. You can do this by choosing Model > Stochasticity and clicking on the 'Use demographic stochasticity' dialogue box. How do `metapopulation occupancy' and median time to extinction vary in relation to demographic stochasticity? Explain the variation between these two scenarios.
2. Multiple populations and risk of metapopulation extinction
Try a model with two, three, four and 10 populations with identical size and properties (pop. size (n) = 10, r=1.0, SDO=0.8, demographic stochasticity) with no dispersal. You can add new populations to the model above by going to Model > Populations, and clicking on the `Add' button in the bottom left of the dialogue box. Then add x and y coordinates for each (e.g., x=1, y=0; y=1, x=0; x=1, y=1; x=0, y=0) along with an initial abundance (14=10). For each of these, record: cumulative probability of extinction and metapopulation occupancy in the last time-step. Plot these results with number of populations on the x-axis and (1) cumulative probability of extinction and (2) metapopulation occupancy on the y-axis. Describe what you observe and provide a simple explanation.
3. Dispersal/ isolation effects
(a) With the four-population model and the base population parameter values from 1, link populations through dispersal at the following rates: 0, 0.01, 0.05, 0.1. Dispersal parameters are altered by clicking on the Model' tab > 'Dispersal% Type the values above into each cell of the matrix. Tabulate extinction risk (cumulative probability of extinction) at 30 years. Plot these results with dispersal rate on the x-axis and cumulative probability of extinction and metapopulation occupancy on the y-axis.
What ecological reason is there for the pattern you see?
(b) Model dispersal (m) according to the function (1): m = a.exp(-Dt/b)
Where a = 0.32, b=0.2. c=1, D=2 (a and c are constants, b and D are the average and maximum dispersal distances respectively)
Using RAMAS, plot this dispersal function. What ecological reasons are there for this shape?
(c) Using the dispersal matrix, isolate one of the four populations but hold the dispersal rate among the other populations constant (m=0.1) (hint: make sure you make all linkages to population 2 zero) (i) What is the cumulative probability of extinction at 30 years? Why did it change from 3a? (ii) What is the comparative persistence (local occupancy) of the isolated patch in relation to the connected patches? Why?
(d) Hypothesize about whether multiple populations within a metapopulation proportionately more beneficial for metapopulation population persistence in the connected or unconnected scenarios? (hint: you could try a model where you independently vary number of populations versus dispersal among populations).
4. Population correlations (synchrony)
With the four same-sized population model, n=10 m=0.2, vary population synchrony (correlation) according to four scenarios: 0, 0.5, 0.7, 0.9 correlation. You can do this by going to Model>Correlation and altering the values in the matrix as you did for dispersal. Plot the relationship between extinction risk (cumulative extinction risk; y-axis) and correlation (x-axis). Plot the relationship between metapopulation occupancy (y-axis) and correlation (x-axis) (this can be on the same graph). (a) Provide an explanation for what you observe. (b) Is the 90% correlation scenario a metapopulation?
5. How would you incorporate the effects of the matrix into a metapopulation model?
6. Define 'metapopulation'. Give examples of species/ systems where meta-population models apply and explain why. Are metapopulations common or a rare and special case?
7. Design a simple virtual study to address the effects of habitat loss versus fragmentation. Show results for metapopulation occupancy and cumulative probability of extinction.