Markovian Properties of Forest Succession

Transcription

1 Markovian Properties of Forest Succession What to bring to lab: We will be going outside so be sure to wear warm clothes and boots. Also bring a pencil so you can write even if it s cold. Be sure to bring this lab manual and a calculator with you too. Background: Introduction: Succession in ecology can be broadly defined as the progression and changes in species composition a community undergoes over time. Often this follows a disturbance of some kind whether it is a natural disturbance such as a fire or a hurricane, or an anthropogenic disturbance such as clearing land for agriculture. Following the disturbance there is natural, predictable series of steps the community goes through beginning with a pioneer community and ending in a climax community. A pioneer community consists of the organisms that are able to tolerate the harshest conditions. There are two different types of succession that can be differentiated by knowing the initial conditions. The first is primary succession. This type of succession occurs on sites that initially lack any living organisms. Secondary succession occurs after a disturbance in which some organisms survive. Although both types of succession refer to all organisms, one of the most commonly studied types of succession is plant succession and even more specifically forest succession. One feature of forest succession is that there are often characteristic associations of species that can be recognized throughout a given region. Moreover, sites that start out with very different plant communities often converge on the same end state or climax community. If undisturbed, these "climax communities" are apparently stable for an indefinite period of time. There has been much debate over the mechanisms of forest succession and the existence of climax communities in general. In the 1920s Frederick Clemens described climax communities as a sort of "super-organism" with set patterns of development. Others, notably Henry Gleason, favored the idea that each species responded independently to environmental variation and that there was no stereotypical climax community. The debate continues today, although most people recognize that both sides contain some elements of the truth. We will use a simple mathematical model of forest succession to predict the future composition of a patch of forest and compare that with the species composition of an older portion of the Centennial Woods. We will examine forest succession as a tree-by-tree

2 replacement process. For each tree in the forest, we will estimate the probability that it will be replaced by another of its kind or by another species. From a matrix of these probabilities, we can calculate how many trees of each species should be found at any stage of succession. Simplified example: We go into the forest and find 20 canopy trees. We find 80 saplings under these trees, all within 10m of the canopy tree. Raw data: Saplings Canopy species A B C D Total This means that we found 6 saplings of species A under the species A canopy trees; 10 B saplings under the A canopy trees; etc. Assuming that the relative abundance of each sapling species under each canopy species is the predictor of that particular sapling species replacing the canopy species (when it dies), then we calculate the percent of each sapling species represented under each canopy species. Saplings Canopy trees A 25% B C D Interpretation: 25% of the saplings under canopy species A are species A (6/24); 43% of the saplings under species B are species A (12/28), etc.. Using this transition matrix (the probability that a particular sapling species will replace a canopy species), we can predict what the forest composition will be in the next generation (remember, we assume that all trees are replaced synchronously, i.e. all canopy species die at the same time). For example, we can calculate the number of B species in the next "generation" by finding all species in the current canopy that have some B saplings in their understory (namely all 4 canopy species in our example) and summing their current abundances times the probability that each will be replaced by B. From the table above, "B" (next generation) =.42A +.53B +.50C +.56D This should make intuitive sense: since 42% of the sapling species under canopy species A are species B, there is a 42% chance that B will replace A when A dies.

3 Similarly, "A" (next generation) =.25A +.43B +.19D. And you can do the same for predicting the abundances of C and D in the next generation. So, what we need now is the present abundances of A, B, C, and D as canopy trees. If we collected the data correctly, we can just count how many of each canopy species we censused. For now, we'll say there were 3 A species, 8 B, 5 C, and 4 D species. The relative abundances of the canopy trees are: A=3/20=.15; B=8/20=.40; C=5/20=.25; D=4/20=.20. We plug these numbers into the above equations to predict the relative abundances of the 4 species in the next generation (i.e. assume that all canopy trees died simultaneously). "A" (next generation) =.25(.15) +.43(.40) +.19(.20) =.25 "B" (next generation) =.42(.15) +.53(.40) +.50(.25) +.56(.20) =.51 "C" (next generation) =.125(.15) +.06(.20) =.03 "D" (next generation) =.21(.15) +.04(.40) +.50(.25) +.19(.20) =.21 We can then use the same transition matrix and these new relative abundances to calculate the abundances of the species in the second generation. Below is a table with predictions of forest composition for generations 0-3. Canopy species generation As you can see, through progressive generations, the forest composition is converging on one dominated by species B, with species C becoming rare. This makes sense because, from the transition matrix we can see that species C is rare in the understory and therefore, it is poor at replacing dying canopy trees. If you know linear algebra... This model of succession can be described very simply in matrix notation. Call the matrix of transition probabilities P and the column vector of species abundances N. The recursion equation becomes N1 = P N0. Similarly, N2 = P N1 which is equal to N2 = P P N0. Using this logic, the forest composition t generations in the future can be predicted by knowing merely the initial composition and the transition probabilities: Nt = P t N0. From this it can be shown that the final stable species composition is the eigenvector of P and is independent of the starting forest composition. Assumptions of the model: 1) All trees are replaced synchronously by a new generation that arises from their understory. 2) The probability that a given species will be replaced by another given species is proportional to the number of saplings of the latter in the understory of the former.

4 3) Succession has "no memory", in other words the transition probabilities depend only on the present composition of the forest and not on events that occurred previously. 4) There is no spatial dependence, so the transitions are independent of the species of neighboring trees. Clearly, there are exceptions to most of these assumptions, but we will try to see whether this simple model can capture some of the major features of forest succession. Shortcomings of this model may help identify key biological processes that should not be ignored. *************************************************** The data we will collect in Centennial Woods are as follows: In each of two forest stands, randomly choose a canopy tree and identify it using the key. (Look up and locate the tallest tree directly above you, call that the canopy dominant). Place a tick mark next to the canopy species on the data sheet- - this information will be used to determine the current composition of the forest canopy. Identify all saplings within 5 m of the canopy tree. Using the string 5m long, circumscribe a circle around the trunk of the canopy tree (have one person stand at the trunk with one end of the string, one person walks around the tree at the length of the string, and one person identifies all the saplings within that circle (with the help of the other two people). Enter these numbers on one line on the data sheet, under the appropriate canopy species. Repeat repeatedly.

5 Sub-Canopy Tree Species Succession Data Sheet: Canopy Tree Species White Pine Red Sugar Yellow Paper Hemlock White Pine Red Sugar Yellow Paper Hemlock Beech Oak Beech Oak TOTALS