1. Cycling and Cycling Indices Ecosystem Ecology 2015 Author: Ana Brodar Menthor: prof. dr. Marko Debeljak University of Nova Gorica Faculty for Environmental Sciences Environment II.

2. Introduction The same material will be repeatedly make useful by different organisms. This phenomenon can be calling “recycling or cycling” of energy and matter. Cycling and cycling indices in ecosystem ecology depending on modeling ecosystem. A general definition of cycles are taken from graph theory and concept of the cycling is applied to: 1. FOOD WEBS (who eats whom in the ecosystem) 2. ECOLOGICAL NETWORKS (weighted and mass balanced version of food webs)

3. Definition of cycle We can describing ecosystem meaning by graphs which are composed by NODES and ARROWS. Nodes representing species or function group of species, Arrows representing relationship between species. For sketching ecosystems we can simply use graphs of the food web representation. Figure 1: Example of food web containing ten species and thirten feeding relation (arrows). Food web representation can be also associated with a matrix that expresses the relationship between species.

4. ADJACENCY MATRIX DIFFERENT KIND OF PATHS: Open paths connect two different nodes (a) (simple paths with no repeated nodes) and compound paths with repeated nodes (b). Closed paths which can start and end at the same nodes, divided into simple cycles with no repeated nodes except the initial one (c) and compound cycles which representing repeated cycles (cycle is traversed twice) (d). Represents direct interations (yield chains of indirect interactions) between species. This can be the sequences of nodes and edges that are called “paths”.

5. Every pathways can be classified according to its length that is given by the numbers of nodes involved.

6. Cycles in food webs Two main classes: 1. Feeding cycles (cannibalism = rare in published food webs) 2. Nonfeeding cycles (extremely abundant in published net works) The number of feeding cycles becomes more significant when age structured populations are considered (aquatic food webs). Figure 2: Generalized aquatic food web. Parasites, among the most diverse species in the food web, are not shown.

7. Structure of Cycles in Ecological Networks: Strongly Connected Components (SCC) Two nodes A and B belong to the same strongly connected component (SCC) - if we can find a path going from A to B and a path coming back from B to A. Example of Baltic Sea ecosystem: One canindividuate 6 SCCs: 4 of them are composed by a single node, while 2 of them comprise more than 1 node (Figure 3b). If we compact every single node, we produce an acyclic graph (Figure 3c). Further analysis shows how one component contains just pelagic species and the other one just benthic species. Acycling graphs are intrinsically hierarchical. With number 1 are label the primary producer (Figure 3c). The same structure was found for other aquatic net works as well. This feature depends on the presence/absence of resuspension of nutrients (the network present several SCCs if this is negligible). When remineralization is strong, the process joins the benthic and pelagic components, thus forming a giant SCC. Figure 3a, 3b and 3c

8. Finn’s Cycling Index (FCI) Simplest one FCI adapted from the one developed in 1980 by J. T. Finn. Ecological networks are food webs where the edges are quantified and represent exchanges of nutrients (usually carbon, but also nitrogen or phosphorous) or energy. Inputs to and outputs from the system are represented by flows involving “special compartments” (nodes that act as a source (imports) or sink (respirations as an exports) for the system). A system can be described using flow matrix T where each coefficient t ij describes the flow of energy – matter from the row compartment (i) to the column compartment (j). If the food web contains no cycles, the matrix will contain just zeros; but if contains cycles, the powers never converge to 0.

9. Figure 4: An example of network and its matrix representation. (a)Shows schematic representation of cone spring ecosystem with two imports (to Plants and Detritus) and with three exports (from Plants, Detritus and Bacteria) and five dashed arrows. (b)The network can be associated with a matrix of transfers (first row represent imports, the last two columns stand for exports and dashed arrows and the internal 5 x 5 part depicts intercompartment flows.

10. Limitations of FCI FCI consider only for paths starting and ending at the same node. FCI accounts for simply cycles and compound cycle but does not consider the contribution of compound paths (they never aprear on the diagonal). Compound paths contain cycles that should be included in the definition of cycling index. Each quantum of matter can be recycled into the same compartment many times (also moved around compound paths many times), that’s mean that Plants, Detritus, Detritus feeders, and Bacteria will not contribute to any diagonal coefficient, even if it contains a cycle.

11. Finding Cycles in Ecological Networks Finding cycles in graphs is a difficult task = published ecosystems contain a few hundred nodes and the low connectance. The number of simple cycles is much lower that the theoretical case illustrated above (all possible cycles are presented). The idea behind most algorithms for cycle search: One should construct a path inside the network until the same node is found twice. Path is either a cycle or a compound path. DFS (“depth first search” = is an algorithm for traversing or searching tree or graph data structures) that means that DFS is possible ways of searching cycles and the easiest to implement.

12. Ecological Applications of Cycle Analysis The recycling of energy – matter is an important process that occurs in every ecosystem. Recycling has been undone in many theoretical models, concentrated on communities. Food web ecologist had an ambivalent attitude toward cycling: First collection of food webs showed that cycle are very rare (destabilizing system) because they introduce positive feedback. Microbial loop in some aquatic ecosystems receive more than 50 % of primary production, remineralizes it and feeds it back to higher trophic levels.

13. Importance of cycling in ecological networks comes from work of Lindenman (1942). He described food webs as cycling material and energy.

14. Some considerations suggest that cycling could be seen as a homeostatic response to stress: impact on ecosystems free nutrients from the higher trophic levels. Ecosystem would show decrease in cycle length and an increase in total cycling (because responding to stress). SCC can be divided into a few subsystems that are connected by linear chains of energy transfer. SCC analysis can also shows a subdivision into pelagic and benethic components of the ecosystem.

15. Conclusion Cycling is an important aspect of ecosystem dynamics. Cycles seem to be rare in published community food webs and models (number is very large when detritus compartments are considered). Cycles is also important to stress that the role of the microbial loop. Large organisms can dramatically change the cycling performance of the system. The network building process is probable to determine the outcome in terms of cycling. Figure 5: Example of shortest paths in a complex food web

16. Questions 1.What depending on cycling and cycling indices in ecosystem ecology and for what is cycling important? 2. What represent adjacency matrix and how can we called the sequences of nodes and edges? 3. What can we use for sketching ecosystem? 4. List two main classes of cycles in food webs. 5. What is ecological network? 6. Who was Lindenman and what he described in 1942?