The goal of this assignment is to learn to ask good questions in conducting ecological research and get experience in integrating field and other information to create a food web model to answer an ecological question. In other words, you will be conducting a study framed by your observations, research, and loop model results to answer your ‘best question’. This assignment is to be done individually.
Appendices – your 20 questions, community matrix, community effects matrix, network measures that I provide you from your community matrix
Appendix A
Instructions for Community Matrix Calculations – BIOL 3061 (prepared by Amelié Paulin). Send your Community Matrix to me (Chris) by November 5th so I can process it through the loop program and send you back the results.
Predator 
Prey 
For this assignment, you will be drawing your own loop diagram. It is essentially a graphical representation of the network of the community you chose. Each loop variable comprises a node, and the links between each loop variable are edges. In a loop diagram, an edge has one of two values (+1 or 1) depending on the nature of the interaction between two variables. In a standard predatorprey relationship, one would expect the predator to receive a gain from the prey. In this case, the link from prey to predator would be positive. Conversely, the prey suffers a loss by being eaten by the predator. Thus, the link from predator to prey is negative. To represent this graphically, we would draw our two loop variables (the predator and the prey) as two distinct nodes in our network graph like so:
Prey 
Predator 
Then we would draw the links between them. In a loop diagram, positive links are drawn as a standard arrow, from the variable creating the effect to the variable being affected. The prey has a positive effect on the predator, therefore:
Prey 
Predator 
Negative links are drawn as an arrow as well, but instead of an arrowhead, they are represented with a circlehead. The predator has a negative effect on the prey, therefore:
Prey 
Predator 
Now we want to represent the complete relationship between predator and prey at once. We could draw each link separately, but loop diagrams conventionally have such twoway links drawn as one line with both rrow and circleheads drawn at either end as follows. But remember that even though only one line is showing, the presence of both arrow and circleheads indicates that this is a twoway relationship.
Prey 
Predator 
Loop variables can sometimes not only have effects on other variables, but can have effects on themselves. In such cases, positive effect is deemed selfenhancing (very rare) and a negative effect is deemed selfdampening (more common). In a loop diagram, these are demonstrated as a curved line starting from the loop variable and coming back to itself with either an arrowhead (for selfenhancing) or a circlehead (for selfdampening) at its end. If our prey variable were selfdamped, it would look as such:
Now our diagram is showing two loop variables/nodes (prey and predator) and three links/edges: the positive effect of prey on predator, the negative effect of predator on prey, and the negative effect of the prey on itself.
Now we want to take our loop diagram and convert it into a community matrix. The community matrix contains the same information as the loop diagram, but is in a format that can be easily read by computers for further analyses. So, how do we make a community matrix? A community matrix is a square matrix with N rows and N columns, where N corresponds to the number of loop variables/nodes in your loop diagram. For our simple loop diagram above, our community matrix would be laid out as such:

Prey 
Predator 
Prey 
α_{1,1} = α_{prey, prey} 
α_{1,2} = α_{prey, predator} 
Predator 
α_{2,1 }= α_{predator, prey} 
α_{2,2} = α_{predator, predator} 
The shaded cells are going to contain the values of all the relationships in our loop diagram (denoted by α). The numbers in subscript denote the row and column number (in that order). For example, row 1 column 2 is indicated by: 1,2. But how does this translate to our loop diagram? To read a community matrix, you start from the column name and then across to its row name and read as: the effect of (column name) on (row name). Essentially, you read α_{1,2} or α_{prey, predator }in reverse: the effect of the predator on the prey. You can see below what each shaded cell corresponds to by following the arrows.
The effect of prey on prey:

Prey 
Predator 
Prey 


Predator 


The effect of predator on prey:

Prey 
Predator 
Prey 


Predator 


The effect of prey on predator:

Prey 
Predator 
Prey 


Predator 


The effect of predator on predator:

Prey 
Predator 
Prey 


Predator 


Then it’s only a matter of looking back to your loop diagram and finding the values behind these effects. The effect of prey on prey, as shown by the line with a circlehead connecting the prey back to itself, is negative so you will fill the appropriate square with the value 1. The effect of predator on prey, as shown by the line with a circlehead going from predator to prey, is negative so you will fill the appropriate matrix square with the value 1. The effect of prey on predator, as shown by the line with an arrowhead going from prey to predator, is positive so you will fill the appropriate matrix square with the value 1. The effect of predator on predator… Oh wait, there isn’t one. In cases where no relationship exists, you will simply fill in the appropriate matrix square with the value 0. So our final completed table will look like this:

Prey 
Predator 
Prey 
1 
1 
Predator 
1 
0 
Now you try! Exercises from ABC’s of loop modelling?
You will be handing this community matrix in, so make sure all values are entered correctly! Further analyses will be performed based on the community matrix. These include the community effects matrix, stability measures, connectivity, connectance, and number and levels of pathways, feedback loops, and other network motifs.
You will be handing in the community matrix using a .csv format. To do this, you open up Excel as normal and input your community matrix. Be sure to keep both your row names and column names as done above. It should look like this:
Now you try! Exercises from ABC’s of loop modelling?
You will be handing this community matrix in, so make sure all values are entered correctly! Further analyses will be performed based on the community matrix. These include the community effects matrix, stability measures, connectivity, connectance, and number and levels of pathways, feedback loops, and other network motifs.
You will be handing in the community matrix using a .csv format. To do this, you open up Excel as normal and input your community matrix. Be sure to keep both your row names and column names as done above. It should look like this:
Then you click File, Save As, and save as the Comma Delimited (.csv) format as below.
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