A multiple-loop model of an urban ecological system might include the following variables: number of people in the city $(P)$, modernization $(M)$, migration into the city $(C)$, sanitation facilities $(S)$, number of diseases $(D)$, bacteria/area $(B)$, and amount of garbage/area $(G)$, where the symbol for the variable is given in parentheses. The following causal loops are hypothesized:
1. $P \rightarrow G \rightarrow B \rightarrow D \rightarrow P$
2. $P \rightarrow M \rightarrow C \rightarrow P$
3. $P \rightarrow M \rightarrow S \rightarrow D \rightarrow P$
4. $P \rightarrow M \rightarrow S \rightarrow B \rightarrow D \rightarrow P$
Sketch a signal-flow graph for these causal relationships, using appropriate gain symbols. Indicate whether you believe each gain transmission is positive or negative. For example, the causal link $S$ to $B$ is negative because improved sanitation facilities lead to reduced bacteria/area. Which of the four loops are positive feedback loops and which are negative feedback loops?