SAILA and PARRISH: EXPLOITATION EFFECTS 



Figure 7. — An illustration of the effect of predation (as 

 measured by biomass ratios) on competition as mea- 

 sured by changes in the ratio of the resource accessibility 

 coefficient d for the two species. 



The results shown in Figure 7 clearly indicate 

 that some of the competitive coefficients have a 

 very large influence on the relative stability of 

 interacting systems. They suggest that if the 

 stress of exploitation or other environmental 

 stresses interact with other model coefficients as, 

 for example, in a simple predator-prey interac- 

 tion, the system may respond very violently, with 

 the rapid extinction of one or the other of the 

 competing species. 



In some instances it may be desirable to have 

 some rough empirical measure of the stability of 

 exploited ecosystems consisting of interacting 

 species. As Margalef (1969) has indicated, an 

 adequate measure of community stability must 

 include a measure of diversity as well as a mea- 

 sure of persistence. Furthermore, Margalef at- 

 tempted to formulate a generalized mathematical 

 model for their interdependence. It is suggested 

 that an additional application of graph theory 

 may also be utilized to provide some en\pirical 

 indication of stability and persistence of com- 

 munities subjected to either environmental or 

 exploitive stresses, assuming certain types of 

 background information are available. 



Consider the following hypothetical example. 

 Three communities of fishes (A, B, C) are sub- 

 jected to various levels of exploitation. Assume 



that some crude index of diversity or community 

 structure has been established which permits 

 identification of the three communities as mu- 

 tually exclusive groups. Assume that the three 

 communities are sampled again during the 

 course of a year, and that the frequency of sam- 

 ples which resemble the previously defined com- 

 munity as well as the frequency of samples which 

 resemble the other two communities are listed. 

 These frequencies can be displayed in the form 

 of a network as shown in Figure 8. The data 



50 



200 



100 



M: 



M' 



Po= [■ 



50 200 100 



G 



•] 



68.50 111.25 170.25 



G 



Figure 8. — Example of a hypothetical network showing 

 the frequencies of samples resembling their initial struc- 

 ture as well as those of the other two community struc- 

 tures. In this example Fg is the matrix of frequencies 

 at the end of the first sampling period, M is the cor- 

 responding probability matrix, M^ is the square of the 

 probability matrix and Pg is the vector of frequencies 

 by community type. P^M^ is the matrix-vector product 

 expressing the expected new frequencies by community 

 type at the end of the second sampling period under the 

 assumption that the probability matrix remains constant 

 during the time interval. 



391 



