The speed of extinction for some generalized Jiřina processes {Xn} is discussed. We first discuss the geometric speed. Under some mild conditions, the results reveal that the sequence {cn}, where c does not equal the pseudo-drift parameter at x = 0, cannot estimate the speed of extinction accurately. Then the general case is studied. We determine a group of sufficient conditions such that Xn/cn, with a suitable constant cn, converges almost surely as n → ∞ to a proper, nondegenerate random variable. The main tools used in this paper are exponent martingales and stochastic growth models.

Benthic macroinvertebrates collected at seven different streams displaying different pollution levels were used to investigatespecies abundance patterns in polluted streams. Community response to disturbances in streams was analysed using speciesabundance distribution (SAD) for benthic macroinvertebrates across different levels of pollution. The slopes of rank abundancewere characteristically steeper with decreasing species richness at the polluted sample sites, while the slopes were less steep withhigher species richness at the clean or slightly disturbed sample sites. The SADs were broadly fitted to the log normaldistribution in benthic macroinvertebrate communities across different levels of pollution. A geometric series was partly acceptedfor the communities at the severely polluted sites where new species could not be readily introduced. A power law was applied tothe SADs, and the parameters reflected the states pertaining to the sample sites. The SADs were also efficient in revealingecological state of communities where physico-chemical indicators could not be easily differentiated for stressful conditions instreams.