Behavior persistence in defining threshold switch in stepwise response of aquatic organisms exposed to toxic chemicals

• Mathematical behavior persistence construction inspired by bacteria persistence model.
• Defining threshold switch according to behavior modes.
• Homeostatic mechanics in explaining the mathematical behavior persistence model.

As a characteristic in bacterial colony, persistence model described the dynamics of two subpopulations (normal (n) and persister (p)). In order to illustrate the switch of “Threshold” in the stepwise behavior responses of organisms, it is hypothesized that total behavior (Bt) of organisms consists of two types in behavior tendency, intoxication (Bp) and normal/recovery behavior (Bn). Both Bp and Bn could be concurrently affected by environmental stress E, and behavior response modes (M) are decided by the relationship between E and toxicity threshold of test organisms (Ti). The results suggested stress constant λ was decided by the constant rates gnE,gpE, an and ap. Due to different stress constant λ, the behavior responses of indicators showed great difference in different M, which included ‘safe mode’ (Ms), ‘acclimation mode’ (Mac), ‘adjustment mode’ (Maj) and ‘toxic effect’ (Mte). Usually, Bt during Ms could maintain around 0.8, and Mte would happen once it is lower than 0.2. According to the relationship between Bt values and E changes in 7 Majs, behavior persistence relying on adjustment could reflect the behavior homeostasis of organisms under environmental stress and be regarded as a threshold switch for the stepwise behavior responses. The mathematical analysis of behavior persistence allows making a quantitative prediction on environment assessment that would promote the emergence of persistence, as well as evaluating its ecological implications.

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