The name is absent



Many natural systems can be divided into domains with distinct system dynamics. In such
multistate systems, the equation of motion changes discontinuously or nonlinearly when system
variables such as climate, nutrient flux, or human harvesting rates are changing gradually [20, 27].
For example, shifts in system dynamics have been observed in ecosystems such as freshwater
lakes [28], coral reefs [15], riparian meadows [6], tropical forests [29], and savanna [26]. At a
much larger scale, multiple stable states separated by discontinuous shifts are also thought to be
important processes in climate change and global biogeochemical cycles [3, 30]. A key feature
of multistate ecosystems is that environmental monitoring that occurs in one stable domain of the
system has little or no predictive power about proximity to a threshold and shifts to alternative sta-
bility domains [27]. Consequently, ecosystem management strategies that are based strictly around
the attainment of fixed environmental targets, or that view small perturbations to such targets as
sustainable, may lead to unexpected, catastrophic collapse and accompanying ecologic and eco-
nomic damages to ecosystem functions [25]. Recent research in ecology has emphasized the need
to increase the resilience1 and stability domains of desirable ecosystem states as the primary goals
of scientifically-based ecosystem management [20, 27].

In this study, we analyze a multistate system with two distinct domains that are separated by a
possibly unknown, reversible threshold. We assume that the underlying stochastic natural process
and management actions together determine which domain the system is in, and thus the appropri-
ate equation of motion. The contributions of this paper are as follows: First, under our model setup
we obtain a differentiable value function, even at the threshold. Thus, while earlier studies had
to rely on numerical simulations, we use stochastic dynamic programming to obtain an analytical
solution as well as comparative statics results on precautionary behavior. Second, we show that
utility maximization yields a decision rule with precautionary behavior if the system is close to
the threshold, thereby increasing system resilience. Third, as the variance in the stochastic com-
ponent of the
natural system that determines whether the threshold is passed increases, the level
of precautionary behavior may first increase, but for large enough variance will eventually always
decrease. Fourth, we show that there is also a nonmonotonic relationship between the uncertainty
of the
utility maximizer about the unknown threshold and precautionary behavior. Intuitively, if a
decisionmaker knows with certainty that he/she is right below the threshold, there is no expected
benefit from engaging in precautionary reductions. Once uncertainty increases (either about the
natural system or the utility maximizer’s belief about the threshold), so does the probability that

1There are several definitions of resilience in the ecology literature. The Resilience Alliance research consortium
defines it as ”the capacity of an ecosystem to tolerate disturbance without collapsing into a qualitatively different state
that is controlled by a different set of processes.”



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