138 research outputs found
Range contraction enables harvesting to extinction
No full textEconomic incentives to harvest a species usually diminish as its abundance declines, because harvest costs increase. This prevents harvesting to extinction. A known exception can occur if consumer demand causes a declining species’ harvest price to rise faster than costs. This threat may affect rare and valuable species, such as large land mammals, sturgeons, and bluefin tunas. We analyze a similar but underappreciated threat, which arises when the geographic area (range) occupied by a species contracts as its abundance declines. Range contractions maintain the local densities of declining populations, which facilitates harvesting to extinction by preventing abundance declines from causing harvest costs to rise. Factors causing such range contractions include schooling, herding, or flocking behaviors–which, ironically, can be predator-avoidance adaptations; patchy environments; habitat loss; and climate change. We use a simple model to identify combinations of range contractions and price increases capable of causing extinction from profitable overharvesting, and we compare these to an empirical review. We find that some aquatic species that school or forage in patchy environments experience sufficiently severe range contractions as they decline to allow profitable harvesting to extinction even with little or no price increase; and some high-value declining aquatic species experience severe price increases. For terrestrial species, the data needed to evaluate our theory are scarce, but available evidence suggests that extinction-enabling range contractions may be common among declining mammals and birds. Thus, factors causing range contraction as abundance declines may pose unexpectedly large extinction risks to harvested species.Peer reviewe
The compact support property for measure-valued processes
Get PDFThe purpose of this article is to give a rather thorough understanding of the compact support property for measure-valued processes corresponding to semi-linear equations of the form u(t) = Lu + beta u - alpha u(p) in R-d x (0, infinity), p is an element of (1, 2]; u(x, 0) = f(x) in R-d; u (x, t) >= 0 in R-d x [0, infinity). In particular, we shall investigate how the interplay between the underlying motion (the diffusion process corresponding to L) and the branching affects the compact support property. In [J. Englander, R. Pinsky, On the construction and support properties of measure-valued diffusions on D subset of R-d with spatially dependent branching, Ann. Probab. 27 (1999) 684-730], the compact support property was shown to be equivalent to a certain analytic criterion concerning uniqueness of the Cauchy problem for the semi-linear parabolic equation related to the measured valued process. In a subsequent paper [J. Englander, R. Pinsky, Uniqueness/nonuniqueness for nonnegative solutions of second-order parabolic equations of the form u(t) = Lu + Vu - gamma u(p) in R-n, J. Differential Equations 192 (2003) 396-428], this analytic property was investigated purely from the point of view of partial differential equations. Some of the results obtained in this latter paper yield interesting results concerning the compact support property. In this paper, the results from [J. Englander, R. Pinsky, Uniqueness/nonuniqueness, for nonnegative solutions of second-order parabolic equations of the form u(t) = Lu + Vu - gamma u(p) in R-n, J. Differential Equations 192 (2003) 396-428] that are relevant to the compact support property are presented, sometimes with extensions. These results are interwoven with new results and some informal heuristics. Taken together, they yield a rather comprehensive picture of the compact support property. Inter alia, we show that the concept of a measure-valued process hitting a point can be investigated via the compact support property, and suggest an alternate proof of a result concerning the hitting of points by super-Brownian motion. (c) 2005 Elsevier SAS. All rights reserved
Building confidence in projections of the responses of living marine resources to climate change
No full textThe Fifth Assessment Report of the Intergovernmental Panel on Climate Change highlights that climate change and ocean acidification are challenging the sustainable management of living marine resources (LMRs). Formal and systematic treatment of uncertainty in existing LMR projections, however, is lacking. We synthesize knowledge of how to address different sources of uncertainty by drawing from climate model intercomparison efforts. We suggest an ensemble of available models and projections, informed by observations, as a starting point to quantify uncertainties. Such an ensemble must be paired with analysis of the dominant uncertainties over different spatial scales, time horizons, and metrics. We use two examples: (i) global and regional projections of Sea Surface Temperature and (ii) projection of changes in potential catch of sablefish (Anoplopoma fimbria) in the 21st century, to illustrate this ensemble model approach to explore different types of uncertainties. Further effort should prioritize understanding dominant, undersampled Dimensions of uncertainty, as well as the strategic collection of observations to quantify, and ultimately reduce, uncertainties. Our proposed framework will improve our understanding of future changes in LMR and the resulting risk of impacts to ecosystems and the societies under changing ocean conditions.Peer reviewe
Strong law of large numbers and mixing for the invariant distributions of measure-valued diffusions
No full textAbstractLet M(Rd) denote the space of locally finite measures on Rd and let M1(M(Rd)) denote the space of probability measures on M(Rd). Define the mean measure πν of ν∈M1(M(Rd)) byπν(B)=∫M(Rd)η(B)dν(η),forB⊂Rd.For such a measure ν with locally finite mean measure πν, let f be a nonnegative, locally bounded test function satisfying 〈f,πν〉=∞. ν is said to satisfy the strong law of large numbers with respect to f if 〈fn,η〉/〈fn,πν〉 converges almost surely to 1 with respect to ν as n→∞, for any increasing sequence {fn} of compactly supported functions which converges to f. ν is said to be mixing with respect to two sequences of sets {An} and {Bn} if∫M(Rd)f(η(An))g(η(Bn))dν(η)−∫M(Rd)f(η(An))dν(η)∫M(Rd)g(η(Bn))dν(η)converges to 0 as n→∞ for every pair of functions f,g∈Cb1([0,∞)). It is known that certain classes of measure-valued diffusion processes possess a family of invariant distributions. These distributions belong to M1(M(Rd)) and have locally finite mean measures. We prove the strong law of large numbers and mixing for many such distributions
Managing living marine resources in a dynamic environment: The role of seasonal to decadal climate forecasts
No full textRecent developments in global dynamical climate prediction systems have allowed for skillful predictions of climate variables relevant to living marine resources (LMRs) at a scale useful to understanding and managing LMRs. Such predictions present opportunities for improved LMR management and industry operations, as well as new research avenues in fisheries science. LMRs respond to climate variability via changes in physiology and behavior. For species and systems where climate-fisheries links are well established, forecasted LMR responses can lead to anticipatory and more effective decisions, benefiting both managers and stakeholders. Here, we provide an overview of climate prediction systems and advances in seasonal to decadal prediction of marine-resource relevant environmental variables. We then describe a range of climate-sensitive LMR decisions that can be taken at lead-times of months to decades, before highlighting a range of pioneering case studies using climate predictions to inform LMR decisions. The success of these case studies suggests that many additional applications are possible. Progress, however, is limited by observational and modeling challenges. Priority developments include strengthening of the mechanistic linkages between climate and marine resource responses, development of LMR models able to explicitly represent such responses, integration of climate driven LMR dynamics in the multi-driver context within which marine resources exist, and improved prediction of ecosystemrelevant variables at the fine regional scales at which most marine resource decisions are made. While there are fundamental limits to predictability, continued advances in these areas have considerable potential to make LMR managers and industry decision more resilient to climate variability and help sustain valuable resources. Concerted dialog between scientists, LMR managers and industry is essential to realizing this potential.Peer reviewe
Spectral gap and rate of convergence to equilibrium for a class of conditioned Brownian motions
No full textAbstractIf a Brownian motion is physically constrained to the interval [0,γ] by reflecting it at the endpoints, one obtains an ergodic process whose exponential rate of convergence to equilibrium is π2/2γ2. On the other hand, if Brownian motion is conditioned to remain in (0,γ) up to time t, then in the limit as t→∞ one obtains an ergodic process whose exponential rate of convergence to equilibrium is 3π2/2γ2. A recent paper [Grigorescu and Kang, J. Theoret. Probab. 15 (2002) 817–844] considered a different kind of physical constraint—when the Brownian motion reaches an endpoint, it is catapulted to the point pγ, where p∈(0,12], and then continues until it again hits an endpoint at which time it is catapulted again to pγ, etc. The resulting process—Brownian motion physically returned to the point pγ—is ergodic and the exponential rate of convergence to equilibrium is independent of p and equals 2π2/γ2. In this paper we define a conditioning analog of the process physically returned to the point pγ and study its rate of convergence to equilibrium
The Behavior of the Life Span for Solutions tout=Δu+a(x)upinRd
No full textAbstractLetT*(λ,φ) denote the life span of the positive, bounded solutionu(x,t) to the equationut=Δu+a(u)upinRdandu(x,0)=λφ(x), where 0≨a(x)∈Cα(Rd), 0≨φ(x)∈Cb(Rd),p>1, andλ>0 is a parameter. Depending ona,φ,p, andd, it is possible thatT*(λ,φ)=∞, forλ>0 sufficiently small, or thatT*(λ,φ)<∞, for allλ>0, in which case limλ→0T*(λ,φ)=∞. It is always true that limλ→∞T*(λ,φ)=0. In this paper we investigate the asymptotic behavior ofT*(λ,φ) asλ→0 in the case thatT*(λ,φ)<∞, for allλ>0, and asλ→∞ in all cases. The asymptotic order depends heavily ona,φ,p, anddin the case thatλ→0, whereas in the case thatλ→∞, it depends only on whether there exists anx0witha(x0),φ(x0)≠0, or whether the supports ofaandφare separated by a positive distance
On comparing the solutions of linear diffusion equations with those of singular nonlinear “fast” diffusion equations
No full textAbstractWe bound the solution of the nonlinear fast diffusion equation, above and below, by solutions of corresponding linear equations run on fact clocks
Transience/recurrence and the speed of a one-dimensional random walk in a “have your cookie and eat it” environment
No full textStrong law of large numbers and mixing for the invariant distributions of measure-valued diffusions
No full textLet denote the space of locally finite measures on Rd and let denote the space of probability measures on . Define the mean measure [pi][nu] of byFor such a measure [nu] with locally finite mean measure [pi][nu], let f be a nonnegative, locally bounded test function satisfying =[infinity]. [nu] is said to satisfy the strong law of large numbers with respect to f if / converges almost surely to 1 with respect to [nu] as n-->[infinity], for any increasing sequence {fn} of compactly supported functions which converges to f. [nu] is said to be mixing with respect to two sequences of sets {An} and {Bn} ifconverges to 0 as n-->[infinity] for every pair of functions f,g[set membership, variant]Cb1([0,[infinity])). It is known that certain classes of measure-valued diffusion processes possess a family of invariant distributions. These distributions belong to and have locally finite mean measures. We prove the strong law of large numbers and mixing for many such distributions.Measure-valued diffusions Invariant distributions Strong law of large numbers Mixing Random measures
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