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Maximum sustainable yield

In population ecology and economics, maximum sustainable yield (MSY) is theoretically, the largest yield (or catch) that can be taken from a species' stock over an indefinite period. Fundamental to the notion of sustainable harvest, the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population, allowing the population to continue to be productive indefinitely. Under the assumption of logistic growth, resource limitation does not constrain individuals' reproductive rates when populations are small, but because there are few individuals, the overall yield is small. At intermediate population densities, also represented by half the carrying capacity, individuals are able to breed to their maximum rate. At this point, called the maximum sustainable yield, there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the large number of reproducing individuals. Above this point, density dependent factors increasingly limit breeding until the population reaches carrying capacity. At this point, there are no surplus individuals to be harvested and yield drops to zero. The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield.

MSY is extensively used for fisheries management. Unlike the logistic (Schaefer) model,[1] MSY has been refined in most modern fisheries models and occurs at around 30% of the unexploited population size.[2][3] This fraction differs among populations depending on the life history of the species and the age-specific selectivity of the fishing method.

History edit

The concept of MSY as a fisheries management strategy developed in Belmar, New Jersey, in the early 1930s.[4][5][6] It increased in popularity in the 1950s with the advent of surplus-production models with explicitly estimate MSY.[1] As an apparently simple and logical management goal, combined with the lack of other simple management goals of the time, MSY was adopted as the primary management goal by several international organizations (e.g., IWC, IATTC,[7] ICCAT, ICNAF), and individual countries.[8]

Between 1949 and 1955, the U.S. maneuvered to have MSY declared the goal of international fisheries management (Johnson 2007). The international MSY treaty that was eventually adopted in 1955 gave foreign fleets the right to fish off any coast. Nations that wanted to exclude foreign boats had to first prove that its fish were overfished.[9]

As experience was gained with the model, it became apparent to some researchers that it lacked the capability to deal with the real world operational complexities and the influence of trophic and other interactions. In 1977, Peter Larkin wrote its epitaph, challenging the goal of maximum sustained yield on several grounds: It put populations at too much risk; it did not account for spatial variability in productivity; it did not account for species other than the focus of the fishery; it considered only the benefits, not the costs, of fishing; and it was sensitive to political pressure.[10] In fact, none of these criticisms was aimed at sustainability as a goal. The first one noted that seeking the absolute MSY with uncertain parameters was risky. The rest point out that the goal of MSY was not holistic; it left out too many relevant features.[9]

Some managers began to use more conservative quota recommendations, but the influence of the MSY model for fisheries management still prevailed. Even while the scientific community was beginning to question the appropriateness and effectiveness of MSY as a management goal,[10][11] it was incorporated into the 1982 United Nations Convention for the Law of the Sea, thus ensuring its integration into national and international fisheries acts and laws.[8] According to Walters and Maguire, an ‘‘institutional juggernaut had been set in motion’’, climaxing in the early 1990s with the collapse of northern cod.[12]

Modelling MSY edit

Population growth edit

The key assumption behind all sustainable harvesting models such as MSY is that populations of organisms grow and replace themselves – that is, they are renewable resources. Additionally it is assumed that because the growth rates, survival rates, and reproductive rates increase when harvesting reduces population density,[4] they produce a surplus of biomass that can be harvested. Otherwise, sustainable harvest would not be possible.

Another assumption of renewable resource harvesting is that populations of organisms do not continue to grow indefinitely; they reach an equilibrium population size, which occurs when the number of individuals matches the resources available to the population (i.e., assume classic logistic growth). At this equilibrium population size, called the carrying capacity, the population remains at a stable size.[13]

 
Figure 1

The logistic model (or logistic function) is a function that is used to describe bounded population growth under the previous two assumptions. The logistic function is bounded at both extremes: when there are not individuals to reproduce, and when there is an equilibrium number of individuals (i.e., at carrying capacity). Under the logistic model, population growth rate between these two limits is most often assumed to be sigmoidal (Figure 1). There is scientific evidence that some populations do grow in a logistic fashion towards a stable equilibrium – a commonly cited example is the logistic growth of yeast.

The equation describing logistic growth is:[13]

  (equation 1.1)

The parameter values are:

 =The population size at time t
 =The carrying capacity of the population
 = The population size at time zero
 = the intrinsic rate of population increase (the rate at which the population grows when it is very small)

From the logistic function, the population size at any point can be calculated as long as  ,  , and   are known.

 
Figure 2

Differentiating equation 1.1 give an expression for how the rate of population increases as N increases. At first, the population growth rate is fast, but it begins to slow as the population grows until it levels off to the maximum growth rate, after which it begins to decrease (figure 2).

The equation for figure 2 is the differential of equation 1.1 (Verhulst's 1838 growth model):[13]

  (equation 1.2)

  can be understood as the change in population (N) with respect to a change in time (t). Equation 1.2 is the usual way in which logistic growth is represented mathematically and has several important features. First, at very low population sizes, the value of   is small, so the population growth rate is approximately equal to  , meaning the population is growing exponentially at a rate r (the intrinsic rate of population increase). Despite this, the population growth rate is very low (low values on the y-axis of figure 2) because, even though each individual is reproducing at a high rate, there are few reproducing individuals present. Conversely, when the population is large the value of   approaches 1 effectively reducing the terms inside the brackets of equation 1.2 to zero. The effect is that the population growth rate is again very low, because either each individual is hardly reproducing or mortality rates are high.[13] As a result of these two extremes, the population growth rate is maximum at an intermediate population or half the carrying capacity ( ).

MSY model edit

 
Figure 3

The simplest way to model harvesting is to modify the logistic equation so that a certain number of individuals is continuously removed:[13]

  (equation 1.3)

Where H represents the number of individuals being removed from the population – that is, the harvesting rate. When H is constant, the population will be at equilibrium when the number of individuals being removed is equal to the population growth rate (figure 3). The equilibrium population size under a particular harvesting regime can be found when the population is not growing – that is, when  . This occurs when the population growth rate is the same as the harvest rate:

 

Figure 3 shows how growth rate varies with population density. For low densities (far from carrying capacity), there is little addition (or "recruitment") to the population, simply because there are few organisms to give birth. At high densities, though, there is intense competition for resources, and growth rate is again low because the death rate is high. In between these two extremes, the population growth rate rises to a maximum value ( ). This maximum point represents the maximum number of individuals that can be added to a population by natural processes. If more individuals than this are removed from the population, the population is at risk for decline to extinction.[14] The maximum number that can be harvested in a sustainable manner, called the maximum sustainable yield, is given by this maximum point.

Figure 3 also shows several possible values for the harvesting rate, H. At  , there are two possible population equilibrium points: a low population size ( ) and a high one ( ). At  , a slightly higher harvest rate, however there is only one equilibrium point (at  ), which is the population size that produces the maximum growth rate. With logistic growth, this point, called the maximum sustainable yield, is where the population size is half the carrying capacity (or  ). The maximum sustainable yield is the largest yield that can be taken from a population at equilibrium. In figure 3, if   is higher than  , the harvesting would exceed the population's capacity to replace itself at any population size (  in figure 3). Because harvesting rate is higher than the population growth rate at all values of  , this rate of harvesting is not sustainable.

An important feature of the MSY model is how harvested populations respond to environmental fluctuations or illegal offtake. Consider a population at   harvested at a constant harvest level  . If the population falls (due to a bad winter or illegal harvest) this will ease density-dependent population regulation and increase yield, moving the population back to  , a stable equilibrium. In this case, a negative feedback loop creates stability. The lower equilibrium point for the constant harvest level   is not stable however; a population crash or illegal harvesting will decrease population yield farther below the current harvest level, creating a positive feedback loop leading to extinction. Harvesting at   is also potentially unstable. A small decrease in the population can lead to a positive feedback loop and extinction if the harvesting regime ( ) is not reduced. Thus, some consider harvesting at MSY to be unsafe on ecological and economic grounds.[14][15] The MSY model itself can be modified to harvest a certain percentage of the population or with constant effort constraints rather than an actual number, thereby avoiding some of its instabilities.[14]

The MSY equilibrium point is semi-stable – a small increase in population size is compensated for, a small decrease to extinction if H is not decreased. Harvesting at MSY is therefore dangerous because it is on a knife-edge – any small population decline leads to a positive feedback, with the population declining rapidly to extinction if the number of harvested stays the same.[14][15]

The formula for maximum sustained harvest ( ) is one-fourth the maximum population or carrying capacity ( ) times the intrinsic rate of growth ( ).[16]

 

For demographically structured populations edit

The principle of MSY often holds for age-structured populations as well.[17] The calculations can be more complicated, and the results often depend on whether density dependence occurs in the larval stage (often modeled as density dependent reproduction) and/or other life stages.[18] It has been shown that if density dependence only acts on larva, then there is an optimal life stage (size or age class) to harvest, with no harvest of all other life stages.[17] Hence the optimal strategy is to harvest this most valuable life-stage at MSY.[19] However, in age and stage-structured models, a constant MSY does not always exist. In such cases, cyclic harvest is optimal where the yield and resource fluctuate in size, through time.[20] In addition, environmental stochasticity interacts with demographically structured populations in fundamentally different ways than for unstructured populations when determining optimal harvest. In fact, the optimal biomass to be left in the ocean, when fished at MSY, can be either higher or lower than in analogous deterministic models, depending on the details of the density dependent recruitment function, if stage-structure is also included in the model.[21]

Implications of MSY model edit

Starting to harvest a previously unharvested population will always lead to a decrease in the population size. That is, it is impossible for a harvested population to remain at its original carrying capacity. Instead, the population will either stabilize at a new lower equilibrium size or, if the harvesting rate is too high, decline to zero.

The reason why populations can be sustainably harvested is that they exhibit a density-dependent response.[14][15] This means that at any population size below K, the population is producing a surplus yield that is available for harvesting without reducing population size. Density dependence is the regulator process that allows the population to return to equilibrium after a perturbation. The logistic equation assumes that density dependence takes the form of negative feedback.[15]

If a constant number of individuals is harvested from a population at a level greater than the MSY, the population will decline to extinction. Harvesting below the MSY level leads to a stable equilibrium population if the starting population is above the unstable equilibrium population size.

Uses of MSY edit

MSY has been especially influential in the management of renewable biological resources such as commercially important fish and wildlife. In fisheries terms, maximum sustainable yield (MSY) is the largest average catch that can be captured from a stock under existing environmental conditions.[22] MSY aims at a balance between too much and too little harvest to keep the population at some intermediate abundance with a maximum replacement rate.

Relating to MSY, the maximum economic yield (MEY) is the level of catch that provides the maximum net economic benefits or profits to society.[23][24] Like optimum sustainable yield, MEY is usually less than MSY.

Limitations of MSY approach edit

Although it is widely practiced by state and federal government agencies regulating wildlife, forests, and fishing, MSY has come under heavy criticism by ecologists and others from both theoretical and practical reasons.[15] The concept of maximum sustainable yield is not always easy to apply in practice. Estimation problems arise due to poor assumptions in some models and lack of reliability of the data.[8][25] Biologists, for example, do not always have enough data to make a clear determination of the population's size and growth rate. Calculating the point at which a population begins to slow from competition is also very difficult. The concept of MSY also tends to treat all individuals in the population as identical, thereby ignoring all aspects of population structure such as size or age classes and their differential rates of growth, survival, and reproduction.[25]

As a management goal, the static interpretation of MSY (i.e., MSY as a fixed catch that can be taken year after year) is generally not appropriate because it ignores the fact that fish populations undergo natural fluctuations (i.e., MSY treats the environment as unvarying) in abundance and will usually ultimately become severely depleted under a constant-catch strategy.[25] Thus, most fisheries scientists now interpret MSY in a more dynamic sense as the maximum average yield (MAY) obtained by applying a specific harvesting strategy to a fluctuating resource.[8] Or as an optimal "escapement strategy", where escapement means the amount of fish that must remain in the ocean [rather than the amount of fish that can be harvested]. An escapement strategy is often the optimal strategy for maximizing expected yield of a harvested, stochastically fluctuating population.[26]

However, the limitations of MSY, does not mean it performs worse than humans using their best intuitive judgment. Experiments using students in natural resource management classes suggest that people using their past experience, intuition, and best judgement to manage a fishery generate far less long term yield compared to a computer using an MSY calculation, even when that calculation comes from incorrect population dynamic models.[27]

For a more contemporary description of MSY and its calculation see [28]

Orange roughy edit

An example of errors in estimating the population dynamics of a species occurred within the New Zealand Orange roughy fishery. Early quotas were based on an assumption that the orange roughy had a fairly short lifespan and bred relatively quickly. However, it was later discovered that the orange roughy lived a long time and had bred slowly (~30 years). By this stage stocks had been largely depleted.[citation needed]

Criticism edit

The approach has been widely criticized as ignoring several key factors involved in fisheries management and has led to the devastating collapse of many fisheries. Among conservation biologists it is widely regarded as dangerous and misused.[29][12]

Overfishing edit

Across the world there is a crisis in the world's fisheries.[30] In recent years an accelerating decline has been observed in the productivity of many important fisheries.[31] Fisheries which have been devastated in recent times include (but are not limited to) the great whale fisheries, the Grand Bank fisheries of the western Atlantic, and the Peruvian anchovy fishery.[32] Recent assessments by the United Nations Food and Agriculture Organization (FAO) of the state of the world's fisheries indicate a levelling off of landings in the 1990s, at about 100 million tons.[33]

In addition, the composition of global catches has changed.[34] As fishers deplete larger, long-lived predatory fish species such as cod, tuna, shark, and snapper, they move down to the next level – to species that tend to be smaller, shorter-lived, and less valuable.[35]

Overfishing is a classic example of the tragedy of the commons.[32]

Optimum sustainable yield edit

In population ecology and economics, optimum sustainable yield is the level of effort (LOE) that maximizes the difference between total revenue and total cost. Or, where marginal revenue equals marginal cost. This level of effort maximizes the economic profit, or rent, of the resource being utilized. It usually corresponds to an effort level lower than that of maximum sustainable yield. In environmental science, optimum sustainable yield is the largest economical yield of a renewable resource achievable over a long time period without decreasing the ability of the population or its environment to support the continuation of this level of yield.

See also edit

References edit

  1. ^ a b Schaefer, Milner B. (1954), "Some aspects of the dynamics of populations important to the management of commercial marine fisheries", Bulletin of the Inter-American Tropical Tuna Commission (reprinted in Bulletin of Mathematical Biology, Vol. 53, No. 1/2, pp. 253-279, 1991 ed.), 1 (2): 27–56, doi:10.1007/BF02464432, hdl:1834/21257, S2CID 189885665
  2. ^ Bousquet, N.; Duchesne, T.; Rivest, L.-P. (2008). "Redefining the maximum sustainable yield for the Schaefer population model including multiplicative environmental noise" (PDF). Journal of Theoretical Biology. 254 (1): 65–75. Bibcode:2008JThBi.254...65B. doi:10.1016/j.jtbi.2008.04.025. PMID 18571675.
  3. ^ Thorpe, R.B.; LeQuesne, W.J.F.; Luxford, F.; Collie, J.S.; Jennings, S. (2015). "Evaluation and management implications of uncertainty in a multispecies size-structured model of population and community responses to fishing". Methods in Ecology and Evolution. 6 (1): 49–58. doi:10.1111/2041-210X.12292. PMC 4390044. PMID 25866615.
  4. ^ a b Russell, E. S. (1931). "Some theoretical Considerations on the "Overfishing" Problem". ICES Journal of Marine Science. 6 (1): 3–20. doi:10.1093/icesjms/6.1.3. ISSN 1054-3139.
  5. ^ Hjort, J.; Jahn, G.; Ottestad, P. (1933). "The optimum catch". Hvalradets Skrifter. 7: 92–127.
  6. ^ Graham, M. (1935). "Modern Theory of Exploiting a Fishery, and Application to North Sea Trawling". ICES Journal of Marine Science. 10 (3): 264–274. doi:10.1093/icesjms/10.3.264. ISSN 1054-3139.
  7. ^ IATTC, Inter-American Tropical Tuna Commission
  8. ^ a b c d Mace, P.M. (2001). "A new role for MSY in single-species and ecosystem approaches to fisheries stock assessment and management" (PDF). Fish and Fisheries. 2: 2–32. doi:10.1046/j.1467-2979.2001.00033.x.
  9. ^ a b Botsford, L.W.; Castilla, J.C.; Peterson, C.H. (1997). "The management of fisheries and marine ecosystems". Science. 277 (5325): 509–515. doi:10.1126/science.277.5325.509.
  10. ^ a b Larkin, P. A. (1977). "An epitaph for the concept of maximum sustained yield". Transactions of the American Fisheries Society. 106 (1): 1–11. doi:10.1577/1548-8659(1977)106<1:AEFTCO>2.0.CO;2. ISSN 0002-8487.
  11. ^ Sissenwine, M.P. (1978). "Is MSY an adequate foundation for optimum yield?". Fisheries. 3 (6): 22–42. doi:10.1577/1548-8446(1978)003<0022:IMAAFF>2.0.CO;2.
  12. ^ a b Walters, C; Maguire, J (1996). "Lessons for stock assessment from the northern cod collapse". Reviews in Fish Biology and Fisheries. 6 (2): 125–137. doi:10.1007/bf00182340. S2CID 20224324.
  13. ^ a b c d e Milner-Gulland and Mace 1998, pp. 14-17.
  14. ^ a b c d e Jennings, S., Kaiser, M.J. and Reynolds, J.D. (2001), Marine Fisheries Ecology Blackwell Science Ltd. Malden, MA. ISBN 0-632-05098-5
  15. ^ a b c d e Milner-Gulland, E.J., Mace, R. (1998), Conservation of biological resources Wiley-Blackwell. ISBN 978-0-86542-738-9.
  16. ^ Bolden, E.G., Robinson, W.L. (1999), Wildlife ecology and management 4th ed. Prentice-Hall, Inc. Upper Saddle River, NJ. ISBN 0-13-840422-4
  17. ^ a b Reed, William J. (1980-01-01). "Optimum Age-Specific Harvesting in a Nonlinear Population Model". Biometrics. 36 (4): 579–593. doi:10.2307/2556112. JSTOR 2556112.
  18. ^ Boucekkine, Raouf; Hritonenko, Natali; Yatsenko, Yuri (2013). Optimal Control of Age-structured Populations in Economy, Demography, and the Environment. Routledge. ISBN 978-1136920936.
  19. ^ Getz, Wayne M. (1980-01-01). . Mathematical Biosciences. 48 (3–4): 279–292. doi:10.1016/0025-5564(80)90062-0. ISSN 0025-5564. Archived from the original on 2017-02-03. Retrieved 2017-01-28.
  20. ^ Tahvonen, Olli (2009). "Optimal Harvesting of Age-structured Fish Populations". Marine Resource Economics. 24 (2): 147–169. doi:10.5950/0738-1360-24.2.147. S2CID 153448834.
  21. ^ Holden, Matthew H.; Conrad, Jon M. (2015-11-01). "Optimal escapement in stage-structured fisheries with environmental stochasticity". Mathematical Biosciences. 269: 76–85. doi:10.1016/j.mbs.2015.08.021. PMID 26362229.
  22. ^ National Research Council (NRC). 1998. Improving Fish Stock Assessments. National Academy Press, Washington, D.C.
  23. ^ Clark, C.W. (1990), Mathematical Bioeconomics: The Optimal Management of Renewable Resources, 2nd ed. Wiley-Interscience, New York
  24. ^ National Marine Fisheries Service (NMFS). 1996. OUr Living Oceans: Report on the Status of U.S. Living Marine Resources 1995. NOAA Technical Memorandum NMFS0F/SPO-19. NMFS, Silver Springs, Md.
  25. ^ a b c Townsend, C.R., Begon, M., and Harper, J.L. (2008), Essentials of Ecology Blackwell Publishing. ISBN 978-1-4051-5658-5
  26. ^ Reed, William J (1979-12-01). "Optimal escapement levels in stochastic and deterministic harvesting models". Journal of Environmental Economics and Management. 6 (4): 350–363. doi:10.1016/0095-0696(79)90014-7.
  27. ^ Holden, Matthew H.; Ellner, Stephen P. (2016-07-01). "Human judgment vs. quantitative models for the management of ecological resources". Ecological Applications. 26 (5): 1553–1565. arXiv:1603.04518. doi:10.1890/15-1295. ISSN 1939-5582. PMID 27755756. S2CID 1279459.
  28. ^ Maunder, M.N. (2008). "Maximum Sustainable Yield". Encyclopedia of Ecology. pp. 2292–2296. doi:10.1016/B978-008045405-4.00522-X. ISBN 9780080454054.
  29. ^ Larkin PA (1977) "An epitaph for the concept of maximum sustained yield"[permanent dead link] Transactions of the American Fisheries Society, 106: 1–11.
  30. ^ sciencemag.org Worm, Boris, et. a;. "Impacts of Biodiversity Loss on Ocean Ecosystem Services," Science, 3 November 2006.
  31. ^ Christy, F.T., and Scott, A.D. (1965), The common Wealth in Ocean Fisheries, Johns Hopkins Press, Baltimore
  32. ^ a b Clark, C.W. (1973). "The Economics of Overexploitation". Science. 118 (4100): 630–634. Bibcode:1973Sci...181..630C. doi:10.1126/science.181.4100.630. PMID 17736970. S2CID 30839110.
  33. ^ FAO, Review of the State of World Marine Fishery Resources, FAO Technical Paper 335 (1994).
  34. ^ Roberts, C. (2007), The Unnatural History of the Sea, Island Press. ISBN 978-1-59726-102-9
  35. ^ Pauly, D. (1998). "Fishing Down Marine Food Webs". Science. 279 (5352): 860–863. Bibcode:1998Sci...279..860P. doi:10.1126/science.279.5352.860. ISSN 0036-8075. PMID 9452385.

maximum, sustainable, yield, population, ecology, economics, maximum, sustainable, yield, theoretically, largest, yield, catch, that, taken, from, species, stock, over, indefinite, period, fundamental, notion, sustainable, harvest, concept, aims, maintain, pop. In population ecology and economics maximum sustainable yield MSY is theoretically the largest yield or catch that can be taken from a species stock over an indefinite period Fundamental to the notion of sustainable harvest the concept of MSY aims to maintain the population size at the point of maximum growth rate by harvesting the individuals that would normally be added to the population allowing the population to continue to be productive indefinitely Under the assumption of logistic growth resource limitation does not constrain individuals reproductive rates when populations are small but because there are few individuals the overall yield is small At intermediate population densities also represented by half the carrying capacity individuals are able to breed to their maximum rate At this point called the maximum sustainable yield there is a surplus of individuals that can be harvested because growth of the population is at its maximum point due to the large number of reproducing individuals Above this point density dependent factors increasingly limit breeding until the population reaches carrying capacity At this point there are no surplus individuals to be harvested and yield drops to zero The maximum sustainable yield is usually higher than the optimum sustainable yield and maximum economic yield MSY is extensively used for fisheries management Unlike the logistic Schaefer model 1 MSY has been refined in most modern fisheries models and occurs at around 30 of the unexploited population size 2 3 This fraction differs among populations depending on the life history of the species and the age specific selectivity of the fishing method Contents 1 History 2 Modelling MSY 2 1 Population growth 2 2 MSY model 2 3 For demographically structured populations 2 4 Implications of MSY model 2 5 Uses of MSY 2 6 Limitations of MSY approach 2 6 1 Orange roughy 3 Criticism 4 Overfishing 5 Optimum sustainable yield 6 See also 7 ReferencesHistory editThe concept of MSY as a fisheries management strategy developed in Belmar New Jersey in the early 1930s 4 5 6 It increased in popularity in the 1950s with the advent of surplus production models with explicitly estimate MSY 1 As an apparently simple and logical management goal combined with the lack of other simple management goals of the time MSY was adopted as the primary management goal by several international organizations e g IWC IATTC 7 ICCAT ICNAF and individual countries 8 Between 1949 and 1955 the U S maneuvered to have MSY declared the goal of international fisheries management Johnson 2007 The international MSY treaty that was eventually adopted in 1955 gave foreign fleets the right to fish off any coast Nations that wanted to exclude foreign boats had to first prove that its fish were overfished 9 As experience was gained with the model it became apparent to some researchers that it lacked the capability to deal with the real world operational complexities and the influence of trophic and other interactions In 1977 Peter Larkin wrote its epitaph challenging the goal of maximum sustained yield on several grounds It put populations at too much risk it did not account for spatial variability in productivity it did not account for species other than the focus of the fishery it considered only the benefits not the costs of fishing and it was sensitive to political pressure 10 In fact none of these criticisms was aimed at sustainability as a goal The first one noted that seeking the absolute MSY with uncertain parameters was risky The rest point out that the goal of MSY was not holistic it left out too many relevant features 9 Some managers began to use more conservative quota recommendations but the influence of the MSY model for fisheries management still prevailed Even while the scientific community was beginning to question the appropriateness and effectiveness of MSY as a management goal 10 11 it was incorporated into the 1982 United Nations Convention for the Law of the Sea thus ensuring its integration into national and international fisheries acts and laws 8 According to Walters and Maguire an institutional juggernaut had been set in motion climaxing in the early 1990s with the collapse of northern cod 12 Modelling MSY editPopulation growth edit See also Population growth The key assumption behind all sustainable harvesting models such as MSY is that populations of organisms grow and replace themselves that is they are renewable resources Additionally it is assumed that because the growth rates survival rates and reproductive rates increase when harvesting reduces population density 4 they produce a surplus of biomass that can be harvested Otherwise sustainable harvest would not be possible Another assumption of renewable resource harvesting is that populations of organisms do not continue to grow indefinitely they reach an equilibrium population size which occurs when the number of individuals matches the resources available to the population i e assume classic logistic growth At this equilibrium population size called the carrying capacity the population remains at a stable size 13 nbsp Figure 1The logistic model or logistic function is a function that is used to describe bounded population growth under the previous two assumptions The logistic function is bounded at both extremes when there are not individuals to reproduce and when there is an equilibrium number of individuals i e at carrying capacity Under the logistic model population growth rate between these two limits is most often assumed to be sigmoidal Figure 1 There is scientific evidence that some populations do grow in a logistic fashion towards a stable equilibrium a commonly cited example is the logistic growth of yeast The equation describing logistic growth is 13 N t K 1 K N 0 N 0 e r t displaystyle N t frac K 1 frac K N 0 N 0 e rt nbsp equation 1 1 dd The parameter values are N t displaystyle N t nbsp The population size at time t dd K displaystyle K nbsp The carrying capacity of the population dd N 0 displaystyle N 0 nbsp The population size at time zero dd r displaystyle r nbsp the intrinsic rate of population increase the rate at which the population grows when it is very small dd From the logistic function the population size at any point can be calculated as long as r displaystyle r nbsp K displaystyle K nbsp and N 0 displaystyle N 0 nbsp are known nbsp Figure 2Differentiating equation 1 1 give an expression for how the rate of population increases as N increases At first the population growth rate is fast but it begins to slow as the population grows until it levels off to the maximum growth rate after which it begins to decrease figure 2 The equation for figure 2 is the differential of equation 1 1 Verhulst s 1838 growth model 13 d N d t r N 1 N K displaystyle frac dN dt rN left 1 frac N K right nbsp equation 1 2 dd d N d t displaystyle frac dN dt nbsp can be understood as the change in population N with respect to a change in time t Equation 1 2 is the usual way in which logistic growth is represented mathematically and has several important features First at very low population sizes the value of N K displaystyle frac N K nbsp is small so the population growth rate is approximately equal to r N displaystyle rN nbsp meaning the population is growing exponentially at a rate r the intrinsic rate of population increase Despite this the population growth rate is very low low values on the y axis of figure 2 because even though each individual is reproducing at a high rate there are few reproducing individuals present Conversely when the population is large the value of N K displaystyle frac N K nbsp approaches 1 effectively reducing the terms inside the brackets of equation 1 2 to zero The effect is that the population growth rate is again very low because either each individual is hardly reproducing or mortality rates are high 13 As a result of these two extremes the population growth rate is maximum at an intermediate population or half the carrying capacity N K 2 displaystyle N frac K 2 nbsp MSY model edit nbsp Figure 3The simplest way to model harvesting is to modify the logistic equation so that a certain number of individuals is continuously removed 13 d N d t r N 1 N K H displaystyle frac dN dt rN left 1 frac N K right H nbsp equation 1 3 dd Where H represents the number of individuals being removed from the population that is the harvesting rate When H is constant the population will be at equilibrium when the number of individuals being removed is equal to the population growth rate figure 3 The equilibrium population size under a particular harvesting regime can be found when the population is not growing that is when d N d t 0 displaystyle frac dN dt 0 nbsp This occurs when the population growth rate is the same as the harvest rate r N 1 N K H displaystyle rN left 1 frac N K right H nbsp dd Figure 3 shows how growth rate varies with population density For low densities far from carrying capacity there is little addition or recruitment to the population simply because there are few organisms to give birth At high densities though there is intense competition for resources and growth rate is again low because the death rate is high In between these two extremes the population growth rate rises to a maximum value N M S Y displaystyle N MSY nbsp This maximum point represents the maximum number of individuals that can be added to a population by natural processes If more individuals than this are removed from the population the population is at risk for decline to extinction 14 The maximum number that can be harvested in a sustainable manner called the maximum sustainable yield is given by this maximum point Figure 3 also shows several possible values for the harvesting rate H At H 1 displaystyle H 1 nbsp there are two possible population equilibrium points a low population size N a displaystyle N a nbsp and a high one N b displaystyle N b nbsp At H 2 displaystyle H 2 nbsp a slightly higher harvest rate however there is only one equilibrium point at N M S Y displaystyle N MSY nbsp which is the population size that produces the maximum growth rate With logistic growth this point called the maximum sustainable yield is where the population size is half the carrying capacity or N K 2 displaystyle N frac K 2 nbsp The maximum sustainable yield is the largest yield that can be taken from a population at equilibrium In figure 3 if H displaystyle H nbsp is higher than H 2 displaystyle H 2 nbsp the harvesting would exceed the population s capacity to replace itself at any population size H 3 displaystyle H 3 nbsp in figure 3 Because harvesting rate is higher than the population growth rate at all values of N displaystyle N nbsp this rate of harvesting is not sustainable An important feature of the MSY model is how harvested populations respond to environmental fluctuations or illegal offtake Consider a population at N b displaystyle N b nbsp harvested at a constant harvest level H 1 displaystyle H 1 nbsp If the population falls due to a bad winter or illegal harvest this will ease density dependent population regulation and increase yield moving the population back to N b displaystyle N b nbsp a stable equilibrium In this case a negative feedback loop creates stability The lower equilibrium point for the constant harvest level H 1 displaystyle H 1 nbsp is not stable however a population crash or illegal harvesting will decrease population yield farther below the current harvest level creating a positive feedback loop leading to extinction Harvesting at N M S Y displaystyle N MSY nbsp is also potentially unstable A small decrease in the population can lead to a positive feedback loop and extinction if the harvesting regime H 2 displaystyle H 2 nbsp is not reduced Thus some consider harvesting at MSY to be unsafe on ecological and economic grounds 14 15 The MSY model itself can be modified to harvest a certain percentage of the population or with constant effort constraints rather than an actual number thereby avoiding some of its instabilities 14 The MSY equilibrium point is semi stable a small increase in population size is compensated for a small decrease to extinction if H is not decreased Harvesting at MSY is therefore dangerous because it is on a knife edge any small population decline leads to a positive feedback with the population declining rapidly to extinction if the number of harvested stays the same 14 15 The formula for maximum sustained harvest H displaystyle H nbsp is one fourth the maximum population or carrying capacity K displaystyle K nbsp times the intrinsic rate of growth r displaystyle r nbsp 16 H K r 4 displaystyle H frac Kr 4 nbsp For demographically structured populations edit The principle of MSY often holds for age structured populations as well 17 The calculations can be more complicated and the results often depend on whether density dependence occurs in the larval stage often modeled as density dependent reproduction and or other life stages 18 It has been shown that if density dependence only acts on larva then there is an optimal life stage size or age class to harvest with no harvest of all other life stages 17 Hence the optimal strategy is to harvest this most valuable life stage at MSY 19 However in age and stage structured models a constant MSY does not always exist In such cases cyclic harvest is optimal where the yield and resource fluctuate in size through time 20 In addition environmental stochasticity interacts with demographically structured populations in fundamentally different ways than for unstructured populations when determining optimal harvest In fact the optimal biomass to be left in the ocean when fished at MSY can be either higher or lower than in analogous deterministic models depending on the details of the density dependent recruitment function if stage structure is also included in the model 21 Implications of MSY model edit Starting to harvest a previously unharvested population will always lead to a decrease in the population size That is it is impossible for a harvested population to remain at its original carrying capacity Instead the population will either stabilize at a new lower equilibrium size or if the harvesting rate is too high decline to zero The reason why populations can be sustainably harvested is that they exhibit a density dependent response 14 15 This means that at any population size below K the population is producing a surplus yield that is available for harvesting without reducing population size Density dependence is the regulator process that allows the population to return to equilibrium after a perturbation The logistic equation assumes that density dependence takes the form of negative feedback 15 If a constant number of individuals is harvested from a population at a level greater than the MSY the population will decline to extinction Harvesting below the MSY level leads to a stable equilibrium population if the starting population is above the unstable equilibrium population size Uses of MSY edit MSY has been especially influential in the management of renewable biological resources such as commercially important fish and wildlife In fisheries terms maximum sustainable yield MSY is the largest average catch that can be captured from a stock under existing environmental conditions 22 MSY aims at a balance between too much and too little harvest to keep the population at some intermediate abundance with a maximum replacement rate Relating to MSY the maximum economic yield MEY is the level of catch that provides the maximum net economic benefits or profits to society 23 24 Like optimum sustainable yield MEY is usually less than MSY Limitations of MSY approach edit Although it is widely practiced by state and federal government agencies regulating wildlife forests and fishing MSY has come under heavy criticism by ecologists and others from both theoretical and practical reasons 15 The concept of maximum sustainable yield is not always easy to apply in practice Estimation problems arise due to poor assumptions in some models and lack of reliability of the data 8 25 Biologists for example do not always have enough data to make a clear determination of the population s size and growth rate Calculating the point at which a population begins to slow from competition is also very difficult The concept of MSY also tends to treat all individuals in the population as identical thereby ignoring all aspects of population structure such as size or age classes and their differential rates of growth survival and reproduction 25 As a management goal the static interpretation of MSY i e MSY as a fixed catch that can be taken year after year is generally not appropriate because it ignores the fact that fish populations undergo natural fluctuations i e MSY treats the environment as unvarying in abundance and will usually ultimately become severely depleted under a constant catch strategy 25 Thus most fisheries scientists now interpret MSY in a more dynamic sense as the maximum average yield MAY obtained by applying a specific harvesting strategy to a fluctuating resource 8 Or as an optimal escapement strategy where escapement means the amount of fish that must remain in the ocean rather than the amount of fish that can be harvested An escapement strategy is often the optimal strategy for maximizing expected yield of a harvested stochastically fluctuating population 26 However the limitations of MSY does not mean it performs worse than humans using their best intuitive judgment Experiments using students in natural resource management classes suggest that people using their past experience intuition and best judgement to manage a fishery generate far less long term yield compared to a computer using an MSY calculation even when that calculation comes from incorrect population dynamic models 27 For a more contemporary description of MSY and its calculation see 28 Orange roughy edit See also Orange roughy An example of errors in estimating the population dynamics of a species occurred within the New Zealand Orange roughy fishery Early quotas were based on an assumption that the orange roughy had a fairly short lifespan and bred relatively quickly However it was later discovered that the orange roughy lived a long time and had bred slowly 30 years By this stage stocks had been largely depleted citation needed Criticism editThe approach has been widely criticized as ignoring several key factors involved in fisheries management and has led to the devastating collapse of many fisheries Among conservation biologists it is widely regarded as dangerous and misused 29 12 Overfishing editSee also Overfishing Across the world there is a crisis in the world s fisheries 30 In recent years an accelerating decline has been observed in the productivity of many important fisheries 31 Fisheries which have been devastated in recent times include but are not limited to the great whale fisheries the Grand Bank fisheries of the western Atlantic and the Peruvian anchovy fishery 32 Recent assessments by the United Nations Food and Agriculture Organization FAO of the state of the world s fisheries indicate a levelling off of landings in the 1990s at about 100 million tons 33 In addition the composition of global catches has changed 34 As fishers deplete larger long lived predatory fish species such as cod tuna shark and snapper they move down to the next level to species that tend to be smaller shorter lived and less valuable 35 Overfishing is a classic example of the tragedy of the commons 32 Optimum sustainable yield editSee also Optimum sustainable yield In population ecology and economics optimum sustainable yield is the level of effort LOE that maximizes the difference between total revenue and total cost Or where marginal revenue equals marginal cost This level of effort maximizes the economic profit or rent of the resource being utilized It usually corresponds to an effort level lower than that of maximum sustainable yield In environmental science optimum sustainable yield is the largest economical yield of a renewable resource achievable over a long time period without decreasing the ability of the population or its environment to support the continuation of this level of yield See also editAll the Fish in the Sea Maximum Sustainable Yield and the Failure of Fisheries Management Ecological yield Fisheries management List of harvested aquatic animals by weight Maximum economic yield MEY Population dynamics Population dynamics of fisheriesReferences edit a b Schaefer Milner B 1954 Some aspects of the dynamics of populations important to the management of commercial marine fisheries Bulletin of the Inter American Tropical Tuna Commission reprinted in Bulletin of Mathematical Biology Vol 53 No 1 2 pp 253 279 1991 ed 1 2 27 56 doi 10 1007 BF02464432 hdl 1834 21257 S2CID 189885665 Bousquet N Duchesne T Rivest L P 2008 Redefining the maximum sustainable yield for the Schaefer population model including multiplicative environmental noise PDF Journal of Theoretical Biology 254 1 65 75 Bibcode 2008JThBi 254 65B doi 10 1016 j jtbi 2008 04 025 PMID 18571675 Thorpe R B LeQuesne W J F Luxford F Collie J S Jennings S 2015 Evaluation and management implications of uncertainty in a multispecies size structured model of population and community responses to fishing Methods in Ecology and Evolution 6 1 49 58 doi 10 1111 2041 210X 12292 PMC 4390044 PMID 25866615 a b Russell E S 1931 Some theoretical Considerations on the Overfishing Problem ICES Journal of Marine Science 6 1 3 20 doi 10 1093 icesjms 6 1 3 ISSN 1054 3139 Hjort J Jahn G Ottestad P 1933 The optimum catch Hvalradets Skrifter 7 92 127 Graham M 1935 Modern Theory of Exploiting a Fishery and Application to North Sea Trawling ICES Journal of Marine Science 10 3 264 274 doi 10 1093 icesjms 10 3 264 ISSN 1054 3139 IATTC Inter American Tropical Tuna Commission a b c d Mace P M 2001 A new role for MSY in single species and ecosystem approaches to fisheries stock assessment and management PDF Fish and Fisheries 2 2 32 doi 10 1046 j 1467 2979 2001 00033 x a b Botsford L W Castilla J C Peterson C H 1997 The management of fisheries and marine ecosystems Science 277 5325 509 515 doi 10 1126 science 277 5325 509 a b Larkin P A 1977 An epitaph for the concept of maximum sustained yield Transactions of the American Fisheries Society 106 1 1 11 doi 10 1577 1548 8659 1977 106 lt 1 AEFTCO gt 2 0 CO 2 ISSN 0002 8487 Sissenwine M P 1978 Is MSY an adequate foundation for optimum yield Fisheries 3 6 22 42 doi 10 1577 1548 8446 1978 003 lt 0022 IMAAFF gt 2 0 CO 2 a b Walters C Maguire J 1996 Lessons for stock assessment from the northern cod collapse Reviews in Fish Biology and Fisheries 6 2 125 137 doi 10 1007 bf00182340 S2CID 20224324 a b c d e Milner Gulland and Mace 1998 pp 14 17 a b c d e Jennings S Kaiser M J and Reynolds J D 2001 Marine Fisheries Ecology Blackwell Science Ltd Malden MA ISBN 0 632 05098 5 a b c d e Milner Gulland E J Mace R 1998 Conservation of biological resources Wiley Blackwell ISBN 978 0 86542 738 9 Bolden E G Robinson W L 1999 Wildlife ecology and management 4th ed Prentice Hall Inc Upper Saddle River NJ ISBN 0 13 840422 4 a b Reed William J 1980 01 01 Optimum Age Specific Harvesting in a Nonlinear Population Model Biometrics 36 4 579 593 doi 10 2307 2556112 JSTOR 2556112 Boucekkine Raouf Hritonenko Natali Yatsenko Yuri 2013 Optimal Control of Age structured Populations in Economy Demography and the Environment Routledge ISBN 978 1136920936 Getz Wayne M 1980 01 01 The ultimate sustainable yield problem in nonlinear age structured populations Mathematical Biosciences 48 3 4 279 292 doi 10 1016 0025 5564 80 90062 0 ISSN 0025 5564 Archived from the original on 2017 02 03 Retrieved 2017 01 28 Tahvonen Olli 2009 Optimal Harvesting of Age structured Fish Populations Marine Resource Economics 24 2 147 169 doi 10 5950 0738 1360 24 2 147 S2CID 153448834 Holden Matthew H Conrad Jon M 2015 11 01 Optimal escapement in stage structured fisheries with environmental stochasticity Mathematical Biosciences 269 76 85 doi 10 1016 j mbs 2015 08 021 PMID 26362229 National Research Council NRC 1998 Improving Fish Stock Assessments National Academy Press Washington D C Clark C W 1990 Mathematical Bioeconomics The Optimal Management of Renewable Resources 2nd ed Wiley Interscience New York National Marine Fisheries Service NMFS 1996 OUr Living Oceans Report on the Status of U S Living Marine Resources 1995 NOAA Technical Memorandum NMFS0F SPO 19 NMFS Silver Springs Md a b c Townsend C R Begon M and Harper J L 2008 Essentials of Ecology Blackwell Publishing ISBN 978 1 4051 5658 5 Reed William J 1979 12 01 Optimal escapement levels in stochastic and deterministic harvesting models Journal of Environmental Economics and Management 6 4 350 363 doi 10 1016 0095 0696 79 90014 7 Holden Matthew H Ellner Stephen P 2016 07 01 Human judgment vs quantitative models for the management of ecological resources Ecological Applications 26 5 1553 1565 arXiv 1603 04518 doi 10 1890 15 1295 ISSN 1939 5582 PMID 27755756 S2CID 1279459 Maunder M N 2008 Maximum Sustainable Yield Encyclopedia of Ecology pp 2292 2296 doi 10 1016 B978 008045405 4 00522 X ISBN 9780080454054 Larkin PA 1977 An epitaph for the concept of maximum sustained yield permanent dead link Transactions of the American Fisheries Society 106 1 11 sciencemag org Worm Boris et a Impacts of Biodiversity Loss on Ocean Ecosystem Services Science 3 November 2006 Christy F T and Scott A D 1965 The common Wealth in Ocean Fisheries Johns Hopkins Press Baltimore a b Clark C W 1973 The Economics of Overexploitation Science 118 4100 630 634 Bibcode 1973Sci 181 630C doi 10 1126 science 181 4100 630 PMID 17736970 S2CID 30839110 FAO Review of the State of World Marine Fishery Resources FAO Technical Paper 335 1994 Roberts C 2007 The Unnatural History of the Sea Island Press ISBN 978 1 59726 102 9 Pauly D 1998 Fishing Down Marine Food Webs Science 279 5352 860 863 Bibcode 1998Sci 279 860P doi 10 1126 science 279 5352 860 ISSN 0036 8075 PMID 9452385 Retrieved from https en wikipedia org w index php title Maximum sustainable yield amp oldid 1199101176, wikipedia, wiki, book, books, library,

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