The Importance of Functional Form in Optimal Control Solutions of Problems in Population Dynamics

Runge, Michael C.; Johnson, Fred A.

doi:10.2307/3071949

Cited by 37 publications

(66 citation statements)

References 19 publications

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“…In stochastic environments, however, the population growth rate, and therefore the potential harvestable surplus, tends to be lower than that predicted from purely deterministic models (Lande et al 1994, Alvarez 2000. Finally, the actual functional form of the density-dependence function is known to affect the optimal harvesting rates (Runge & Johnson 2002). Thus, care should be taken in advising specific harvesting rates based on our results.…”

Section: Discussionmentioning

confidence: 99%

The Role of Ecological and Economic Factors in the Management of a Spatially Structured Moose Alces alces Population

Nilsen¹,

Skonhoft²,

Mysterud³

et al. 2009

Wildlife Biology

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We present a bioeconomic model for moose Alces alces management in Norway, where two sub‐populations of moose are subject to different site‐specific mortality rates caused by the spatial distribution of territorial wolf Canis lupus packs, and are coupled by the seasonal migration of moose. The costs and benefits of moose are asymmetrically distributed in space, since they congregate in the wolf territory during winter where most browsing damage occurs. Using a class‐structured matrix population model as the basis for bioeconomic analysis, we investigated how the optimal moose management differed between a unified (i.e. maximising overall profit) and a non‐unified (i.e. profit maximised at the level of individual landowners) management scheme. Within the unified management scheme, the combined marginal costs and benefits decide the optimal off‐take rate, and the relative hunting value and damage costs decide the relative allocation of the harvest between the two sub‐populations. In the non‐unified management scheme, harvesting takes place up to the point where the private marginal hunting value equals the private marginal browsing cost, while the relative hunting value and damage costs do not influence the optimal management. As the browsing damage that occurs inside the wolf territory is not taken into account in the costs of the area outside the territory within the non‐unified solution, optimal moose population size will be higher for the outer area than under the unified solution. This results in an overall economic loss, which increases with increasing migration rates. Whenever the boundaries of political or management units do not follow those of ecological processes, ignoring the spatial resolution of the ecological process will result in sub‐optimal management of a renewable resource.

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Section: Discussionmentioning

confidence: 99%

The Role of Ecological and Economic Factors in the Management of a Spatially Structured Moose Alces alces Population

Nilsen¹,

Skonhoft²,

Mysterud³

et al. 2009

Wildlife Biology

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“…However, we have insufficient information about how and when during the annual cycle density affects demographic rates [7,10,11]. This knowledge is needed for effective management and conservation of wildlife populations [12].…”

Section: Introductionmentioning

confidence: 99%

Non-breeding season habitat quality mediates the strength of density-dependence for a migratory bird

et al. 2015

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Our understanding of when natural populations are regulated during their annual cycle is limited, particularly for migratory species. This information is needed for parametrizing models that can inform management and conservation. Here, we use 14 years of data on colour-marked birds to investigate how conspecific density and habitat quality during the tropical non-breeding period interact to affect body condition and apparent annual survival of a long-distance migratory songbird, the American redstart (Setophaga ruticilla). Body condition and survival of birds in high-quality mangrove habitat declined as density increased. By contrast, body condition improved and survival did not vary as density increased in adjacent, lower quality scrub habitat, although mean condition and survival were almost always lower than in mangrove. High rainfall enhanced body condition in scrub but not in mangrove, suggesting factors such as food availability outweighed consequences of crowding in lower quality habitat. Thus, survival of overwintering redstarts in mangrove habitat, disproportionately males, appears to be regulated by a crowding mechanism based on densitydependent resource competition. Survival of individuals in scrub, mostly females, appears to be limited by density-independent environmental factors but not regulated by crowding. The contrasting effects of density and food limitation on individuals overwintering in adjacent habitats illustrate the complexity of processes operating during the non-breeding period for migratory animals, and emphasize the need for long-term studies of animals in multiple habitats and throughout their annual cycles.

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“…Следовательно, изменение доли изъятия молоди не влияет на баланс численностей полов в популяции. В пространстве параметров модели (5) при переходе через гиперплоскость (8) происходит переключение принципа образования пар согласно формуле (8). Вследствие этого область устойчивости системы (5) определяется бифуркационными линиями, ограничивающими равновесие (6) или (7) (рис.…”

Section: промысловое изъятие неполовозрелых особейunclassified

“…Рациональное использование природных ресурсов во все времена определяло необходимость разработки оптимальных стратегий их эксплуатации [1,[4][5][6][7][8]. Научно обоснованная эксплуатация биологических ресурсов, рациональное и экономически выгодное управление численностью животных без угрозы исчезновения видов не возможны без детального изучения их популяционной структуры (прежде всего, возрастной и половой) [1,[9][10][11][12].…”

Section: Introductionunclassified

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Influence of Harvest on the Dynamics of Populations with Age and Sex Structures

Revutskaya¹,

Неверова²,

Frisman³

2018

Math.Biol.Bioinf.

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The paper investigates influence of sex- and age-specific harvest on the dynamics of structured populations based on the mathematical model with discrete time. We assume birth rate depends on the population sex ratio and is described by the modified harmonic mating function with switching. The population size is regulated by decreasing juvenile survival rate with growth of sex-age class sizes. The aim is to study the mechanisms of formation and evolution of dynamic modes for the exploited structured population models due to harvesting intensity. Conditions for sustainable development of the exploited population are received. Dynamic modes of the population models are studied. Influence of birth, survival, and self-regulation rates, the formation process of the mating pairs, and sex- and age-specific harvest on transitions between different dynamic modes are investigated. Sex-specific harvest of mature females or males will change the pair formation if the sex class, whose number of individuals is more, is exploited. Depending on values of the population parameters, the sex- and age-specific harvest (juveniles, mature females or males) can result in both damping of the oscillations, which stabilizes population dynamics, and the oscillation appearance, including two-year or quasiperiodic population fluctuations. The model of exploited population reveals the phenomenon of multistability, which is typical for a population without harvesting. The multistability is the result of complex bifurcations occurring due to both the system nonlinearity and the changing pair formation principle.

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The Importance of Functional Form in Optimal Control Solutions of Problems in Population Dynamics

Cited by 37 publications

References 19 publications

The Role of Ecological and Economic Factors in the Management of a Spatially Structured Moose Alces alces Population

The Role of Ecological and Economic Factors in the Management of a Spatially Structured Moose Alces alces Population

Non-breeding season habitat quality mediates the strength of density-dependence for a migratory bird

Influence of Harvest on the Dynamics of Populations with Age and Sex Structures

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