Strategic Review of Tropical Fisheries Management

This project addresses the constraints to tropical fisheries development with sustainable exploitation through a strategic assessment of tropical fisheries management with the following purposes: (1) To evaluate relevant research methods for the development of assessment models appropriate to the circumstances of tropical coastal fisheries; and (2) To evaluate the utility of existing strategies for the implementation of management advice. The report consists of three substantive chapters. Chapter 2 contains a detailed socio-economic assessment of various instruments and implementation strategies applicable to tropical capture fisheries. In Chapter 3, a detailed assessment of the fisheries for tropical large marine ecosystems has been conducted using a technique developed by FAO (Granger & Garcia 1996). The data used were the FAO statistics published regularly by FAO. This analysis has been conducted for each of the tropical large marine ecosystems and indicates that there is the potential for increased fishing in a number of these ecosystems. One of the clear requirements identified in Chapter 2 and implicit in Chapter 3, is that there is a significant need for simple and robust fisheries assessment methods which can estimate the potential of a particular resource, its capacity in terms of the level of fishing effort and its current status ie whether it is currently exploited sustainably or not. In Chapter 4, these problems are addressed directly and, using two approaches, significant simplification of fishery methods is developed. In the first approach, simple empirical relationships between the life history parameters of a species are used to develop models of potential yield which can be determined by a simple assessment of fish growth. In the second approach, optimal life history theory is applied to the key demographic parameters of exploited fish populations and using estimates of the Beverton & Holt invariants a significant simplifying of the basic stock assessment equations is developed

The Time Invariance Principle, Ecological (Non)Chaos, and A Fundamental Pitfall of Discrete Modeling

This paper is to show that most discrete models used for population dynamics in ecology are inherently pathological that their predications cannot be independently verified by experiments because they violate a fundamental principle of physics. The result is used to tackle an on-going controversy regarding ecological chaos. Another implication of the result is that all continuous dynamical systems must be modeled by differential equations. As a result it suggests that researches based on discrete modeling must be closely scrutinized and the teaching of calculus and differential equations must be emphasized for students of biology

On the Properties of a Class of Impulsive Competition Beverton–Holt Equations

This paper is devoted to a type of combined impulsive discrete Beverton–Holt equations in ecology when eventual discontinuities at sampling time instants are considered. Such discontinuities could be interpreted as impulses in the corresponding continuous-time logistic equations. The set of equations involve competition-type coupled dynamics among a finite set of species. It is assumed that, in general, the intrinsic growth rates and the carrying capacities are eventually distinct for the various species. The impulsive parts of the equations are parameterized by harvesting quotas and independent consumptions which are also eventually distinct for the various species and which control the populations’ evolution. The performed study includes the existence of extinction and non-extinction equilibrium points, the conditions of non-negativity and boundedness of the solutions for given finite non-negative initial conditions and the conditions of asymptotic stability without or with extinction of the solutions.This research was supported by the Spanish Government through grant RTI2018-094336-B-100 (MCIU/AEI/FEDER, UE) and by the Basque Government through grant IT1207-19

Optimal Capacity Decisions in a Developing Fishery

The problem of estimating optimal fishing capacity for a developing fishery is discussed, using the methods of Bayesian decision analysis. The results obtained indicate that quite good decisions can often be made on the basis of limited prior information as to fish stock productivity, particularly if a conservative approach allowing for subsequent increases in capacity is employed.Environmental Economics and Policy, International Development, International Relations/Trade, Resource /Energy Economics and Policy,

Bioeconomic Analysis of Management Options for Tropical Fisheries Using a Bicriteria Programming Model

A possible approach to the management of the multispecies multi-gear fishery in a developing country was explored. The small petagics fishery in central Philippines was analyzed in three stages. A dynamic pool model represented the dynamics of the stocks. The optimal allocation of catch across competing fleets was modeled having regard for the pursuit of two conflicting objectives, maximizing employment and fishing profits. Alternative management schemes were then explored. On the basis of the criteria used, the optimal fleet size was a small fraction of the existing fleet size. Calculation of increased target yields through regulation of fishing mortality and selectivity showed that the increase in optimal feet size would be moderate because the current level of exploitation is close to that producing the maximum yield-per-recruit. An agenda for exploration of further management alternatives appropriate to the social and economic policy objectives of a developing country is discussed.bioeconomics, Philippines, small pelagics, multicriteria decision making, fishery economics, fishery management, tropical fisheries, Environmental Economics and Policy, Production Economics,

Local and Global Dynamics in a Neoclassical Growth Model with NonConcave Production Function and NonConstant Population Growth Rate

In this paper we analyze the dynamics shown by the neoclassical one-sector growth model with differential savings as in Bohm and Kaas [J. Econom. Dynam. Control, 24 (2000), pp. 965--980] while assuming a sigmoidal production function as in [V. Capasso, R. Engbers, and D. La Torre, Nonlinear Anal., 11 (2010), pp. 3858--3876] and the labor force dynamics described by the Beverton--Holt equation (see [R. J. H. Beverton and S. J. Holt, Fishery Invest., 19 (1957), pp. 1--533]). We prove that complex features are exhibited, related both to the structure of the coexisting attractors (which can be periodic or chaotic) and to their basins (which can be simple or nonconnected). In particular we show that complexity emerges if the elasticity of substitution between production factors is low enough and shareholders save more than workers, confirming the results obtained with concave production functions. Anyway, in contrast to previous studies, the use of the S-shaped production function implies the existence of a poverty trap: by performing a global analysis we study the properties of the regions generating trajectories converging to it

Structured parametric epidemic models

A stage-structured model for a theoretical epidemic process that incorporates immature, susceptible and infectious individuals in independent stages is formulated. In this analysis, an input interpreted as a birth function is considered. The structural identifiability is studied using the Markov parameters. Then, the unknown parameters are uniquely determined by the output structure corresponding to an observation of infection. Two different birth functions are considered: the linear case and the Beverton-Holt type to analyse the structured epidemic model. Some conditions on the parameters to obtain non-zero disease-free equilibrium points are given. The identifiability of the parameters allows us to determine uniquely the basic reproduction number Script capital R-0 and the stability of the model in the equilibrium is studied using Script capital R-0 in terms of the model parameters.This work has been partially supported by MTM2010-18228. The authors wish to express their thanks to the reviewers for helpful comments and suggestions.Cantó Colomina, B.; Coll, C.; Sánchez, E. (2014). Structured parametric epidemic models. International Journal of Computer Mathematics. 91(2):188-197. https://doi.org/10.1080/00207160.2013.800864188197912Allen, L. J. S., & Thrasher, D. B. (1998). The effects of vaccination in an age-dependent model for varicella and herpes zoster. IEEE Transactions on Automatic Control, 43(6), 779-789. doi:10.1109/9.679018Ben-Zvi, A., McLellan, P. J., & McAuley, K. B. (2004). Identifiability of Linear Time-Invariant Differential-Algebraic Systems. 2. The Differential-Algebraic Approach. Industrial & Engineering Chemistry Research, 43(5), 1251-1259. doi:10.1021/ie030534jBoyadjiev, C., & Dimitrova, E. (2005). An iterative method for model parameter identification. Computers & Chemical Engineering, 29(5), 941-948. doi:10.1016/j.compchemeng.2004.08.036Cantó, B., Coll, C., & Sánchez, E. (2011). Identifiability for a Class of Discretized Linear Partial Differential Algebraic Equations. Mathematical Problems in Engineering, 2011, 1-12. doi:10.1155/2011/510519Cao, H., & Zhou, Y. (2012). The discrete age-structured SEIT model with application to tuberculosis transmission in China. Mathematical and Computer Modelling, 55(3-4), 385-395. doi:10.1016/j.mcm.2011.08.017Diekmann, O., Heesterbeek, J. A. P., & Metz, J. A. J. (1990). On the definition and the computation of the basic reproduction ratio R 0 in models for infectious diseases in heterogeneous populations. Journal of Mathematical Biology, 28(4). doi:10.1007/bf00178324Dion, J.-M., Commault, C., & van der Woude, J. (2003). Generic properties and control of linear structured systems: a survey. Automatica, 39(7), 1125-1144. doi:10.1016/s0005-1098(03)00104-3Emmert, K. E., & Allen, L. J. S. (2004). Population Persistence and Extinction in a Discrete-time, Stage-structured Epidemic Model. Journal of Difference Equations and Applications, 10(13-15), 1177-1199. doi:10.1080/10236190410001654151Farina, L., & Rinaldi, S. (2000). Positive Linear Systems. doi:10.1002/9781118033029Van den Hof, J. M. (1998). Structural identifiability of linear compartmental systems. IEEE Transactions on Automatic Control, 43(6), 800-818. doi:10.1109/9.679020T. Kailath,Linear Systems, Prentice-Hall, Englewood Cliffs, NJ, 1980.Li, C.-K., & Schneider, H. (2002). Applications of Perron-Frobenius theory to population dynamics. Journal of Mathematical Biology, 44(5), 450-462. doi:10.1007/s002850100132Li, X., & Wang, W. (2005). A discrete epidemic model with stage structure☆. Chaos, Solitons & Fractals, 26(3), 947-958. doi:10.1016/j.chaos.2005.01.063Ma, J., & Earn, D. J. D. (2006). Generality of the Final Size Formula for an Epidemic of a Newly Invading Infectious Disease. Bulletin of Mathematical Biology, 68(3), 679-702. doi:10.1007/s11538-005-9047-7Wang, W., & Zhao, X.-Q. (2004). An epidemic model in a patchy environment. Mathematical Biosciences, 190(1), 97-112. doi:10.1016/j.mbs.2002.11.00

Frequency responses of age-structured populations: Pacific salmon as an example

Increasing evidence of the effects of changing climate on physical ocean conditions and long-term changes in fish populations adds to the need to understand the effects of stochastic forcing on marine populations. Cohort resonance is of particular interest because it involves selective sensitivity to specific time scales of environmental variability, including that of mean age of reproduction, and, more importantly, very low frequencies (i.e., trends). We present an age-structured model for two Pacific salmon species with environmental variability in survival rate and in individual growth rate, hence spawning age distribution. We use computed frequency response curves and analysis of the linearized dynamics to obtain two main results. First, the frequency response of the population is affected by the life history stage at which variability affects the population; varying growth rate tends to excite periodic resonance in age structure, while varying survival tends to excite low-frequency fluctuation with more effect on total population size. Second, decreasing adult survival strengthens the cohort resonance effect at all frequencies, a finding that addresses the question of how fishing and climate change will interact.Comment: much revised: the version accepted by Theoretical Population Biolog

Stage-dependent structured discrete time models for mosquito population evolution with survivability : solution properties, equilibrium points, oscillations, and population feedback controls

This paper relied on the investigation of the properties of the stage-structured model of coupled larvae and adult mosquito populations' evolution when parameterized, in general, by time-varying (or stage-dependent) sequences. In particular, the investigated properties were the non-negativity of the solution under non-negative initial conditions, the boundedness of the sequence solutions under any finite non-negative initial conditions, the equilibrium points, and the convergence conditions to them in the event that the parameterizing sequences converge to finite limits. Some further properties that were investigated relied on deriving the oscillation conditions of the solutions under certain conditions of the parameterizations. The use of feedback controls to decrease the foreseen numbers of alive mosquitoes in future evolution stages is also proposed. The proposed control actions are exerted on the birth rate and/or the maximum progression rate sequences. Some illustrative examples are also given