Abstract
This paper studies the triad “concentration, diversification and dominance” in an ecosystem \((\Omega _{t})\) defined as the macro-fishery comprised by the entire commercial fish species landed in a specific geographical area and time horizon (1986:1–2011:12). This is faced computing alternative monthly concentration indices (CIs) based on the income shares of individual species and, afterwards, analysing the structural features and overall dynamics of the monthly time series related to each of the CIs. Special attention will be paid on categorising not only the long-term cycles, but also the seasonal components found in the series.
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Notes
The Basque offshore fleet belongs to the so-called Spanish 300, mainly operating in the Grand Sole.
Three main fleets compound the Basque fishing fleet. The inshore fleet (operating in relatively nearby (VIIId), the offshore fleet mainly made up by the Basque trawlers belonging to the so-called Spanish 300 operating in the Grand Sole, and the tuna freezer fleet operating out of European waters.
There is no rule for the determination of the value k, so the number of species included in the concentration index is in fact an arbitrary decision.
\(n_{e}\) is the number of equally sized species, which would generate the same value of concentration measure as that derived from the given size distribution. For example, if a particular size distribution generates HHI \(=\) 0.25, then 4 equal-sized species would also generate a value of 0.25 for this index \(((0.25)^{2}+(0.25)^{2}+(0.25)^{2}+(0.25)^{2}=0.25)\). In the literature of diversity \(n_{e}\) is also known as the effective number of species or true diversity.
HHI can be rearranged and related to the reciprocal of the species richness \((1/n_{t})\) and a direct function of the income share’s variance about the mean \((\sigma ^{2}):{\hbox {HHI}}=(1/n_{t})+n_{t}\sigma ^{2}\) . This presentation points up that HHI is directly related to both, the number of species in the ecosystem \((n_{t})\) and the inequality in income shares among the different species. Accordingly, the relation between \(n_{t}\) and HHI is not a simple one. Given the species richness \((n_{t})\), HHI increases with the variance, which is as well a function of \(n_{t}\).
The base of the log is in fact an arbitrary issue. Common values are 2, Euler’s number e, and 10. We have chosen base e.
EN weights each species exactly according to its share, while HHI pays more attention to the most dominant species since it involves the sum of the squares of the share, and the square of a very small number is a very very small number. So, uncommon species hardly contribute to the sum. That is way the effective number of species from the HHI will always be less than or equal to the effective number of species from EN.
We have taken advantage of R and the package uroot (Lopez-de-Lacalle and Díaz-Emparanza 2009).
We are not presenting the results for avoiding excessive number of pages, but they are available if someone asks for them.
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The authors are very grateful to the Managers of Santa Clara Fishermen Guilt of Ondarroa for having made available the data set used in this paper, Aintzina Oienarte for her assistance in data preparation and last, but not least, to the valuable comments of the editor and two anonymous referees. Del Valle and Astorkiza gratefully acknowledge financial support from Spanish Ministry of Economics and Competitiveness (MINECO/Project Ref: ECO2013-44436-R) and Díaz-Emparanza from (MINECO/Project Ref: ECO2013-40935-P) and UPV/EHU “Econometrics Research Group” (Basque Government Grant IT642-13). All the errors and opinions are the author’s responsibility.
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del Valle, I., Astorkiza, K. & Díaz-Emparanza, I. Measuring species concentration, diversification and dependency in a macro-fishery. Empir Econ 52, 1689–1713 (2017). https://doi.org/10.1007/s00181-016-1102-8
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DOI: https://doi.org/10.1007/s00181-016-1102-8
Keywords
- Macro-fishery
- Concentration index
- Time series
- Deterministic–stochastic trend
- Deterministic–stochastic seasonality
- Seasonal unit roots