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This paper aims to quantify the loss (or leakage) of organic cattle to conventional value chains in Ireland and assess its economic and environmental impacts.

The paper adopts a Bio-economy Input-Output (BIO) model, a quantitative economic model representing the interdependencies between different sectors of the economy, to assess the economic and environmental impacts of organic leakage in the Irish beef sector.

The study reveals that 17% of organic cattle aged under 1 year old leave the organic value chain, leaking to the conventional market as a result of imbalances in the development of the beef value chain. The economic cost of this organic leakage is 5.66 million euros. Leakage also has environmental effects because of changes in lifecycle methane and nitrogen emissions based on longer finishing times on organic farms and chemical fertilisers applied on conventional farms. The organic leakage results in a reduction of 82 tons of methane emission and 52 additional tons of nitrogen emission, which leads to 11,484 tons of net global warming potential (GWP) for a 100-year time horizon.

Because of data availability, the research focussed on the baseline year 2015, which had national data available for disaggregation in Ireland. Therefore, researchers are encouraged to assess the economic and environmental impacts when more recent data are available and to analyse the change in the impacts over the years.

This study contributes to the discussion on organic conversion and provides valuable insights for stakeholders, especially policymakers, for the design of future organic schemes.

This is the first paper to assess organic leakage in the beef sector.

The traditional grey relational models directly describe the behavioural characteristics of the systems based on the sample point connections. Few grey relational models can measure the dynamic periodic fluctuation rules of the objects, and most of these models do not have affinities, which results in instabilities of the relational results because of sequence translation. The paper aims to discuss these issues.

Fourier transform functions are used to fit the system behaviour curves, redefine the area difference between the curves and construct a grey relational model based on discrete Fourier transform (DFTGRA).

To verify its validity, feasibility and superiority, DFTGRA is applied to research on the correlation between macroeconomic growth and marine economic growth in China coastal areas. It is proved that DFTGRA has the superior properties of affinity, symmetry, uniqueness, etc., and wide applicability.

DFTGRA can not only be applied to equidistant and equal time sequences but also be adopted for non-equidistant and unequal time sequences. DFTGRA can measure both the global relational degree and the dynamic correlation of the variable cyclical fluctuation between sequences.