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--- the_capri_data_base [2024/05/31 13:48] – massfeller
+++ the_capri_data_base [2026/03/13 13:20] (current) – add herd dynamics (Anna) massfeller
@@ Line 1826: / Line 1826: @@
 |Bull fattening (BULF)	|BULL: 20% lower meat output, variable inputs besides feed an young animals at 80% of average	|BULH: 20% higher meat output, variable inputs besides feed an young animals at 120% of average|
 |Heifers fattening (HEIF)|	HEIL: 20% lower meat output, variable inputs besides feed an young animals at 80% of average	|HEIH: 20% higher meat output, variable inputs besides feed an young animals at 120% of average| \\ Source: CAPRI Modelling System
+=== Implementation of herd dynamics in coding ===
+The dynamic relationships shown in Fig 3 are implemented in the animal sector specific equations in file coco1_estimA.gms, more specifically equations “e_yanib” (young animal balance) and “e_stocksA” (animal stock change equivalence):
+{{ :e_yanib.jpg?nolink&800 |}}
+Equation e_yaniB defines the stock change of all young animal types as the difference between production of young  animals and their use to source the flow of slaughtered animals. At the example of piglets ready for fattening or becoming young sows:
+Equation 1
+\begin{align}
+\text{STCM}_{YPIG}(t) = \text{GROF}_{YPIG}(t) - \text{GROF}_{IPIG}(t)
+\end{align}
+{{ :e_stocksa.jpg?nolink&800 |}}
+Equation e_stocksA is more complex, because it handles basically 3 different cases. The first is the situation in the non-cattle sectors (pigs, poultry, sheep) where production of young animals by breeding activites (sows, hens, ewes) and their raising is assumed to take place within the current year. Taking into account the mappings in the code, then the equation e_stocksA reads for the case of piglets:
+Equation 2
+\begin{align}
+&\text{SOWS}_{LEVL}(t+1) - \text{SOWS}_{LEVL}(t) = \text{STCM}_{YPIG}(t) \\
+&= \text{GROF}_{YPIG}(t) - \text{GROF}_{IPIG}(t)
+\end{align}
+As the input use of piglets only covers their use for slaughtered animals (either fatteners or replacement of old sows), the excess of piglet production and this “replacement” use matches with the change in the size of the breeding stock (sows) in the next year. Conversely, a piglet production falling short of the replacement need (STCMYPIG(t) < 0) means that the sow herd will be lower in the next year.
+In the cattle sector raising from calves to the adult animals may extend over several years and is therefore represented with specific raising activities that produce one animal category for the next stage, for example raising of male calves to become young bulls for the final fattening process. In this example (case #2), equation e_stocksA reads for the case of young bulls:
+Equation 1
+\begin{align}
+&\text{CAMR}_{LEVL}(t) - \text{CAMR}_{LEVL}(t-1) = \text{STCM}_{YBUL}(t) \\
+&= \text{GROF}_{YBUL}(t) - \text{GROF}_{IBUL}(t)
+\end{align}
+This equation is more intuitive considering that the activity level CAMRLEVL(t) is defined to be equal to the output = production of young bulls GROFYBUL(t) in the current year such that this appear on both sides of the equation, which may be simplified to read:
+Equation 1
+\begin{align}
+&\text{GROF}_{YBUL}(t) - \text{CAMR}_{LEVL}(t-1) =\\
+&\text{GROF}_{YBUL}(t) - \text{GROF}_{IBUL}(t) \\
+&\iff \text{CAMR}_{LEVL}(t-1) = \text{GROF}_{IBUL}(t)
+\end{align}
+In this form the equation just states that the current input use of young bulls (into the fattening activities BULL and BULH) must have been raised from young calves in the previous year such that e_stocksA just ensures this aspect of the herd category linkages in the cattle sector.
+The third case handeled by equation e_stocksA is the dynamics for young cows where the equation reads as follows:
+Equation 1
+\begin{align}
+&\text{HEIR}_{LEVL}(t) - \text{HEIR}_{LEVL}(t-1) \\
+&\quad + \text{COWS}_{LEVL}(t+1) - \text{COWS}_{LEVL}(t) \\
+&= \text{STCM}_{YCOW}(t) \\
+&= \text{GROF}_{YCOW}(t) - \text{GROF}_{ICOW}(t)
+\end{align}
+Considering again that it holds for the activity level of the raising process that HEIRLEVL(t) = GROFYCOW(t), the equation boils down to the requirement
+Equation 1
+\begin{align}
+&\text{COWS}_{LEVL}(t+1) - \text{COWS}_{LEVL}(t) \\
+&= \text{GROF}_{YCOW}(t-1) - \text{GROF}_{ICOW}(t)
+\end{align}
+The change in the total cow herd (DCOW+SCOW) in the next year must be equal to the excess of last year’s production of young cows (thus ready to enter the current cow herd) over the replacement need derived from slaughterings of old cows in the current year.
 ====Input allocation for feed====
@@ Line 2068: / Line 2136: @@
   * Output of manure at tail –depending on animal type, regional animal population and animal yields, as final weights or milk yields (see section on Output at tail).
   * Manure imports and exports (to the region)
-  * Input of mineral fertiliser –as given from national statistics at sectoral level. For details see [[The Regionalised Data Base (CAPREG)|"Annex: Fertilizer data used in Capri" in the CAPREG description ]]
+  * Input of mineral fertiliser –as given from national statistics at sectoral level. For details see[[https://www.capri-model.org/dokuwiki_help/doku.php?id=the_capri_data_base#annexfertilizer_data_used_in_capri|"Annex: Fertilizer Data used in CAPRI" in the CAPREG description]]
   * Input of crop residues, biological fixation, atmospheric deposition
   * Emissions (NH3, NOx, N2, N2O, CO2, CH4, NO3, C from soil erosion) only for nitrogen and carbon, and removals (carbon sequestration) only for carbon