# Modelling a Transition from Purebred Romney to Fully Shedding Wiltshire–Romney Crossbred

^{*}

## Abstract

**:**

## Simple Summary

## Abstract

## 1. Introduction

^{2}) Wiltshire–Romney cross flock to achieve a fully shedding flock. System dynamics modelling was used in this analysis to capture flock dynamics with associated feed demand, production, cashflow, and profit implications before, during, and post-grading up transition.

## 2. Materials and Methods

#### 2.1. Flock Dynamics

#### 2.1.1. Flock Dynamics of Self-Replacing Romney Flock

_{i}) class (Y

_{i}) each year were the sum of ewes in the previous age class (Y

_{i−1}) minus ewes leaving the flock due to deaths (D

_{i−1}) and culling (C

_{i−1}) (Equation (1)). The ewe flock was therefore the sum of ewes in six age classes (Equation (2)). When a self-replacing flock was modelled, it was held at a constant size with the flock replacement requirements (R) calculated as the sum of all ewes leaving the flock due to death and culling (Equation (3)). Death rates of 5.2% for Y

_{2 to 6}ewes and 2% for Y

_{1}ewes were assumed [2]—this included missing ewes, with a flock replacement rate of 25% that is typical of New Zealand sheep breeding flocks [21]. All ewes in Y

_{6}were culled after their lambs were weaned.

_{i}), L (the average flock lambing rate as lambs weaned per ewe presented for breeding; 132%) [2], P (proportion of ewes bred with a Wiltshire sire, i.e., when modelling the self-replacing Romney flock P = 0 to produce only purebred Romney lambs), and the relative reproductive performance for each ewe age class (RR

_{i}peaking in Y

_{5}, as detailed in [16]). The number of lambs born as singles and twins depended on whole flock reproductive performance [22]. Sheep farmers in New Zealand choose whether to first breed ewes to lamb at 14 months or two years of age; in this study, it was assumed that ewes had their maiden lambing at two years of age (Y

_{2}), so RR

_{1}= 0.

#### 2.1.2. Flock Dynamics During Transition

_{i}consistent between crosses.

_{1 to 6}). The size and age structure of crossbred flocks during transition were determined primarily by ewes entering (such as ewe lambs entering the Y

_{1}age class according to Equation (5) and then aging according to Equation (1)) and leaving the flock. Numbers of crossbred ewe lambs entering Y

_{1}during transition were determined by the selection intensity (S) of 50% applied to all weaned crossbred ewe lambs after shedding scoring in January (Equation (5)). Lambs were approximately five months old in January, which has been identified as the best time to assess fleece shedding in New Zealand lambs [7]. The selection event occurred for crossbred ewe lambs each year, and ewe lambs with the highest shedding scores remained on-farm to enter crossbred ewe flocks. Crossbred ewe lambs not selected, and ram lambs were sold prior to winter.

#### Ewe Culling during Transition

_{2–6}ewes and 2% for Y

_{1}ewes, consistent with the self-replacing Romney flock. The numbers of ewes in each age class and flock were estimated according to Equations (1), (2), and (5) for all crosses. Cull rates differed between the flocks of various crosses during transition in order to limit the changes in the total annual sheep feed demand and to hasten the time taken to replace the base Romney flock with an approximately equivalent flock of the desired final cross (Table 1). Cull rates were 4% for Y

_{2–3}ewes of all crosses during the grading up transition, assuming that only barren ewes in these age classes were culled [23]; this assumed cull rates were minimised when aiming to increase ewe numbers for the desired final cross. For the self-replacing Romney flock pre-transition and the flock of the desired final cross (either ⅞W⅛R or straightbred), there were six age classes of ewes, with all Y

_{6}ewes culled after weaning. When modelling a grading up transition, flocks not of the desired final cross (not either ⅞W⅛R or straightbred) only had five age classes of ewes, with all Y

_{5}ewes culled after weaning and no ewes in Y

_{6}. Additionally, to maintain a consistent annual sheep feed demand, the cull rate was varied for ewes in Y

_{4}for different crosses (Table 1), and at specific time points, all remaining ewes not of the desired final cross were culled (timings shown in results). Once the ewe flock of desired final cross (⅞W⅛R or straightbred) achieved the same feed demand as the base Romney flock, it was modelled as a self-replacing flock (Figure 1) with six age classes and a replacement rate of approximately 25% calculated from Equation (3).

#### 2.2. Wool Production

_{i}; w

_{0.5}= 0.50, w

_{1}= 0.95, w

_{2}= 1.01, w

_{3}= 1.08, w

_{4}= 1.05, w

_{5}= 1.01, and w

_{6}= 0.97) [24,25,26] and the numbers of sheep in each age class (Y

_{i}) in Equation (6). The wool production of the Wiltshire–Romney crossbred flocks was also estimated using Equation (6), with W altered according to shedding score.

#### Wool Shedding

#### 2.3. Feed Demand

#### 2.4. Economics

#### 2.4.1. Income

#### 2.4.2. Expenses

#### 2.4.3. Net Present Value Analysis

_{Sheep}) on a per ha basis was calculated based on changes in sheep numbers and production. A stable beef enterprise COS (COS

_{Beef}) of $81.24/cattle stock unit was assumed [2]. The grading up transition period was up to 15 years and included the total time taken for the flock of desired final cross ewes to reach a size with a similar feed demand to the base Romney flock. Changes in the numbers of ewes in each age class of the desired final cross flock occurred up until approximately 25 years from the beginning of the grading up transition, affecting flock productivity and COS. Therefore, NPV analyses were also conducted for 25-year periods.

_{Sheep}is the proportion (0 ≤ Feed

_{Sheep}≤ 1) of the total farm feed consumed by sheep (60% for the base Romney flock), and Area is the farm total effective area of 530 ha [2]. Feed

_{Sheep}varied during the grading up transition between approximately 55% and 65% according to changes in the total annual sheep feed demand. Additionally, t = each year during the time period analysed, either the grading up transition period only or 25 years from transition start. Discount rates (r) of 10% to reflect long-term New Zealand business lending interest rates [43] and 6% to reflect current lower interest rates, i.e., 2017/18 rates [44], were used. Economic values in this analysis were all in real 2017/18 terms, and the discount rates represented the real opportunity expenses for farmers investing in the grading up transition scenarios investigated.

#### 2.4.4. Wool Price Sensitivity Analysis

#### 2.4.5. Operating Profit

_{Sheep}was estimated using 2018 national average market values of $123 for replacement ewe lambs, $179 per one-year-old ewe, $160 per ewe aged two-to-six years, and $289 per ram [47]. A base V

_{Beef}value of $441,438 was adjusted in accordance with changes in the proportion of farm feed consumed by sheep. Changes in V

_{Sheep}and V

_{Beef}for annual OP were derived from the capital value of the current year (closing value) minus the capital value of the previous year (opening value). The ΔV

_{Sheep}= 0 and ΔV

_{Beef}= 0 for the base self-replacing Romney flock when it was assumed stock numbers were steady.

## 3. Results and Discussion

#### 3.1. Shedding Score

#### 3.2. Flock Dynamics

#### Ewe Age

#### 3.3. Feed Demand

#### 3.4. Production

#### 3.5. Economics

#### 3.5.1. Cashflow During Transition

#### 3.5.2. Net Present Value Analysis

#### 3.5.3. Wool Price Sensitivity Analysis

#### 3.5.4. Operating Profit

#### 3.6. General Discussion

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Simplified diagram of the flock dynamics for a flock grading up transition from purebred Romney (Rom) to either a third (3X or ⅞W⅛R) or fourth (4X or straightbred) generation crossbred. Lambs weaned (LW) for each cross are a product of P (proportion of ewes bred with a Wiltshire sire), L (lambs weaned per ewe presented for breeding), flock (number of ewes in the flock), and RRi (relative reproductive performance of ewes for each age class in the flock)—where P = 1 produces crossbred lambs closer to a Wiltshire breed than their dams to further the grading up transition. Rom, 3X, and 4X flocks can be self-replacing when P = 0 by calculating replacement ewe lamb requirements (R) based on numbers of ewes leaving to flock due to culling and death. First (1X or ½Wiltshire½Romney (½W½R)) and second (2X or ¾W¼R) cross flocks can only produce lambs of further crosses (and 3X flock will produce only 4X lambs if the 4X flock is the desired final cross). The selection intensity (S) of crossbred ewe lambs determines the proportion that enter the crossbred flocks, with all remaining lambs sold

^{1}.

^{1}The symbols in the diagram are as follows: rectangles represents stocks (or groups) of sheep of a specific age and breed; white arrows are flows representing the movement of sheep between groups or, where there is a cloud, entering or leaving the flock; circles are convertors with functions affecting flows; and black arrows are connectors that join stocks, flows, and convertors.

**Figure 2.**Simplified example of the effect of a selection intensity of 50% on the average shedding score in ½W½R ewe lambs from Romney dam with a score of 0 and Wiltshire sire with a score of 5.

**Figure 3.**Proportion of ewes of each Wiltshire–Romney cross (e.g., ½W½R was ½Wiltshire½Romney and straightbred was assumed to be a stable Wiltshire breed) with each shedding score.

**Figure 4.**Numbers of ewes of each cross and total ewe numbers during a grading up transition from base Romney to either (

**a**) ⅞Wiltshire⅛Romney or (

**b**) straightbred. ↓ Where the grading up transition period has finished and the desired final cross flock (either ⅞W⅛R or straightbred) has reached an equivalent feed demand to the base Romney flock.

**Figure 5.**Proportion of total farm feed supply consumed by sheep, constrained between 0.55 and 0.65 of total farm feed supply, for a grading up transition from base Romney to a desired final cross of either ⅞W⅛R or straightbred. ↓ Where the grading up transition period has finished and the desired final cross flock (⅞W⅛R or straightbred) has reached an equivalent feed demand to the base Romney flock.

**Figure 6.**Total lambs weaned, sold, and wool sold during a grading up transition from base Romney to a desired final cross of either (

**a**) ⅞W⅛R or (

**b**) straightbred. RHS = right hand side vertical axis. ↓ Where the grading up transition period has finished and the desired final cross flock (⅞W⅛R or straightbred) has reached an equivalent feed demand to the base Romney flock.

**Figure 7.**Total sheep enterprise income, expenses, and cash operating surplus (COS) during a grading up transition from base Romney to a desired final cross of either (

**a**) ⅞W⅛R or (

**b**) straightbred, with the base Romney sheep enterprise COS for comparison. RHS = right hand side vertical axis. ↓Where the grading up transition period has finished and the desired final cross flock (⅞W⅛R or straightbred) has reached an equivalent feeddemand to the base Romney flock.

**Figure 8.**Annual operating profit during a grading up transition from base Romney to a desired final cross of either a). ⅞W⅛R or b). Straightbred, with the base Romney operating profit for comparison. ↓ Where the grading up transition period has finished and the desired final cross flock (⅞W⅛R or straightbred) has reached an equivalent feed demand to the base Romney flock.

**Table 1.**Cull rates (%) for ewes of each age class and Wiltshire–Romney cross during the whole-flock breed grading up transition from Romney to a final cross of either ⅞Wiltshire⅛Romney (⅞W⅛R) or straightbred

^{1}.

Cull Rate for Ewes of Various Age Classes (%) ^{2} | |||
---|---|---|---|

Ewe Type | Base Romney | Final Cross ⅞W⅛R | Final Cross Straightbred |

Self-replacing base Romney | Two-to-five-year-olds: 19 Six-year-olds: 100 | - | - |

Romney | - | Two-to-four-year-olds: 4 Five-year-olds: 100 | Two-to-four-year-olds: 4 Five-year-olds: 100 |

½W½R | - | Two-to-three-year-olds: 4 Four-year-olds: 33 Five-year-olds: 100 | Two-to-three-year-olds: 4 Four-year-olds: 33 Five-year-olds: 100 |

¾W¼R | - | Two-to-three-year-olds: 4 Four-year-olds: 33 Five-year-olds: 100 | Two-to-four-year-olds: 4 Five-year-olds: 100 |

⅞W⅛R | - | Two-to-five-year-olds: 4 | Two-to-four-year-olds: 4 Five-year-olds: 100 |

Straightbred | - | - | Two-to-five-year-olds: 4 |

Self-replacing ⅞W⅛R | - | Two-to-five-year-olds: 19 Six-year-olds: 100 | - |

Self-replacing straightbred | - | - | Two-to-five-year-olds: 19 Six-year-olds: 100 |

^{1}Outside of the grading up transition period, self-replacing flocks (initial Romney and the final cross once the desired size was reached) had a replacement rate of 25% with death rates of 5.2%, and all six-year-old ewes were culled after weaning. For example, during the transition to a final flock of straightbred ewes, two-to-four-year-old ewes in the straightbred flock had a culling rate of 4%, and all five-year-old ewes were culled. Then once the transition period was finished, the straightbred flock was self-replacing and had a culling rate of 21% for two-to-five-year-old ewes, and all six-year-old ewes were culled.

^{2}Cull rates were applied to ewes in each specific age class before they would have moved into the next age class, e.g., when four-year-old ewes had a cull rate of 33%, 66% of live four-year-old ewes would move into the fifth ewe age class. All one-year-old ewes were assumed to not be culled.

**Table 2.**Prices for sold sheep, ewes of various age classes (Yi), and lambs sold either prime (direct to slaughter) or store (for another farmer to grow for slaughter).

Sheep Class | Timing of Sale | Value ($/head) ^{1} | Price Data |
---|---|---|---|

Y_{3 to 6} ewes | Early December ^{2} | 113.73 | [2] |

Y_{2} ewes | 134.64 | ||

Prime lambs | Early February | 107.44 | [39] |

Mid-February | 107.10 | ||

Store lambs | Mid-February | 84.00 |

^{1}Prices per head for lamb sales were estimated from weekly schedule prices per kg of carcass weight and their weight at sale.

^{2}The majority of ewes were culled in early December at weaning, with a small proportion culled in June at scanning.

**Table 3.**Expenses for shearing of sheep with various shedding scores [7] based on 2017/18 New Zealand shearing contract rates reported by [41]. Romney shearing expenses consisted of per head expenses of $4.89 for a full summer shear, $4.09 for a second winter shear (with twice yearly shearing policies), and $2.00 for a full crutch

^{1}.

Shedding Score | Equivalent Shearing Required | Expense ($/head) |
---|---|---|

0–0.99 | Twice per year and crutch | 10.98 |

1.00–1.99 | Twice per year | 8.98 |

2.00–2.99 | Once per year | 4.89 |

3.00–3.99 | Back wool removal ^{2} | 2.00 |

4.00–5.00 | Nil ^{3} | 0.00 |

^{1}Crutching is the removal of wool from the belly and breech.

^{2}Assuming only a small volume of wool requires removal from the back of the sheep, with the equivalent expense as crutching.

^{3}Assuming the volume of unshed wool is minimal and does not require removal through shearing.

**Table 4.**Predicted average shedding scores of sheep of varying crosses (e.g., ½W½R is a first cross ½Wiltshire½Romney) for a whole flock grading up transition from Romney to either ⅞Wiltshire⅛Romney or straightbred—this shows the effect of applying a selection intensity of 50% to crossbred ewe lambs.

Cross | Pre-selection Average Shedding Score with Standard Deviation | Post-selection Average Shedding Score |
---|---|---|

Romney | 0 ± 0 | 0 |

½W½R | 2.5 ± 0.95 | 3.14 |

¾W¼R | 4.07 ± 0.33 | 4.29 |

⅞W⅛R | 4.64 ± 0.23 | 4.8 |

Straightbred | 4.9 ± 0.10 | 4.97 |

**Table 5.**Average age of ewes in flock of different crosses at various time points (T) from the start of a grading up transition from Romney to a desired final cross of either ⅞W⅛R or straightbred.

Final Cross ⅞W⅛R | Final Cross Straightbred | |||
---|---|---|---|---|

Cross | T (years) | Flock Average Age (years) | T (years) | Flock Average Age (years) |

Romney | T0 | 3.45 | T0 | 3.45 |

T4 | 4.46 | T4 | 4.46 | |

½W½R | T7 | 4.02 | T7 | 4.02 |

¾W¼R | T11 | 4.48 | T9 | 3.77 |

⅞W⅛R | T13 | 3.92 | T15 | 4.99 |

T25 | 3.48 | - | - | |

Straightbred | T16 | 3.45 | ||

T25 | 3.40 |

**Table 6.**Net present values of annual farm cash operating surplus (sheep and beef enterprises combined) of the maintenance of the status quo Romney flock compared with the grading up transition from Romney to a desired final cross of either ⅞W⅛R or straightbred. Net present analyses were also conducted for each scenario with varying farmgate wool prices.

Scenario | 15 Years ^{1} | 25 Years | ||
---|---|---|---|---|

6% Discount Rate ^{2} | 10% Discount Rate | 6% Discount Rate | 10% Discount Rate | |

Wool Price $2.15/kg Greasy ^{3} | ||||

Base Romney | 3,622,240 | 2,910,060 | 4,660,704 | 3,407,450 |

Final cross ⅞W⅛R | 3,875,321 | 3,115,634 | 4,980,752 | 3,645,054 |

Final cross straightbred | 3,871,501 | 3,116,354 | 4,978,018 | 3,646,396 |

Wool price $1.15/kg Greasy | ||||

Base Romney | 3,378,108 | 2,713,927 | 4,346,581 | 3,177,795 |

Final cross ⅞W⅛R | 3,772,669 | 3,021,288 | 4,878,100 | 3,550,708 |

Final cross straightbred | 3,806,774 | 3,046,451 | 4,910,665 | 3,575,082 |

Wool Price $3.15/kg Greasy | ||||

Base Romney | 3,872,050 | 3,110,753 | 4,982,132 | 3,642,447 |

Final cross ⅞W⅛R | 3,978,503 | 3,210,510 | 5,083,974 | 3,739,946 |

Final cross straightbred | 4,012,361 | 3,235,480 | 5,116,252 | 3,764,111 |

Wool Price 4.15 $/kg Greasy | ||||

Base Romney | 4,116,182 | 3,306,886 | 5,296,255 | 3,872,103 |

Final cross ⅞W⅛R | 4,092,195 | 3,311,438 | 5,223,204 | 3,853,103 |

Final cross straightbred | 4,097,288 | 3,319,807 | 5,218,817 | 3,857,043 |

^{1}NPV analysis was conducted for either 15 (focusing only on the grading up transition period) or 25 years (including the time taken for ewe numbers in each age class of the final cross flock to stabilise).

^{2}Discount rates representing current 2018 interest rates of 6% [44] and long-term business lending interest rates of 10% [43].

^{3}Wool price used in the main part of the analysis for the 2017/18 production year [2].

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**MDPI and ACS Style**

Farrell, L.J.; Morris, S.T.; Kenyon, P.R.; Tozer, P.R.
Modelling a Transition from Purebred Romney to Fully Shedding Wiltshire–Romney Crossbred. *Animals* **2020**, *10*, 2066.
https://doi.org/10.3390/ani10112066

**AMA Style**

Farrell LJ, Morris ST, Kenyon PR, Tozer PR.
Modelling a Transition from Purebred Romney to Fully Shedding Wiltshire–Romney Crossbred. *Animals*. 2020; 10(11):2066.
https://doi.org/10.3390/ani10112066

**Chicago/Turabian Style**

Farrell, Lydia Jane, Stephen Todd Morris, Paul R. Kenyon, and Peter R. Tozer.
2020. "Modelling a Transition from Purebred Romney to Fully Shedding Wiltshire–Romney Crossbred" *Animals* 10, no. 11: 2066.
https://doi.org/10.3390/ani10112066