Appendix F: Example input data set

The description of the simulation model in Chapter 3 identified the data requirements of each individual component.

This appendix presents a complete example data set for the model. Much of the data are entered into the model in an interactive mode, and the computer code prompts the user to enter a certain data item or items. E a data item is inconsistent with previously entered data the user is prompted accordingly. Table F.1 presents an example of forage data and the associated distances walked. Three year-types are used to represent the range of forage conditions occurring for this illustrative system. Although they have been labelled 'poor', 'average' end 'good' according to dry matter yield and timing of plant growth, such labels have no operational significance in the model. The sum of the probabilities of the three year-types must equal unity.

Table F.2 illustrates the minimum data needed to estimate average liveweight growth curves and associated liveweight boundaries using the procedure presented in Appendix A. This procedure need not be used if sufficient data are available to specify these curves more precisely. The data presented in Table F.2 are consistent and satisfy the restrictions on the functions given in Appendix A. E data are entered which are not consistent, the user is prompted that the data must be revised.

Table F.3 presents example data for an approximate specification of the relationships associated with milk production, using the procedures in Appendices B and C which are appropriate when sufficient data are not available for exact specification of these functions. The data are entered interactively and checked for consistency.

Table F.4 presents data on reproduction, assuming that relevant field data are inadequate and the procedures given in Appendix D are applied to estimate the necessary relationships. Table F.5 presents the data required to estimate the mortality functions used in the model for deaths due to natural causes, such as stillbirths, predators, etc. Deaths due directly to starvation are accounted for separately in the model. The age effect on mortality for the whole range of ages is estimated using this minimum data set according to the procedure given in Appendix E.

F.1 Sample data for the specification of forage on offer and distances walked

a. Monthly details for each year-type

Calendar Month	Year- Types
	'poor'			'average'			'good'
	Q a	d b	D c	Q	d	D	Q	d	D
1 = Jan.	2.5	0.56	11	3.0	0.62	10	3.5	0.62	9
2	2.3	0.54	11	2.8	0.56	11	3.3	0.59	10
3	2.0	0.46	12	2.5	0.53	12	2.9	0.54	11
4	1.7	0.44	15	2.1	0.50	12	2.6	0.50	12
5	1.3	0.42	15	1.7	0.48	12	2.2	0.48	12
6	1.0	0.40	17	1.3	0.42	15	1.8	0.47	12
7	0.7	0.40	17	0.9	0.40	16	1.5	0.40	12
8	0.6	0.38	17	1.4	0.40	16	1.7	0.55	11
9	1.2	0.40	17	1.9	0.55	11	2.5	0.60	10
10	2.1	0.60	10	2.7	0.60	10	3.0	0.62	10
11	2.7	0.60	8	3.4	0.62	8	3.9	0.65	8
12= Dec.	2.8	0.60	8	3.3	0.62	8	3.7	0.65	8

b. Other details for each year-type

Parameter	Year-types
	'poor'	'average'	'good'
Probability of occurrence	0.25	0.50	0.25
Month of start of growing season	9	9	8
Threshold forage quantity on offer (t/ha) below which intake is reduced (Q*)	0.8	0.8	0.8
Threshold distance walked (km) above which intake is reduced (D*)	14	14	14

^a Q = quantity of dry matter on offer (t/ha).
^b d = digestibility (fraction)
^c D = distance walked (km/day).

Table F.2 Sample data for the estimation of average liveweight growth curves and associated liveweight boundaries

Parameter	Males	Females
Average liveweight at birth (kg)	25	22
Age at the point of inflection (months)	20	18
Average liveweight at the point of inflection (kg)	240	200
Age at maturity (months)	52	48
Average liveweight at maturity (kg)	400	350
Coefficient of liveweight variation for mature animals a	0.25	0.25

^a The coefficient of liveweight variation is defined as the ratio between the standard deviation of liveweight and average liveweight at a given age. The value given here is applicable for animals older than 18 months. For younger animals, see Section 3.3.2.1 for the values of this coefficient assumed in the model.

Table F.3 Sample data for the estimation of relationships associated with milk production

Parameter	Value
Age interval (t2 - t3) a during which cows achieve their maximum milk yield (years)	6-8
Maximum milk yield per lactation for cows within this age interval (kg)	1 000
Age less than t2 for which milk yield is known (t1) b (years)	3
Fraction of maximum milk yield achieved at age t1	0.8
Age greater than t3 for which milk yield is known (t4) c (years)	13
Fraction of maximum milk yield achieved at age t4	0.6
Maximum length of lactation (months)	9
Fraction of total lactation milk yield produced during first 2 months post-partum	0.35
Fraction of cows in the population that let down milk for human consumption in the absence of a suckling calf	0.7
Fraction of potential milk yield let down by these cows	0.8
Average energy content of milk (MJ/kg) d	3.6

^a Age t₂ must he less than t₃.

^b For best estimation of the age effect on milk yield, this should be the youngest age (i.e. age at first calving) for which milk yield is known.

^c For the best estimation of the age effect on milk yield, this should be the oldest age for which milk yield is known.

^d Computed according to relationship (2.15), given the butter fat and solids-not-fat contents of milk.

Table F.4 Sample data for the estimation of relationships associated with reproduction

Parameter	Value
Minimum age at first calving of heifers in best liveweight condition (months)	36
Average age at first calving of heifers in average liveweight condition (months)	42
Maximum age at first calving of heifers in poorest liveweight condition (months)	52
Age interval (t2 - t3) a during which cows achieve maximum fertility (years)	5-8
Average annual calving rate for cows within this age interval (fraction)	0.80
Age less than t2 for which the calving rate is known (t1) b (years)	4
Average calving rate at age t1 (fraction)	0.60
Age greater than t3 for which the calving rate is known (t4) c (years)	12
Average calving rate at age t4 (fraction)	0.50
Fraction of barren females in the population	0.05
Fraction of females in the population with bad conformation	0.03

^a Age t₂ must be less than t₃.

^b For best estimation of the age effect on reproduction, this age should he the youngest age (i.e. age at first calving) for which calving rates are known.

^c For best estimation of age effect on reproduction, this should he the oldest age for which calving rates are known.

Table F.6 illustrates the data needed to specify an initial herd. In this example, the initial herd consists of six animals, including two (animals 2 and 6) calves at foot. This data set must be consistent with the calendar date at the start of the simulation, in this example September 1981.

The data set for each animal in Table F.6 can best he illustrated by elaboration of the details for animal 5. This animal is in class 15, so it is a cow with a suckling calf at foot to which it is linked. The calf is number 6 as indicated in the 2nd column of row 5. Dams and suckling calves are linked forwards and backwards because they are treated together in terms of their food energy demands. Animal 5 weighs 305 kg at the beginning of September 1981 and has had one calf, the calf currently at foot which was horn in May 1981 (date 8105). This cow conceived again in August 1981 (date 8108) and therefore is expected to calve again in May 1982. Finally, the last column of row 5 specifies that the cow would be expected to let down 75% of her milk yield if she were milked after her calf is weaned.

Table F.5 Sample data for the estimation of relationships associated with mortality due to natural causes other than starvation

Parameter	Value
Average calf survival rate up to 3 months (fraction)	0.85
Average calf survival rate up to 1 year (fraction)	0.80
Age interval (t2 - t3) a of lowest average mortality rate (years)	3-9
Average annual mortality rate within this interval (fraction)	0.03
Age less than t2 for which the mortality rate is known (t1) b (years)	2
Average annual mortality rate at age t1 (fraction)	0.04
Age greater than t3 for which the mortality rate is known (t4) c (years)	13
Average annual mortality rate at age t4 (fraction)	0.10

^a Age t₂ must be less than t₃.

^b For best estimation of the age effect on mortality, this should be 2 years.

^c For best estimation of the age effect on mortality, this should he the oldest age for which mortality rates are known.

Table F.6 Attributes of animals in herd at the start of simulation, as of September 1981 (8109)

Animal No.	No. of Linked Dam or Calf a	Birth Date	Animal Class b	Current Live-weight (kg)	No. of Known Parturition	Date of Last Calving	Date of Conception	Let-Down Fraction
1	2	7303	15	340	4	8107	-	0.0
2	1	8107	1	50	-	-	-	-
3	-	7501	14	358	2	7908	8107	0.0
4	-	7912	11	180	0	-	-	0.75
5	6	7610	15	305	1	8105	8108	0.75
6	5	8105	8	65	0	-	-	0.75

^a In the case of a cow with a calf at foot, provides the corresponding serial number of the calf and vice-versa.

^b The codes used in the model for different classes of cattle are:

1 = male calf at foot
4 = weaned male (after class 1)
6 = barren female calf at foot
7 = female calf at foot with bad conformation
8 = fertile female calf at foot with good conformation
9 = barren heifer (after class 6)
10 = heifer with bad conformation (after class 7)
11 = fertile heifer with good conformation (after class 8)
12 = barren female in the breeding herd (after class 9)
13 = had conformation female in the breeding herd (after class 10)
14 = non-lactating female in the breeding herd (after class 11)
15 = lactating female with calf at foot
16 = lactating female without calf at foot.

^c In this example, some cows let down milk when a calf is not suckling; others, such as no.1, do not. The let-down fraction of 0.75 for cow no. 5 implies that 75% of her potential milk production can be extracted for human consumption after the weaning of her calf.