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SID 5
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SID 5 (2/05)
Project identification
1.
Defra Project code
2.
Project title
LS3307
Seasonal infertility in the domestic pig; database
analyses to evaluate factors responsible
3.
Contractor
organisation(s)
University of Nottingham
Roslin Institute
54. Total Defra project costs
5. Project:
Page 1 of 17
£
136,585
start date ................
01 January 2002
end date .................
31 August 2005
6. It is Defra’s intention to publish this form.
Please confirm your agreement to do so. ................................................................................... YES
NO
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Executive Summary
7.
The executive summary must not exceed 2 sides in total of A4 and should be understandable to the
intelligent non-scientist. It should cover the main objectives, methods and findings of the research, together
with any other significant events and options for new work.
Background and approach adopted
The major manifestation of seasonal infertility in domestic pigs are low litter sizes in those animals
conceiving in summer (number born alive: NBA). There have been numerous extensive reviews of this
subject published in the literature in recent years ranging from assessments of breeding activity in closed
populations of the European wild pig to detailed physiological studies which have attempted to examine
endocrinological patterns in response to changes in daylength, exogenous treatment (e.g. administration
of melatonin), nutrient inputs, impact of ambient temperature and interactions between these, and other,
factors; seasonal patterns in the boar (as evidenced by, for example, changes in semen quality and libido
which are not thought to be influenced by those ambient temperatures normally encountered in the UK)
are also important. A ‘boar’ effect in expression of seasonality in sows is also possible. All these
investigations have been based only on an assessment of phenotypic differences.
It is considered by many that the problem of seasonality in domestic pigs, particularly those
maintained outdoors, is related to the Wild pig from which the domesticate is derived. This suggests a
genetic component to the problem as seasonality is not normally a selection trait in breeding programmes
However, magnitude of genetic variation in addition to the underlying physiological mechanisms governing
seasonality remain to be adequately defined.
Defining the extent of the problem is a fundamental initial step in any investigation. In addition,
and bearing in mind the possible genetic component of seasonality, analyses of data should involve
estimation of genetic and environmental effects as well as phenotypic effects. It is this complete analysis
that has been essentially absent from previous studies.
The analysis was conducted along the following broad lines: investigations to determine the
existence of seasonal fluctuation in weekly mean NBA and successful (resulting in ‘to term’ pregnancy)
service number (SERVE) were conducted on data from the database of fertility records belonging to
Cotswold Pig Development Company (now part of JSR Genetics Ltd). The records came from eighteen
indoor units throughout the UK, over the period 1979 to 2001. Analyses included the time (of farrowing) of
year of each record and its interactions between sire and unit / year cohort using a sire model, to
determine variation in average sire daughters or unit / year cohort NBA and SERVE over time of year.
Where significant, the sire by time of year interaction could be interpreted as unambiguous evidence of
seasonality, since sire variance cannot be affected by the time of year. Interactions between unit / year
cohort and time of year would provide evidence of a link between season and factor level, the ‘seasonal’
nature of the effect to be decided by causality. In addition to allowing an assessment of the phenotypic
extent of the problem of seasonality by examining reproductive performance in individual sows, the data
also allowed boar reproductive traits to be examined.
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Results
The results presented in the current final study have failed to detect significant fluctuations in litter size and
successful service (i.e. leading to pregnancy) over the year, with both the linear and polynomial time of
year effects being small and indistinguishable from zero. The failure to detect genetic variation in any
fluctuations in NBA or SERVE over the year confirms that there is little or no additive genetic basis to
susceptibility of NBA and SERVE to the time of year of farrowing. Even examination of the mean weekly
residuals from the preliminary analyses, which contained no time of year component, does not reveal a
convincing seasonal trend. Thus, one might conclude that there is no seasonal influence on litter size or
successful serve. Yet the topic has been documented many times in the past, although the effect on litter
size appears smaller than those reported for other traits. The identification of a significant unit by year
interaction with the time of year may provide a partial explanation to the persistence of the issue. The
differential ‘seasonal’ effect on litter size and successful serves over years is likely to be due to factors that
affect some but not all units and years. Thus, doubt would be cast on photoperiod being a causal factor
since it is consistent over years and fairly similar over the UK (even more so considering all units used
indoor housing); but factors such as summer temperature and the requirement and quality of staffing
cover, which will show greater differences between years and units will be more plausible as causal
factors. Evidence supporting this viewpoint comes from Tantasuparuk et al. (2000), who detected smaller
litter total number born in a distinct wet season in the tropics, but with little change in daylength. Therefore,
what appears to as a seasonal effect on litter size, may in fact be an environmental effect that coincides
with seasonal changes.
Conclusion
The current study has determined only very small, insignificant, fluctuations of NBA and SERVE over
weeks 3 to 50 of the year, with no significant linear or polynomial effect of time of year detectable.
Analyses including interactions of sire with linear and polynomial time of year covariates demonstrated
that these interactions between sire and season were not significant and could be safely removed from a
mixed model of NBA or SERVE, and indicated a lack of detectable genetic variation causing fluctuation of
NBA and SERVE over the time of year. Linear and polynomial interactions of unit / year cohort and season
were very small but significant, indicating that the method employed is sufficient to detect small effects
Project Report to Defra
8.
As a guide this report should be no longer than 20 sides of A4. This report is to provide Defra with
details of the outputs of the research project for internal purposes; to meet the terms of the contract; and
to allow Defra to publish details of the outputs to meet Environmental Information Regulation or
Freedom of Information obligations. This short report to Defra does not preclude contractors from also
seeking to publish a full, formal scientific report/paper in an appropriate scientific or other
journal/publication. Indeed, Defra actively encourages such publications as part of the contract terms.
The report to Defra should include:
 the scientific objectives as set out in the contract;
 the extent to which the objectives set out in the contract have been met;
 details of methods used and the results obtained, including statistical analysis (if appropriate);
 a discussion of the results and their reliability;
 the main implications of the findings;
 possible future work; and
 any action resulting from the research (e.g. IP, Knowledge Transfer).
1 Introduction
Vestiges of a seasonal fluctuation in reproductive performance have been documented in the domestic pig
despite selection over many generations for all-year-round reproduction, with reports of depressed litter size in
spring / summer (after winter / spring matings; Martinet-Botte et al., 1987) and larger litters in winter after autumn
matings (Claus and Wieler, 1985), and optimal returns to oestrus after weaning and conception rates in autumn
months (Claus and Weiler, 1987). However, the inconsistent pattern of the problem ensures that the exact nature
of seasonality in pigs remain vague. Furthermore, it is unknown how changes in season, presumably mediated
through changing daylight hours, might trigger physiological mechanisms affecting fertility since investigations into
diurnal fluctuations in melatonin levels in the pig are equivocal. Finally it should be noted that phenotypic
seasonality may not be associated with a genetic predisposition for such a response.
SID 5 (2/05)
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The programme concentrated on numbers born alive (NBA) as this is the parameter most likely to be influenced
by seasonal influences. The seasonal effect, if indeed there is one, on NBA appears small at less than one piglet
per litter (Claus and Weiler, 1987; Martinat-Botté et al, 1987), and dependable detection requires a large number
of records. However, the phenotypic depression of NBA and other fertility traits (such as post-weaning return to
oestrus and conception rates) in summer months, which is often cited as evidence of a seasonal effect on pig
fertility, coincides with the period when management conditions are most likely to have an influence on
reproductive performance (i.e. through summer holiday cover). This leads to the possibility that the purported
seasonal fluctuation in litter size might actually be a seasonal management effect.
Identification of variation in the interaction of a measure of season with a source of variation in a fertility trait
among sows would confirm definitively the existence of seasonal fluctuation as a physiological phenomenon so
long as the source of variation is incapable of being directly influenced by season itself. Genetic variation is a
perfect example of a source of variation that is immune to the surrounding environment, so causality of variation
in the interaction must lie in the genetic variation rather than the measure of season. Any variation in the
interaction between sire effect on a trait and season would indicate that there is a genetic component to
susceptibility to seasonal fluctuation in the trait, and indicate the degree to which susceptibility to seasonal
influences on such trait is heritable.
On the other hand, if the source of variation interacting with season is not independent from the environment,
such as among / beywween units or years, then identification of variation in the interaction simply proves a
connection between the two which may be caused by season directly affecting the source of variation, for
example in unit or year through temperature or differences in management etc.
The aim of the current study was to analyse fertility data from the Cotswold database (provided by JSR Genetics)
with a sire model to detect, where present, a phenotype of seasonal fluctuations in performance, and to determine
whether susceptibility to seasonal fluctuations in fertility are genetically mediated. Analyses included interactions
of a measure of season with sire, to determine any genetic effect, but also a unit / year cohort and mating type to
establish whether there is a seasonal effect of these factors.
2 Materials and methods
2.1 Overview of analysis
The initial phase of the project was concerned with cleaning up, preparation and amalgamation of breeding data
from the Cotswold data-base. A commercial pig production operation was also to have been involved in the
programme but initial enquiries revealed that mating strategies were inappropriate for a systematic investigation
of breeding data (e.g. use of mixed semen from several boars per insemination, lack of detailed records).
2.1.1 Sequence of analysis
The analysis was conducted along the following broad lines: investigations to determine the existence of seasonal
fluctuation in weekly mean NBA and successful (resulting in ‘to term’ pregnancy) service number (SERVE) were
conducted on data from the database of fertility records belonging to Cotswold Pig Development Company (now
part of JSR Genetics Ltd). The records came from eighteen indoor units throughout the UK, over the period 1979
to 2001. Analyses included the time (of farrowing) of year of each record and its interactions between sire and
unit / year cohort using a sire model, to determine variation in average sire daughters or unit / year cohort NBA
and SERVE over time of year. Where significant, the sire by time of year interaction could be interpreted as
unambiguous evidence of seasonality, since sire variance cannot be affected by the time of year. Interactions
between unit / year cohort and time of year would provide evidence of a link between season and factor level, the
‘seasonal’ nature of the effect to be decided by causality.
2.1.2 Method of examining seasonality
The method of random smoothing splines rather than random polynomial regressions was selected for the
analysis of the seasonal fluctuations in fertility, despite random regressions having a simpler functional form using
fewer parameters, since splines are piecewise polynomial functions that are smoother and more flexible, and are
not susceptible to instability at higher orders of polynomials.
The use of splines was described by White, Thompson and Brotherstone (1999) as a semi-parametric approach
in their modelling of lactation curves involving parametric curves with fixed or random coefficients. This method
can also be applied to NBA with respect to season. The intricacies of cubic splines and the mixed model
formulation are described by White et al. (1999).
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A cubic spline is a piecewise cubic function constrained so that the function and its first two derivatives are
continuous at the breakpoints or knot points between one cubic segment and another (White et al., 1999). The
number of knot points () influences the smoothness of the curve, for example, where  = 2 corresponds to a
straight line, and where  = the number of data points produces the best fit line with no smoothing. However,
White et al. (1999) demonstrate that the number of knot points may be equal to the number of data points and the
smoothing nature of splines can be determined by a roughness penalty α, where the trade-off between fidelity to
the data and smoothness is determined by this parameter. Given , White et al. (1999) determine the best value
of α from a likelihood equation.
The inclusion of spline functions of the time of year covariate in the analyses acts as a polynomial covariate, and
the interactions of both the linear and polynomial (spline) component of time of year with other factors (such as
sires) may be estimated. Thus, the components of the analyses include an overall linear regression of NBA and
SERVE on time of year, a sire and sire by linear time of year interaction, and a polynomial time of year
component (spline) and sire by polynomial of time of year interaction. Interactions of other factors (such as unit /
year cohort) with the linear and polynomial time of year covariates may be added as required.
More detail on the inclusion of splines in the analysis is given later in the methods.
2.2 Data and pre-analysis validation
Parity and litter data were extracted for all pure Large White gilts and sows. A data record of an individual
farrowing consisted of: sow identity; sow sire and dam; parity number; service information; previous litter
information; and NBA. The service information included the successful (resulting in to term pregnancy) service
number within a specific parity (SERVE), mating type (AI or natural service), the number of inseminations within a
recorded service, and the unit and date of insemination. Previous litter information included lactation length (LL)
and weaning to first service interval (WTFS).
2.2.1 Validation of sire data
The intention was to use a sire model and so all records where sow sire was unknown were eliminated from the
analyses.
2.2.2 Christmas Period
Uncertainty over the level and quality of regular staffing cover over the Christmas and New Year holidays on the
Cotswold farms cast doubt on the validity of data from this period. To avoid inclusion of data that might purport to
show a seasonal effect but that is in fact due to a seasonal effect on management, a decision was taken to
eliminate data from days 1 to 14 and 352 to 365 from the analyses.
2.2.3 Validation of data according to other factors
The data were edited to validate and simplify the data structure for analysis. Where the number of records of a
particular factor level was less than 100, that factor level was rejected to avoid potential confounding of levels
within different factors. The factors in question and the total number of records removed were year (102 from 3
years), unit (99 from 9 units), parity (88 from 5 levels), SERVE (45 from 2 levels) and number of inseminations per
serve (11 from 2 levels). This resulted in a total of 345 records being eliminated from the analysis, less than 0.01
of the initial dataset resulting in a final dataset of 34,315 Large White farrowing records.
2.3 Univariate Linear Models
2.3.1 Mixed Model notation
The univariate linear models fitted to NBA / SERVE were sire models and were of the following form:
Y = Xb + Zu + Wc + Vs + e
where Y is the vector of observations; X, U, V and W are known incidence matrices; b is the vector of fixed
effects; u is the vector of random effects for sires assumed to be distributed MVN with parameters (0,Iσ2u); s is
the vector of random effects for service boar and distributed MVN with parameters (0,Iσ2s); c is the vector of
random permanent non-genetic effects of each individual distributed MVN with parameters (0,Iσ2c), and e is the
SID 5 (2/05)
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vector of residuals distributed MVN with parameters (0,Iσ2e); I is an identity matrix of the appropriate size. The
subscripts u, c, s and e denote sire, permanent non-genetic, boar and residual variances respectively.
2.3.2 Mixed Model effects
When univariate linear models were fitted to NBA, the fixed effects fitted as factors were parity (1 to 10), SERVE
(1 to 3), number of inseminations in the successful service (IPS, 1 to 4), type of mating for service resulting in
conception (AI or natural service), and cohort (defined by the unit by year sub-classes). A linear component of LL
(14-28 days) was included as a covariate in the analyses. Sire of sow and service boar were included as random
effects. When univariate linear models were fitted to SERVE, the fixed effects fitted as factors were parity (1 to
10), NBA from previous litter, type of mating, WTFS and cohort (defined by the unit by year sub-classes). A linear
component of LL (14-28 days) was included as a covariate in the analyses. Sire of sow and service boar were
included as random effects. Furthermore, time of year (day/365), sire by linear time of year and sire by polynomial
time of year component interactions, and unit / year cohort by linear time of year and unit / year by polynomial
time of year component interactions were included as covariates in addition to the effects listed above.
The aim was to estimate NBA / SERVE using a derivation of the following equation:
yi =
parity + unit / year cohort + trait specific fixed effects
+ b0 + b1ti
+ b i0 + b i1ti
+ ∑ vkzk(ti) + ∑ vikzk(ti)
+ ei
Where yi = NBA or SERVE from daughters of sire i, and t = time of year of farrowing, and zk(ti) is the spline
function.
The first two terms represent an overall linear regression on time of year, the third and fourth terms (sire and sire
x linear) show the deviation from the overall regression model for sire i, and the fifth and sixth terms (spline and
sire x spline) correspond to a mean spline deviation and the deviation from the mean spline for sire i. The term ei
is the residual error with variance σ2e.
2.3.4 Spline parameters
Since the ‘time of year’ covariate consists of over 300 data points (day/365 for weeks 15-351 inclusive), the
inclusion of a knot point () for every data point as outlined by White et al. (1999) in section 2.1.2 would have
been computationally unfeasible. Preliminary analyses using mean weekly residuals from analyses with a full
model except with factors relating to time of year increased the number of knot points in the spline equating to the
polynomial of time of year in a stepwise manner until no change was observed in the pattern of predicted values.
Results suggested that 26 knot points were more than sufficient to describe the effect of season. Such a
restriction to 26 knot points was implemented in all analyses incorporating splines.
2.4 Analyses with further data
Initial investigations using data from weeks 3 to 50 inclusive showed that the putative ‘seasonal’ fluctuation in
NBA was small, and further analyses were undertaken using data from weeks showing a tendency to fluctuation
in NBA, estimated using the weekly mean residuals from analysis with all factors except one pertaining to time of
year. As a result data incorporating records of sows farrowing between the 7 th and 37th weeks, and between the
20th and 37th weeks of the year were analysed according to the methods outlined in section 2.3.3. These data
groups comprised of 22,334 and 13,018 Large White farrowing records respectively.
In addition to the linear and polynomial of time of year with sire interactions (see section 2.3.3), the significance of
unit / year cohort by linear and polynomial of time of year interactions were tested (by including them as random
effects) in the analyses of NBA and SERVE for Large White sows in weeks 3 to 50. These interactions
established the importance of unit / year by season interactions and further verified the rigorousness of using
splines to model parametric curves with fixed or random coefficients.
3 Results
3.1 Analysis of NBA
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3.1.1 Variance components
The heritability, repeatability and service boar effect on NBA from the analyses into seasonal fluctuations in litter
size using the various data groups are shown in table 1. All heritability estimates are significantly larger than zero.
All heritability estimates were consistent in magnitude and not significantly different from estimates reported Lewis
et al. (2005), who used the same Cotswold database. All estimates of the repeatability of NBA were significantly
larger than zero, except that from the data restricted to weeks 7 to 37. None of the repeatability estimates from
the different data groups is different from each other. All estimates of repeatability were consistent with those
Lewis et al. (2005) except that yielded from using the data from 20 to 37 weeks only. The only estimates of boar
effect on NBA that were significantly larger than zero were those generated by the data from weeks 20 to 37.
Again, all estimates produced using the various data groups were consistent with each other and with those
reported by Lewis et al. (2005).
h2
0.07 (0.012)
0.07 (0.014)
0.08 (0.019
Data group
Full (weeks 3 to 50)
Weeks 7 to 37
Weeks 20 to 37
Repeatability
0.16 (0.059)
0.14 (0.082)
0.12 (0.014)
Boar effect
0.04 (0.033)
0.04 (0.041)
0.03 (0.005)
Table 1 Heritabilities (h2), repeatabilities and boar effect estimates for NBA produced from analyses using the
various different groups of Large White data.
3.1.2 Time within year effect on NBA
The linear time of year covariate was small in magnitude and not significantly different from zero. The polynomial
time of year effect (predicted by the spline of time of year) was also very small and not significantly larger than
zero. Predicted values of NBA over weeks 3 to 50 using the smoothing curve function of polynomial of time of
year are shown in Figure 1, and although the chart suggests that NBA is lower in summer and autumn farrowing
sows, large standard errors (0.144 to 0.152) mean that no predicted weekly value of NBA is significantly different
from any other.
9.48
9.46
predicted NBA
9.44
9.42
9.40
9.38
9.36
9.34
9.32
3
5
7
9
11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49
w eek
Figure 1 The trend in predicted values of NBA over weeks 3 to 50 using polynomial time of year (not significantly
different from zero). No weekly predicted value is statistically different from any other.
The sire by linear time of year covariate was very small in magnitude and not significantly different from zero and
the sire by polynomial of time of year interaction was bound to zero. Subsequent analyses determined that the
SID 5 (2/05)
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linear and polynomial sire by time of year components were not significant (by twice log likelihood ratio test) and
could effectively be discarded from the model.
3.1.2.2 Data from weeks 7 to 37 and 20 to 37 inclusive
Identical analysis using data only from weeks 7 to 37 and weeks 20 to 37 attempted to focus on the area of most
fluctuation in NBA but yielded similarly insignificant estimates of time of year. Neither the linear nor the polynomial
time of year covariates were significantly larger than zero, using either the weeks 7 to 37 nor weeks 20 to 37 data
group. Predicted values of NBA over weeks 7 to 37 and over weeks 20 to 37 using the smoothing curve function
of polynomial of time of year are shown in Figure 2 and 3 respectively. As with chart 1, although the charts
suggest fluctuation in NBA among sows farrowing in different weeks, large standard errors (0.180 to 0.200 in
week 7 to 37 data and 0.230 to 0.238 in week 20 to 37 data) mean that no predicted weekly value of NBA is
significantly different from any other.
9.50
9.45
predicted NBA
9.40
9.35
9.30
9.25
9.20
9.15
9.10
7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
w eek
Figure 2 The trend in predicted values of NBA over weeks 7 to 37 using polynomial time of year (not significantly
different to zero). No weekly predicted value is statistically different from any other.
SID 5 (2/05)
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9.70
9.65
9.60
predicted NBA
9.55
9.50
9.45
9.40
9.35
9.30
9.25
9.20
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
w eek
Figure 3 The trend in predicted values of NBA over weeks 20 to 37 using polynomial time of year (not
significantly different to zero). No weekly predicted value is statistically different from any other.
In data from weeks 3 to 37 the interaction of sire by linear time of year component was tiny in magnitude and not
significantly different from zero and the sire by polynomial time of year component interaction was bound to zero.
Similarly, in data from weeks 20 to 37 both the sire interactions with linear and polynomial time of year
components were bound to zero. Figure 4 shows predicted values of average NBA in daughters of 9 randomly
selected sires over weeks 7 to 37 using the polynomial time of year component, and illustrates that although there
is a visible, albeit small, seasonal fluctuation in NBA, the variation in the pattern between sires is extremely small
(i.e. the pattern is consistent over all sires). This demonstrates a scaling rather than seasonal effect since
although there is variation in sire daughter average NBA, the average deviation from the mean polynomial of time
of year for each sire is very small. Figure 5 illustrates the same phenomena in the week 20 to 37 data.
10.00
predicted average NBA of daughters
9.80
9.60
9.40
9.20
9.00
8.80
8.60
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
w eek
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Figure 4 Predicted values over weeks 7 to 37 of daughters average NBA for 9 randomly selected sires using the
polynomial component of time of year showing sire variation but little variation in sire by polynomial of time of
year.
10
predicted average NBA of daughters
9.8
9.6
9.4
9.2
9
8.8
8.6
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
w eek
Figure 5 Predicted values over weeks 20 to 37 of daughters average NBA for 9 randomly selected sires using the
polynomial component of time of year showing sire variation but little variation in sire by polynomial of time of
year.
3.1.3 Time of year component interactions with unit / year cohort
In contrast to the sire by linear and polynomial of time of year interactions, results from analyses of Large White
data from all litters showed that both the unit / year cohort by linear time of year covariate and the unit / year by
the polynomial time of year covariate were highly significant (P < 0.01; using twice log likelihood ratio test).
Nevertheless, both components were very small, accounting for 0.00025 and 0.00005 of variation respectively.
This result indicates that the pattern of fluctuation of NBA in Large White sows over time of year shows variation
between different units and different years. Figure 6 shows predicted NBA for 9 unit / year cohorts over weeks 7
to 37 using the polynomial of time of year. It is clear, upon comparison with predicted daughter NBA for 9
randomly selected sires (Figure 4), that there is more variation in the shape of the curves, implying that some
units and years differ in the exhibited seasonal fluctuations in NBA.
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11.00
10.50
Unit/Year predicted NBA
10.00
9.50
9.00
8.50
8.00
7
8
9
10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37
w eek
Figure 6 Predicted values of NBA for 9 randomly selected unit / year cohort classes over spline of weeks 7 to 37
showing variation between cohorts and also variation in cohort deviation from the spline by season effect.
3.2 Analysis of SERVE
3.2.1 Variance components
The heritability and repeatability of SERVE from the analyses into seasonal fluctuations in successful service
number in Large White gilts and sows are shown in table 2. The heritability estimate was indistinguishable from
zero implying little or no additive genetic variation in the service number resulting in pregnancy, a trait that
encompasses conception rate. The repeatability for SERVE is also small, but detectable from zero.
Data group
Large White
h2
0.00 (0.000)
Repeatability
0.02 (0.006)
Table 2 Heritabilities (h2) and repeatability estimates for SERVE.
3.2.2 Time within year effect on SERVE
The linear time of year covariate was small in magnitude and not significantly different from zero. The polynomial
time of year effect (predicted by the spline of time of year) was also very small and not significantly larger than
zero. Predicted values of SERVE over weeks 3 to 50 using the smoothing curve function of polynomial of time of
year are shown in Figure 7, and although the chart suggests that SERVE is higher in summer and autumn, large
standard errors (0.0045 to 0.0067) mean that no predicted weekly value of SERVE is significantly different from
any other.
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1.096
1.094
1.092
predicted serve
1.090
1.088
1.086
1.084
1.082
1.080
3
5
7
9
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
43
45
47
49
w eek
Figure 7 The trend in predicted values of SERVE over weeks 3 to 50 using polynomial time of year (not
significantly different to zero). No weekly predicted value is statistically different from any other.
The sire by linear time of year covariate was bound to zero and the sire by polynomial of time of year interaction
was very small in magnitude and not significantly different from zero. Subsequent analyses determined that the
linear and polynomial sire by time of year components were not significant (by twice log likelihood ratio test) and
could effectively be discarded from the model analysing SERVE.
3.1.3 Time of year component interactions with unit / year cohort
In contrast to the sire by linear and polynomial of time of year interactions, results from analyses of Large White
data showed that both the unit / year cohort by linear time of year covariate and the unit / year by the polynomial
time of year covariate were highly significant (P < 0.01; using twice log likelihood ratio test). Nevertheless, both
components were very small, accounting for 0.0004 and 0.00002 of variation respectively.
This result indicates that the pattern of fluctuation of SERVE in Large White sows over time of year shows
variation between different units and different years.
4 Discussion
4.1 Choice of splines
The decision to use splines, rather than random polynomial regressions, to analyse the fluctuations of NBA over
the year is rooted in their flexibility to vary the curve between the knot points through interpolation. Splines are
piecewise defined polynomials that provide more flexibility than ordinary polynomials when defining smooth
curves. Conversely, random regressions, although simpler functions, are fixed for the period over which the data
is spread and so are less free to model the curve.
White et al. (1999) advocate the use of the maximal number of knot points (i.e. one for every data point), the
addition of a roughness penalty which determines fidelity to the data versus smoothness, and the evaluation of
the roughness penalty by likelihood analysis. Although a valid philosophy, assigning a knot point to every data
point in this data set would result in the use of over 300 knot points; which would have exceeded the available
computational capacity. Some examination suggested that restricting the number of knot points to 26 was more
than ample to describe the effect. Thus for reasons of practicality, the number of knots was restricted to 26.
4.2 Variance components
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The heritabilities, repeatabilities and boar variances for NBA estimated in this study are similar in magnitude to
those reported by Lewis et al. (2005) who used Large White and Landrace data from the same source, and
indicate that the data groups used in these analyses were typical of farrowing data from commercial nucleus
herds. An estimate of zero heritability for SERVE indicates little or no genetic variation in the number of serves
resulting in pregnancy, a trait incorporating conception rate.
4.3 Evidence of seasonal fluctuation in NBA
The evidence from the current study indicates that the seasonal effect on NBA is small, particularly in comparison
to other factors, and statistically indistinguishable from zero. Preliminary analyses showed that mean weekly
residuals yielded from analysis with a full model except a seasonal component fluctuated over about 0.3 piglets
NBA, but that standard errors indicated that almost all residuals are not significantly different from each other or
from zero. This figure is lower than the seasonal fluctuations in litter size reported in reviews by Claus and Weiler
(1987) and Martinat-Botté et al, (1987). Thus, there is little evidence from the current study of a phenotype of
seasonal fluctuation in NBA.
The linear and polynomial time of year covariates were small and not significantly larger than zero in all analyses
attempted, even when focussing on the weeks where evidence of a fluctuation in NBA appeared strongest. The
charts of predicted NBA over various weeks made using the polynomial time of year covariate in all data groups
(Figures 1, 2 and 3) demonstrated a maximal difference between the nadir and peak of only about 0.25 piglets,
and none of the weekly predicted values for NBA were different from each other. On this evidence it appears that
NBA in the domestic pig does not have a seasonal trend.
4.4 Sire by seasonal components of NBA
Similarly, the current study failed to detect any evidence of a sire by linear, or sire by polynomial time of year
interaction in NBA in the Large White sows of the Cotswold herd, even when data of isolated weeks were
analysed. The absence of a detectable interaction of genetic variation with time of year implies that there is no
differential response in NBA to season due to additive genetic variation, as is borne out by the chart showing 9
sire average daughters NBA over the year (Figure 4). The chart shows a near identical pattern of fluctuation in
NBA over the weeks 7 to 37, with virtually no variation in the pattern between sires. Such variation in the pattern
of individual fluctuation in NBA would surely exist, even to a small extent, if the phenomenon of a seasonal effect
on litter size is to be creditable. The analyses conducted do not take account of genetic variation due to
dominance or epistatic effects, and it is possible that these effects could have some influence. Nevertheless, the
absence of any sire by seasonal interaction in, and the lack of detectable seasonal effect on, NBA must argue
against this hypothesis. The sire by season interaction, were it to exist, was described in the Introduction (section
1) as definitive evidence of seasonality in NBA, since the genetic variation is completely independent of the
environment. Other factors may not be completely independent from the environment, and as such, a regular
‘seasonal’ influence on such factors may appear to be a seasonal effect on NBA.
4.5 Unit / year by seasonal components of NBA
In contrast to insignificant effects of sire by season interactions, small but significant unit / year cohort by linear
and polynomial time of year interactions indicate that the pattern of seasonal fluctuation in NBA varies between
units and years, as shown in Figure 6. This suggests that the triggers to any seasonal depressions in NBA are
environmental, which in turn differ between units and years. Causes of this may be differences in housing that
affect the availability of natural light, which will be linked to day length, protection from external environmental
temperature, or even differences in management due to staffing issues. Nevertheless, the unit / year by time of
year effects are small, indicating that either the effect is small or that a small number of units and years
experience relatively strong seasonal effects on NBA while others might have no problem at all.
The detection of significant linear and polynomial interactions with unit / year cohorts demonstrates that the
methodology employed to detect small seasonal interaction effects is viable, and able to detect effects where they
exist.
4.6 Evidence of seasonal fluctuation in SERVE
The current study indicates that the seasonal effect on the number of services required to achieve pregnancy is
small and statistically indistinguishable from zero. Thus, as with NBA there is little evidence of a phenotype of
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seasonal fluctuation in the elements contributing to the trait SERVE, such as conception rate and early term
abortion of pregnancy.
The linear and polynomial time of year covariates were small and not significantly larger than zero in analysis of
SERVE. The chart of predicted SERVE over various weeks made using the polynomial time of year covariate
(Figure 7) indicates a greater weekly mean SERVE in the summer than winter by only about 0.011; however none
of the weekly predicted values for SERVE were different from each other. On this evidence it appears that the
number of services resulting in pregnancy in the domestic pig does not have a seasonal trend.
4.7 Sire by seasonal components of SERVE
Similarly, the current study failed to detect any evidence of a sire by linear, or sire by polynomial time of year
interaction in determining SERVE in the Large White sows of the Cotswold herd. As was the case with NBA, the
total absence of a detectable interaction of genetic variation with time of year implies that there is no differential
response in SERVE to season due to additive genetic variation.
4.8 Unit / year by seasonal components of SERVE
Small but significant unit / year cohort by linear and polynomial time of year interactions indicate that the pattern
of seasonal fluctuation in SERVE varies between units and years, as it did with NBA. This result implies that there
are differences between units and years that elicit dissimilar fluctuations in performance in fertility traits of pigs
over the year, with likely causes being differences in housing that affect the availability of natural light (which will
be linked to day length) protection from external environmental temperature, or even differences in management
due to staffing issues. Again, as was the case with NBA, the unit / year by time of year effects on SERVE are
small, indicating that either the effect is small or that a small number of units and years experience relatively
strong seasonal effects on the components of SERVE, such as conception rates, while others might have no
problem at all.
4.9 Final Overview
The results presented in the current final study have failed to detect significant fluctuations in litter size and
successful service (i.e. leading to pregnancy) over the year, with both the linear and polynomial time of year
effects being small and indistinguishable from zero. The failure to detect genetic variation in any fluctuations in
NBA or SERVE over the year confirms that there is little or no additive genetic basis to susceptibility of NBA and
SERVE to the time of year of farrowing. Even examination of the mean weekly residuals from the preliminary
analyses, which contained no time of year component, does not reveal a convincing seasonal trend. Thus, one
might conclude that there is no seasonal influence on litter size or successful serve. Yet the topic has been
documented many times in the past, although the effect on litter size appears smaller than those reported for
other traits. The identification of a significant unit by year interaction with the time of year may provide a partial
explanation to the persistence of the issue. The differential ‘seasonal’ effect on litter size and successful serves
over years is likely to be due to factors that affect some but not all units and years. Thus, doubt would be cast on
photoperiod being a causal factor since it is consistent over years and fairly similar over the UK (even more so
considering all units used indoor housing); but factors such as summer temperature and the requirement and
quality of staffing cover, which will show greater differences between years and units will be more plausible as
causal factors. Evidence supporting this viewpoint comes from Tantasuparuk et al. (2000), who detected smaller
litter total number born in a distinct wet season in the tropics, but with little change in daylength. Therefore, what
appears to as a seasonal effect on litter size, may in fact be an environmental effect that coincides with seasonal
changes.
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5 Conclusion
The current study has determined only very small, insignificant, fluctuations of NBA and SERVE over weeks 3 to
50 of the year, with no significant linear or polynomial effect of time of year detectable. Analyses including
interactions of sire with linear and polynomial time of year covariates demonstrated that these interactions
between sire and season were not significant and could be safely removed from a mixed model of NBA or
SERVE, and indicated a lack of detectable genetic variation causing fluctuation of NBA and SERVE over the time
of year. Linear and polynomial interactions of unit / year cohort and season were very small but significant,
indicating that the method employed is sufficient to detect small effects.
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References to published material
9.
This section should be used to record links (hypertext links where possible) or references to other
published material generated by, or relating to this project.
Brandt, H. and Grandjot, G. (1998) Genetic and environmental effects of male fertility of AI-boars.
Proceedings of the 6th World Congress on Genetics Applied to Livestock Production, Armidale. 23: 527530.
Claus, R. and Weiler, U. (1985) Influence of light and photoperiodicity on pig prolificacy. Journal of
Reproduction and Fertility, 33: 185-197.
Claus, R. and Weiler, U. (1987) Seasonal variations of fertility in the pig and its explanation through
hormonal profiles. In Definition of the summer infertility problem in the pig, Eds E. Seren & M. Mattioli.
Proceedings of a seminar in the Community programme for the coordination of agricultural research.
Published by the Office for official publications of the European Communities.
Colenbrander, B., Feitsma, H. and Grooten, H. J. (1993) Optimizing semen production for artificial
insemination in swine. Journal of Reproduction and Fertility Supplement, 48: 207-215.
Kennedy, B. W. and Wilkins, J. N. (1984) Boar, breed and environmental factors influencing semen
characteristics of boars used in artificial insemination. Canadian Journal of Animal Science, 64: 833843.
Lewis, T. W., Wiseman, J. and Woolliams, J. A. (2005) Genotype by mating type interaction for litter
size in Landrace and Large White sows. Animal Science, 81: 331-335.
Martinet-Botte, F., Thatcher, W. W. and Terqui, M. (1987) Seasonal variations of pig litter size. In
Definition of the summer infertility problem in the pig, Eds E. Seren & M. Mattioli. Proceedings of a
seminar in the Community programme for the coordination of agricultural research. Published by the
Office for official publications of the European Communities.
Tantasuparuk, W., Lundeheim, N., Dalin, A-M., Kunavongkrit, A. and Einarsson, S. (2000)
Reproductive performance of purebred Landrace and Yorkshire sows in Thailand with special reference to
seasonal influence and parity number. Theriogenology, 54: 481-496.
Tummaruk, P., Lundeheim, N., Einarsson, S. and Dalin, A-M. (2001) Reproductive performance of
purebred Hampshire sows in Sweden. Livestock Production Science, 68: 67-77.
White, I. M. S., Thompson, R. and Brotherstone, S. (1999) Genetic and environmental smoothing of
lactation curves with cubic splines. Journal of Dairy Science, 82: 632-638.
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