Factors affecting the length of productive life in U.S. Katahdin ewes

Abstract

The length of ewe productive life (LPL), defined as the number of days between the first and last lambing, is a key indicator of ewe longevity and is directly related to the sustainability of the sheep industry. Therefore, the primary objective of this study was to investigate systematic effects influencing LPL in Katahdin sheep. The LPL of 10,474 Katahdin ewes (69.5% with uncensored and 30.5% with right-censored observations) born between 1992 and 2021 in 58 flocks located across the United States were analyzed. The Kaplan–Meier (K-M) and Cox proportional hazard (Cox PH) methods were used to estimate survival probability. Four Cox PH models were evaluated. Model 1 included contemporary group (CG; flock–year–season of ewe birth) as a random effect and the ewe’s dam’s age (EDA), ewe’s own birth-rearing type (BR; 1/1, 2/1, 2/2, 3/2, 3/3, with the digit-3 including lamb counts ≥ 3), and age at first lambing (AFL) as fixed effects. Models 2 to 4 were an extension of model 1. Model 2 also included average lamb birth weight (ABW) per ewe lifetime, while model 3 included average lamb weaning weight (AWW) per ewe lifetime. Both ABW and AWW were fitted as fixed effects. Model 4 fitted all previous effects together. The factors CG, BR, ABW, and AWW affected LPL (P < 0.05) in all models in which these effects were fitted. The EDA effect only influenced LPL (P < 0.05) in model 1, while AFL had no effect (P > 0.05) in any model. The median LPL ranged from approximately 2 to 3 yr, depending on the risk factors analyzed. In general, Katahdin ewes themselves born in multiple litters, and that produced lambs weighing approximately 5 kg at lambing and 20 to 25 kg at weaning (over their lifespan) had better survival probability. Although the LPL of Katahdin sheep is relatively low, it appears to be a consequence of voluntary culling due to its association with both ABW and AWW. Future studies should quantify the rate of involuntary culling in Katahdin ewes to identify whether longevity indicator traits should be included in more comprehensive breeding objectives.

Katahdin ewes born as a multiple, and that produced lambs with moderate weights at birth (approximately 5 kg) and weaning (20 to 25 kg), had longer productive lives.

Introduction

Increasing ewe productive life positively impacts the efficiency and profitability of sheep enterprises. Previous studies have reported the economic importance of ewe longevity. For example, in Suffolk sheep, a prominent meat breed, the economic value of ewe productive lifetime surpassed that of traditional growth traits (Wolfová et al., 2009a). In dairy sheep, several longevity-related traits were found to have substantial economic value (Legarra et al., 2007; Krupová et al., 2009; Wolfová et al., 2009b). This economic impact is generally associated with reduced annual replacement costs (Legarra et al., 2007) or the increase in milk yield and litter size caused by an increased proportion of older ewes in the flock (Wolfová et al., 2009b). Notter et al. (2018) found that Katahdin ewes generally produced the highest number of lambs born and successfully weaned when they were between 4 and 6 yr of age. Moreover, longer-lived ewes usually had fewer reproductive and health issues, as disease and low fertility were critical reasons for sheep mortality or involuntary culling (McLaren et al., 2020; Flay et al., 2022). Therefore, increasing ewe productive longevity can contribute to decreased annual flock replacement costs and improved overall welfare of the animals.

An appealing and informative way of evaluating the effect of systematic factors on ewe productive life is based on survival models, which enable the estimation of the survival probability across time and the calculation of hazard rates (Moore, 2016). Survival models have some advantages compared to linear models, such as: 1) currently alive animals can also be included in the analyses and considered as censored records; and 2) right-skewness, a typical characteristic of longevity-related traits, is not an issue because survival models do not assume a normal distribution of the residuals. Previous studies, therefore, have used survival models to analyze ewe longevity in various sheep populations (e.g., Riggio et al., 2009; Kern et al., 2010; Abdelqader et al., 2012; Getachew et al., 2015; Milerski et al., 2018).

Several interesting systematic factors were shown to affect ewe longevity in earlier studies. For instance, birth type was reported as having a significant effect on ewe longevity, where ewes born in smaller litters lived longer (McLaren et al., 2020; Hanna et al., 2023). However, this effect was not significant in other ewe longevity studies (Kern et al., 2010; Milerski et al., 2018). age at first lambing (AFL) has been reported as another important factor influencing ewe longevity. In some studies, a younger AFL increased ewe longevity (Riggio et al., 2009; Kern et al., 2010), while in other studies the opposite was observed (Abdelqader et al., 2012; Getachew et al., 2015). This contrast in findings likely reflects differences among breeds or between extensive and intensive production systems or genetic × environmental interactions, as ewe lambs raised in intensive systems usually have more favorable environmental conditions for earlier reproductive activity. Flock, year, and season have also been cited as important factors affecting ewe longevity (Riggio et al., 2009; Abdelqader et al., 2012; McLaren et al., 2020), because both environmental and economic conditions change each year, and culling policies vary across flocks. Survival analysis also enables the evaluation of ewe productivity as a risk factor for early culling. For instance, Getachew et al. (2015) reported a high risk of early culling for ewes that were unable to wean their lambs, while Milerski et al. (2018) found a decreased culling risk for Suffolk ewes with intermediate prolificacy when compared to ewes with lower or higher prolificacy.

Hair sheep breeds have become popular in regions traditionally occupied by wool breeds, due to fluctuations in wool value and increased costs and labor for shearing. The Katahdin is a hair-type composite breed developed in the 1950s in the Northeastern U.S. by crossing Caribbean hair sheep and British sheep breeds (Dearborn et al., 2023). The Katahdin is popular as a maternal breed across the United States (Thorne et al., 2021), particularly in regions of the country where wool breeds are not well suited. Katahdin showed resilience to restricted water availability (Hussein et al., 2020) and is considered to have greater parasite resistance than wool breeds (Weaver et al., 2023). Moreover, pure and crossbreed Katahdin lambs have suitable performance in intensive systems. For instance, Katahdin lambs from Katahdin ewes sired by Suffolk, Texel, and Katahdin rams had 0.38, 0.32, and 0.30 kg/d average daily gain, respectively (Maierle, 2018). Although Katahdin is an important U.S. sheep breed, factors influencing the longevity of Katahdin ewes have not been reported to date. Thus, the primary objectives of this study were to describe the survival probability curve of U.S. Katahdin ewes based on the length of productive life (LPL) and to evaluate systematic factors affecting the survival of these ewes.

Material and Methods

Ethics statement

Approval from the Animal Use and Ethics Committee was not needed for this study as preexisting datasets were provided by the National Sheep Improvement Program (NSIP) and recorded by U.S. Katahdin producers during routine husbandry activities.

Survival data

Data on 26,392 Katahdin ewes that produced 67,397 litters and 118,510 lambs between 1985 and 2023 were provided by NSIP (Ames, IA, USA). Quality filters were first applied to identify and remove ewes with inconsistent data or very low productivity. Ewes with very short (< 150 d) or very long (> 720 d) intervals between consecutive lambing events (n = 1,233) and ewes with very low (< 270 d) or very high (> 1095 d) age at the first lambing (n = 2,666) were removed from subsequent analyses. After applying these filters, 22,493 ewes from 231 flocks remained, which produced 100,981 lambs in 57,436 litters.

The next set of filters was applied to remove flocks with few production year of data, inconsistent data reporting, or few records submitted per year. Only data from flocks that reported lambing events for more than 6 consecutive year were included in the analyses. This threshold ensured each flock was enrolled in NSIP long enough to capture the upper end of the expected productive life of ewes (McLaren et al., 2020; Hanna et al., 2023). Some flocks reported lambing records for more than 6 yr but with a large and abrupt reduction in submitted lamb records in the last year before leaving the NSIP, which was considered as inconsistent flocks. The average number of lambing records across year was calculated for each flock, and 20 ewes with lambing events per year were to be the minimal value for excluding inconsistent flocks. This filter also enabled the exclusion of very small flocks, which reduced environmental noise. After applying the flock filters, data from 17,712 ewes from 58 flocks remained for further analysis. These ewes produced 85,591 lambs in 48,533 litters.

The LPL can be defined as the number of days between the first lambing and removal from the flock due to culling or death (Ducrocq et al., 1988). However, the current software used by NSIP breeders to submit data does not enable them to define culling or death dates. Therefore, LPL in the current study was defined as the difference (in days) between the first and last lambing event recorded for each ewe. For this reason, 5,818 ewes with only one lambing record were excluded, and only ewes with 2 or more lambing records were analyzed. Moreover, 53 ewes themselves with no birth-rearing type information, 1,285 ewes with no dam identification, and 82 ewes with no dam age were also excluded from the analyses. After these additional filtering steps, 10,474 ewes remained for subsequent analyses. These ewes were born between 1992 and 2021 in 58 flocks located across the U.S. and produced 67,344 lambs in 37,384 litters. Moreover, these ewes were daughters of 1218 sires and 6401 dams. The average number of ewes per flock throughout the recording period was 180.6, while the average number of year reporting data per flock was 11.8.

Survival analyses

Survival analyses were performed to describe the probability of ewe survival over time and to test systematic effects on LPL. Survival models allow the analysis of lifetime records from both alive and disposed of (dead or culled) ewes, which are considered censored and uncensored records, respectively. If there was no lambing record from an ewe during the last 2 yr of a flock reporting data to NSIP, she was assumed to have died or been culled (censoring code = 1), while ewes with lambing records in any of the last 2 yr in a flock were assumed to be current (censoring code = 0). Unlike clinical survival studies, where diseases are intrinsic factors of the study and can affect the patient follow-up, in the present study all sheep were assumed to be healthy at the beginning of the follow-up (i.e., the first lambing record). Thus, all censorship was assumed to be non-informative, as there is no reason to believe that a ewe was no longer followed due to any intrinsic characteristic of the present study. The distribution of uncensored and censored ewes depends on the model analyzed, as described in Table 1. The non-parametric Kaplan–Meier (K-M) estimator (Kaplan and Meier, 1958) was used to calculate survival probabilities across time and can be described as:

Table 1.

Description of the survival models evaluated and the number of U.S. Katahdin ewes with productive life records (censored or uncensored) after data editing

Main effects	Type of effect	Model composition
		1	2	3	4
Contemporary group	Random	+	+	+	+
Ewe age class at first lambing	Fixed	+	+	+	+
BR (birth and rearing type effects)	Fixed	+	+	+	+
Dam age	Fixed	+	+	+	+
Class of mean lamb weight at lambing	Fixed	−	+	−	+
Class of mean lamb weight at weaning	Fixed	−	−	+	+
Population characteristics
Number of ewes with uncensored records		7276 (69.5%)	5612 (68.0%)	4407 (70.7%)	3654 (69.2%)
Number of ewes with censored records		3198 (30.5%)	2637 (32.0%)	1823 (29.3%)	1624 (30.8%)
Total number of ewes		10,474 (100%)	8249 (100%)	6230 (100%)	5278 (100%)
Number of ewe’s sires		1218	1045	1004	912
Number of ewe’s dams		6401	5284	4365	3781
Number of flocks		58	57	58	57
Total number of litters produced by the ewes		37,384	28,686	20,571	17,087
Total number of lambs birthed by the ewes		67,344	51,651	36,438	30,170
Total number of lambs weaned by the ewes		62,368	48,667	33,471	28,370

(+) effect included in the model; (−) effect not included.

$${\displaystyle \begin{array}{l}{\displaystyle {\displaystyle \widehat{S}}\left(t\right)={\displaystyle \prod _{j:t_j\le t}}\left(\frac{n_j-d_j}{n_j}\right)}\end{array}}$$

where $\widehat{S}\left(t\right)$ is the survival probability at time t$(0\le \widehat{S}\left(t\right)\le 1)$; $t_j$ is the length of time (LPL) ($j=shortest,\dots ,longest$) when any ewe died (or was culled); $n_j$ is the number of ewes at risk of death or culling immediately before time $t_j$; and $d_j$ is the number of ewes dead or culled at time $t_j$. The {survfit} function of the “survival” R-package (Therneau, 2024) was used to perform the K-M analyses, while the {ggsurvplot} function of the “survminer” R-package (Kassambara et al., 2022) was used to plot the survival probability curves.

The Cox proportional hazard model (Cox PH; Cox, 1972) is often used in survival-censored data analyses when a model with multiple independent covariates is fitted. Cox PH is a semi-parametric method, as no distribution needs to be specified for the baseline function, which makes it a more flexible model. In this study, contemporary group (CG) was defined as the concatenation of flock–year–season of a ewe’s birth. It was assumed that ewes in the same CG shared frailties, i.e., they had the same level of exposure to health issues such as infectious diseases and parasites. Thus, CG was fitted as a random effect. Each ith ewe ($i=1,...,n$) was a member of a single $\mathrm{C}{\mathrm{G}}_j$ ($j=1,...,q$). The Cox-PH model with shared frailty can be described as

$${\displaystyle \begin{array}{l}{\displaystyle {\mathrm{\lambda }}_i\left(t\right)={\mathrm{\lambda }}_0\left(t\right)\times {\mathrm{e}}^{(X_i\beta +Z_i\omega )}}\end{array}}$$

where ${\mathrm{\lambda }}_i\left(t\right)$ is the hazard rate of the ith ewe; $X_i$ and $Z_i$ are the ith rows of covariate matrices X (n × p) and Z (n × p), respectively; β is a vector containing the p fixed effects; ω is a vector containing the q unknown random effects or frailties; and Z is a design matrix with $z_{ij}$ equal to 1 if a ewe i was a member of CG_j, 0 otherwise (Therneau and Grambsch, 2000). The frailty term accounts for unobserved heterogeneity in ewe survival because ewes from the same flock and born in the same year and season shared similar environmental conditions. A gamma distribution was assumed for the (ω) random effect. This was equivalent to assuming a penalized Cox model with the penalty function $p\left(\mathrm{\omega }\right)=(1/\mathrm{\theta })\sum [{\mathrm{\omega }}_i-\mathrm{e}\mathrm{x}\mathrm{p}({\mathrm{\omega }}_i)]$, where θ was the variance of ω_i. For this frailty distribution, the correlation (Kendel’s tau) of ewes within CG can be calculated as $\mathrm{\tau }=\mathrm{\theta }/(2+\mathrm{\theta })$ (Therneau and Grambsch, 2000). Since all survival functions can be related to the hazard functions as $\mathrm{\lambda }\left(t\right)=-\frac{d}{dt}\log S\left(t\right)$, the respective survival function for a Cox PH model was given by

$${\displaystyle \begin{array}{l}{\displaystyle {\displaystyle \widehat{S}}\left(t\right)=\mathrm{e}\mathrm{x}\mathrm{p}[-{\displaystyle \underset{0}{\overset{t}{\int }}}\mathrm{\lambda }\left(t^{\prime }\right)d{t}^{\prime }]}\end{array}}$$

The {coxph} function of the “survival” R-package (Therneau, 2024) was used for the Cox-PH analyses. The log transformation method was used to calculate the 95% confidence interval (95% CI) as $\mathrm{e}\mathrm{x}\mathrm{p}[\mathrm{l}\mathrm{o}\mathrm{g}(p)\pm 1.96\mathrm{S}\mathrm{E}(\mathrm{l}\mathrm{o}\mathrm{g}(p))]$, where $p=S\left(t\right)$ was the survival probability. This 95% CI was better than direct CIs, i.e., $p\pm 1.96\mathrm{S}\mathrm{E}(p)$, mainly when the probability estimates were near 0 and 1 (Therneau, 2024). When a fixed effect was significant (P < 0.05), adjusted survival curves were plotted to analyze the difference between the groups of ewes according to the levels of the fixed effect. For this, “direct” method was used, which has been shown to outperform other methods, especially when strong predictors of the outcome were included in the model (Denz et al., 2023).

Four Cox PH models were evaluated (Table 1). Model 1 included CG (flock–year–season of ewe birth) as a random effect and the ewe’s dam’s age (EDA), ewe’s own birth-rearing type (BR; 1/1, 2/1, 2/2, 3/2, 3/3, with the digit-3 including lamb counts ≥ 3), and age at first lambing (AFL) as fixed effects. Models 2 to 4 were an extension of model 1. Model 2 also included average lamb birth weight (ABW) per ewe lifetime, while model 3 included average lamb weaning weight (AWW) per ewe lifetime. Model 4 fitted all previous effects together.

The sample size varied across the models (Table 1) due to the number of missing values for lamb body weights per ewe at lambing and weaning. Lamb birth weights (BW) were adjusted only for the effect of sex ($\mathrm{B}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}$). The $\mathrm{B}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}$ of the offspring of each ewe were summed to calculate the total body weight lambed, which was then divided by the number of lambs born to obtain the average. Only ewes with 100% of their progeny with a BW recorded were included when average lamb weight at lambing was fitted as a covariate in the model, thereby excluding 2,225 ewes with missing values.

Lamb weaning weights (WW), when recorded between 30 and 90 d of age, were adjusted to 60 d of age $\left(\mathrm{W}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}\right)$ using the equation: $\mathrm{W}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}=[\left(\frac{\mathrm{W}\mathrm{W}-\mathrm{B}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}}{\mathrm{N}}\right)\times 60]+\mathrm{B}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}$, where N is the number of days between the birth and weaning dates. The $\mathrm{W}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}$ of the offspring of each ewe were summed to calculate the total body weight weaned per ewe. These total values were then divided by the number of lambs born, rather than weaned, because twin and triplet lambs usually have higher mortality rates before weaning. This approach accounts for the fact that producers often cull high prolificacy ewes that wean fewer lambs, consequently impacting their longevity. A $\mathrm{W}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}$ of zero was assumed for all lambs that died before weaning. The lambs’ own birth-rearing type was evaluated to determine whether they died before weaning. For instance, if a lamb had a birth-rearing type record of 2/0 and its twin was 2/1, it was assumed that the first lamb died before weaning, and its $\mathrm{W}{\mathrm{W}}_{\mathrm{a}\mathrm{d}\mathrm{j}}$ was zero. On the other hand, when 2 lambs had the birth-rearing type of 2/2 and WW was not recorded for either of them, it was assumed that the lambs were alive at weaning, but their weights were unavailable. Ewes with missing WW (n = 4,244), for any progeny, had missing values for this covariate.

A fundamental assumption of the Cox PH model is proportional hazard ratio (HR) over time, and this assumption was tested with the {cox.zph} function in the “survival” R-package (Therneau, 2024). This function performs a hypothesis test based on the Schoenfeld residuals (Therneau and Grambsch, 2000). However, a high significance with a minimal violation of the Cox PH assumption can be observed when a large sample is analyzed (In and Lee, 2019). Therefore, in addition to the hypothesis test, a subjective graphical analysis was performed by plotting the regression coefficient estimates across time, i.e., β(t).

Another assumption of the Cox PH method is that the covariate has a linear effect on the log hazard function. However, a continuous variable can have a non-linear form. Thus, Martingale residual versus the predictor covariate values were plotted to define the best form of fitting the continuous covariates. The Martingale residual is the difference between the observed time-to-event for an individual and the expected time-to-event based on the fitted model (Thearneau and Grambsch, 2000). After this check, AFL and EDA were fitted as linear effects, while ABW and AWW were fitted with linear and quadratic terms. The effect of continuous variables on LPL was visualized by using the “contsurvplot” R-package (Denz and Timmesfeld, 2023).

Two other essential quality controls of the Cox PH models are whether there are outliers or influential records. For this purpose, 2 graphical analyses were performed: 1) deviance residuals were plotted to identify ewes with high (positive or negative) residuals, and 2) the dfbeta residuals were plotted to observe the changes in the (β) regression coefficients when each LPL record was left out. The {ggcoxdiagnostics} function in the “survminer” R-package (Kassambara et al., 2022) was used for both analyses. All analyses were performed using the R software version 4.3.1 (R Core Team, 2023).

Results

The Cox PH assumption and outlier analyses

The PH assumption was evaluated for all fitted models using hypothesis tests and graphical analyses (Supplementary Figs. 1 to 4). For models 1, 3, and 4, the Schoenfeld hypothesis tests indicated the HR did not change over time for all fixed effects included in these models (P > 0.05). For model 2, however, the test of PH for AFL suggested it changed over time (P = 0.02), although the global test (over all p factors fitted) was not significant (P > 0.05) for this model. In Supplementary Figs. 1 to 4, there is one solid black line, which is bounded by black dashed lines reflecting the 95% CI. When the solid line is nearly straight along the x-axis and positioned close to the zero point (y-axis), the assumption of a proportional hazard is met. Therefore, based on graphical analyses, the Cox PH assumption seems to hold for all fixed effects included in the 4 models, as the estimated regression coefficient of β on time was close to zero even for the effect of AFL in model 2.

Deviance residuals for each ewe were plotted to identify potential outliers (Supplementary Figs. 5 to 8). Deviance residuals are normalized transformations of the martingale residuals and should be symmetrically distributed around zero (Therneau and Grambsch, 2000). Very large deviance residuals (positive or negative) are considered outliers, which the model poorly predicts. If ±3 deviance residuals were assumed as a threshold from which residuals are considered outliers, few extreme deviance residuals were found in these plots. Even when present, an outlier may not significantly affect the Cox regression coefficients, especially when analyzing large datasets. Thus, as a further check to evaluate the possible influence of each LPL on the regression coefficients, dfbeta residuals (Therneau and Grambsch, 2000) and estimated changes in the regression coefficients upon deleting each observation (Supplementary Figs. 9 to 12) were plotted. Although some dfbeta residuals stand out from the others, none had a major influence on the estimates of the regression coefficients. This indicates that there was minimal change in the regression coefficient estimates when each observation was removed.

Survival probabilities

The global likelihood ratio tests (LRT) defined variation in LPL (P < 0.0001) for all Cox PH models (Table 2). AFL did not define variation in LPL in any model (P > 0.05), while EDA did only in model 1 (P < 0.05). Linear and quadratic effects (P < 0.05) of ABW on LPL were observed in both models 2 and 4. AWW had linear and quadratic effects (P < 0.05) on LPL in model 3, while a quadratic effect (P < 0.05) of AWW on LPL was observed in model 4. The variances estimated for the CG were slightly higher in models 2 and 3 than in models 1 and 4, but these differences appear too small to have any major impact on the analyses. The concordance rate (CR) measures how discriminant the models are. It provides information on the model’s ability to predict which ewe of a pair will die (or be culled) sooner, but not necessarily how much sooner. In the present study, CR ranged from 0.70 (Model 1) to 0.73 (Model 4).

Table 2.

Median of the LPL (in days), their 95% confidence intervals, contemporary group variance [V(CG)], concordance rate (CR) ± standard error (SE), likelihood ratio test (LRT), and P-values of survival analysis of the LPL in U.S. Katahdin ewes according to each model used

Model1	Median	Confidence interval		V(CG)	CR (SE)	LRT	Global P-values	P-values2
		Lower	Upper
								CG	BR	AFL-L	EDA-L	ABW-L	ABW-Q	AWW-L	AWW-Q
K-M1	1,037	1,006	1,056
CPH1	944	775	1,028	0.49	0.70 (0.003)	3,143	<0.0001	<0.0001	<0.0001	0.7711	0.0163
K-M2	982	885	1,023
CPH2	778	743	984	0.52	0.72 (0.004)	2,900	<0.0001	<0.0001	0.0003	0.2655	0.1631	<0.0001	<0.0001
K-M3	737	732	744
CPH3	730	723	740	0.55	0.72 (0.004)	2,392	<0.0001	<0.0001	0.0024	0.7708	0.2161			<0.0001	<0.0001
K-M4	730	725	735
CPH4	724	717	734	0.50	0.73 (0.005)	2,058	<0.0001	<0.0001	0.0021	0.7858	0.4610	<0.0001	<0.0001	<0.1273	<0.0001

¹K-M1 to K-M4: Kaplan–Meier based model using the same sample of CPH1 to CPH4 Cox proportional hazard-based models.

²CG: contemporary group; BR: birth and rearing type (classes 1/1, 2/1, 2/2, 3/2, 3/3, with digit-3 including lamb counts ≥ 3); AFL-L: ewe’s age at first lambing linear effect; EDA-L: Ewe’s dam’s age linear effect; ABW-L and ABW-Q: average lamb birth weight linear and quadratic effects, respectively; AWW-L and AWW-Q: average lamb weaning weight linear and quadratic effects, respectively.

The non-parametric K-M method was used to estimate ewe survival probabilities without any predictor fitted in the model, i.e., K-M calculated the probability of ewes dying at the time (t), given that ewes were alive immediately before (t). The Cox PH method estimates this survival probability by adjusting independent predictors that explain the variation in the survival probabilities. The global survival probability curves estimated with K-M and each Cox PH model are presented in Fig. 1. For all models fitted, the Cox PH estimates of survival probabilities were slightly lower across time than those based on K-M.

Figure 1.

Survival curves of U.S. Katahdin ewes according to different Cox proportional hazard (Cox PH) and Kaplan–Meier models, using the LPL as a time-to-event trait.

For a symmetrical normal distribution, the values of the mean and median were similar. However, since survival data are often right-skewed, the median is a better measure of central tendency than the mean. The global median values and their 95% CI estimated by each model are presented in Table 2. Within each model fitted, the global median estimates for LPL based on K-M and Cox PH methods were within overlapping 95% CI, which indicates similar solutions for both methods. On the other hand, a higher median LPL was estimated (non-overlap 95% CI) when fitting models 1 and 2 than with models 3 and 4 for both K-M and Cox PH methods. When fitting models 1 and 2 to the same data used in model 4 analysis, a median of 722 (95% CI: 715 to 731) and 724 (95% CI: 717 to 733), respectively. Therefore, the large differences observed for the median across models are a consequence of the sampling.

Although, based on model 1, EDA had a linear effect on LPL, this effect was not significant in models 2, 3, and 4. Moreover, the EDA was not significant when fitted model 1 with the same dataset used in model 4, which suggested that the consequences of this effect depended on the sampling. On the other hand, BR and average lamb weights at birth and at weaning were significant based on all models, indicating a consistent effect. Regarding the BR effect, 3/3 ewes showed higher survival probabilities throughout the entire survival curve, especially when compared to classes 1/1 and 2/1 (Fig. 2). However, only models 3 and 4 showed differences between the median survival, where 3/3 ewes had a median LPL of approximately 3 yr while 1/1 and 2/1 ewes had approximately 2 yr (Fig. 2). Table 3 shows the HR (and their 95% CI) for U.S. Katahdin ewes, considering the levels of BR in each Cox PH model. A HR > 1 indicates an increased risk of removal from the flock (death or culling) for a specific level of fixed effect, while a HR < 1 indicates a decreased risk. The reference BR class was 1/1, for which was assumed an HR of 1.00. Based on models 1, 2, and 3, the 95% CI of the ewes in BR classes 2/2 and 3/3 did not overlap an HR of 1.00, which indicates a significant difference between these 2 classes and the reference class 1/1. On average, ewes themselves born in BR classes of 2/2 and 3/3 had an 8 to 17% (models 1 and 2) and 11 to 14% (model 3), respectively, lower risk of dying or being culled than ewes in the 1/1 class. Based on model 4, only 3/3 ewes had a lower risk (13%) of dying or being culled than ewes 1/1.

Figure 2.

Adjusted survival curves of U.S. Katahdin ewes according to the birth/rearing type classes and based on Cox proportional hazard (Cox PH) models, using the LPL as a time-to-event trait.

Table 3.

Hazard ratio based on birth-rearing type effect (BR) in U.S. Katahdin ewes

Model1	BR	N	Hazard ratio	95% confidence interval
CPH1	1/1	2,357	1.00	Reference class
	2/1	460	1.04	0.91 to 1.18
	2/2	5,934	0.92	0.86 to 0.98
	3/2	527	0.95	0.84 to 1.08
	3/3	1,196	0.83	0.76 to 0.92
CPH2	1/1	1,782	1.00	Reference class
	2/1	333	1.09	0.93 to 1.27
	2/2	4,730	0.92	0.85 to 0.99
	3/2	4,16	0.97	0.84 to 1.12
	3/3	988	0.83	0.75 to 0.93
CPH3	1/1	1,312	1.00	Reference class
	2/1	277	1.04	0.88 to 1.22
	2/2	3,606	0.89	0.82 to 0.96
	3/2	317	0.94	0.81 to 1.10
	3/3	718	0.86	0.76 to 0.98
CPH4	1/1	1,073	1.00	Reference class
	2/1	216	1.02	0.84 to 1.24
	2/2	3,087	0.92	0.83 to 1.01
	3/2	273	1.01	0.84 to 1.20
	3/3	629	0.87	0.75 to 0.99

¹CPH1 to CPH4: Cox proportional hazard models 1 to 4.

A consistent quadratic effect of the ABW on the survival probability was found with models 2 and 4 (Fig. 3), where the survival probability peaks were always close to 5 kg for all times analyzed. Then, survival curves for weights from 2 to 7 kg at increments of 1 kg were plotted. The 3 best survival curves were found with ABW of 4, 5, and 6 kg, although model 2 showed a greater distance between the 3 curves than model 4. Based on models 2 and 4, ewes that gave birth to very light (2 kg) or very heavy lambs (7 kg) had the shortest survival, with a median LPL lower than 500 d.

Figure 3.

Survival probability of U.S. Katahdin ewes according to the average lamb weight at birth (ABW) based on Cox proportional hazard models 2 (top plots) and 4 (bottom plots). Right plots show survival probabilities at time t in function of ABW, while left plots show survival probability curves in function of the length of productive life (LPL in days) for 6 classes of ABW.

Survival analyses with models 3 and 4 also showed a consistent effect of AWW on LPL (Fig. 4). Based on model 3, the best survival probability was estimated when the AWW was between 20 and 25 kg. Ewes that weaned lambs weighing either 20 or 25 kg had similar survival curves, both with median LPL greater than 1,000 d. Model 4 estimated the highest survival probabilities for ewes that weaned lambs weighing approximately 20 kg, which also showed a median LPL greater than 1,000 d. Ewes that weaned very light (5 kg) or very heavy (35 kg) lambs had substantially shorter LPL, both with a median value of less than 500 d.

Figure 4.

Survival probability of U.S. Katahdin ewes according to the average lamb weight at weaning (AWW) based on Cox proportional hazard models 3 (top plots) and 4 (bottom plots). Right plots show survival probabilities at time t in function of AWW, while left plots show survival probability curves in function of the length of productive life (LPL in days) for 7 classes of AWW.

Discussion

This is the first study using LPL as an indicator of ewe survival or longevity in U.S. Katahdin sheep. For this study, LPL was defined as the difference between the first and last lambing event recorded for each ewe. In practice, ewes can die at any point in the production year and are typically culled when their lambs are weaned 2 or 3 mo after their last lambing. However, the actual death or culling dates were unavailable, and our definition of LPL provided greater consistency in lieu of this information. All ewes without lambing records in the last 2 yr that a flock reported lambing information were assumed as censored data. That was based on the supposition that sheep farmers typically cull ewes after 2 consecutive year of bareness. The moderate percentage of right-censored ewes in the present study (between 29.3% and 32%) could be a consequence of these assumptions. These values are higher than the 12% and 10% reported by Kern et al. (2010) and Getachew et al. (2015), respectively, and near to the 25.8% reported by Milerski et al. (2018). The right-censored data in survival analyses avoids underestimating the overall survival time but may also cause bias, especially in studies with small sample sizes (Lagakos, 1979). However, survival probabilities and HR are generally estimated using large samples in an animal breeding context. Such was the case in the current study. For instance, the lowest number of observations (uncensored ewes) for a category was 216, which was used to calculate an HR of 1.02 (95% CI: 0.84 to 1.24) for ewe’s BR 2/1 in model 4. Even this smallest group had a sample size greater than those usually observed in clinical survival human studies (e.g., Schoenfeld, 1983; Delisle et al., 2022). Thus, even sheep studies with a large percentage of right-censored data, such as 76.4% (Riggio et al., 2009) and 61% (Abdelqader et al., 2012), have previously been conducted.

Residual analyses

A hypothesis test and graphical analyses were carried out to check the assumption of a constant PH over time based on Schoenfeld’s residuals (Schoenfeld, 1982). This is an essential step in survival analyses because one cannot assume that one group will always have a greater hazard than another group when the PH assumption does not hold over time (Therneau and Grambsch, 2000). In the current study, the global hypothesis test for the Cox PH assumption was not rejected across models with only one exception (AFL in model 2). Some significant results are expected in large sample size studies, where a high significance with a minimal violation of the PH assumption is common (In and Lee, 2019). Thus, a graphical analysis was carried out to identify changes in the regression coefficients for the systematic effects over time. The regression of β on LPL generated a consistent slope close to zero even for ewe AFL in model 2, indicating that the PH was consistent across time. Moreover, based on inspection of the plots of the Schonfeld residuals, regardless of the model and systematic effect, there was little indication that the HR was not proportional over time. Therefore, although one hypothesis test associated with model 2 suggested the assumption of a constant PH be rejected, there was little reason for that conclusion based on graphical analyses. Based on these results, survival studies in livestock, especially when large samples are analyzed, should perform both types of analyses (hypothesis test and graphical based on Schoenfeld residuals) and avoid inferences only based on hypothesis tests.

Another important validation of our survival analysis considered the influence of outliers on our predictions. Thus, 2 types of residuals were used, the deviance and dfbeta residuals (Therneau and Grambsch, 2000), which are useful methods for checking the goodness-of-fit of survival models and identifying potential outliers/influential records to a fitted model (Therneau et al., 1990). Based on these analyses, no ewe had a deviance residual that was very different from the others. Therefore, there was no reason to assume that there were outliers in this population. The higher the deviance residual, the lower the ability of the survival model to predict when the ewe would leave the flock. For instance, based on the different Cox PH models, it is expected longer and shorter productive life for ewes of BR 3/3 and 1/1, respectively. However, as with any regression analysis, the Cox PH also has prediction errors. An extreme deviance residual will occur if a sheep breeder decides to cull a 3/3 ewe early because of low prolificacy in her first 2 parities, or if a 1/1 ewe stays in the flock for an extended period due to her high prolificacy. In both cases, large deviance residuals are produced because the true and predicted LPL will not be similar. Therefore, the closer the deviance residual is to zero, the more reliable the model is in predicting LPL.

To check whether some LPL records greatly influenced the regression coefficients, the dfbeta residuals of each ewe on their respective predictors were plotted. Each point in these plots is a dfbeta residual, interpreted as the approximate change in the regression coefficient if the observation is removed (Therneau and Grambsch, 2000). Although some points stand out in the plots, the changes in the regression coefficients were minimal, which suggests that even the extreme values had limited influence on solutions. Therefore, the dfbeta residuals support the hypothesis that there were no influential LPL records in this population, i.e., even if some of the deviance residuals were outliers, they were not exerting great influence on the estimates of regression coefficients.

Katahdin ewe survival

Previous studies have reported that LPL varies within- and between-breeds (Annett et al., 2011; Hanna et al., 2023). Getachew et al. (2015) estimated a mean LPL of 1,079 d (SD 663.4 d) for Ethiopian sheep breeds, with a mean of 2.6 ± 1.4 lambing records per ewe over lifetime. A higher LPL (mean of 1,361 d and SD 788 d) for German sheep breeds, with 3.7 ± 2.1 lambing records per ewe, has also been reported (Kern et al., 2010). Even higher values were reported by Abdelqader et al. (2012) in Najdi sheep (mean of 1,635 d; SE = 11.0 d) and Awassi sheep (mean of 2,204 d; SE = 8.1 d) but with a mean number of litters of 4.1 ± 0.27 (Awassi) and 3.3 ± 0.34 (Najdi). Here, median values instead of the mean were used, as the LPL distribution has a large right-skewness. Our median LPL values are more similar to those of Getachew et al. (2015) than other sheep studies (Kern et al., 2010; Abdelqader et al., 2012). The mean number of litters in the Katahdin population studied was 2.66 ± 1.74, similar to the result reported by Getachew et al. (2015). Hanna et al. (2023) evaluated ewe longevity as age at last lambing (ALL) in 4 U.S. sheep breeds: Columbia, Polypay, Rambouillet, and Targhee. They reported that mean values ranged between 3.4 yr (Polypay) and 3.6 yr (Rambouillet). Then, average ALL was calculated for all uncensored ewes, including those with a single lambing event, and a slightly lower value of 3.0 yr in the Katahdin breed was estimated.

Factors affecting ewe survival

The CG is an important source of variation for LPL in Katahdin ewes. Previous sheep studies reported significant effects such as flock and year of ewe’s birth (Kern et al., 2010; Getachew et al., 2015) but did not analyze the CG effect. Economic factors vary frequently, which may differentially affect sheep breeders. Therefore, culling decisions are expected to vary across flock–year–season levels. This unobserved heterogeneity in culling decisions can be modeled in livestock by including the CG as a random effect in the survival model, which is often highly significant (e.g., Chirinos et al., 2007). In the present study, CG was fitted as a random effect, i.e., a frailty term, because ewes from the same CG were expected to be subjected to similar culling decisions, including productive, economic, and health issues. Replacing the estimates of the variances found for CG in the equation reported by Therneau and Grambsch (2000), the estimate of the correlation between ewes within the same CG was approximately 0.2, which should not be ignored when modeling ewe survival in the Katahdin breed. The CG variances are used to adjust the hazard estimates due to unobserved heterogeneity caused by many factors that may affect the longevity of a group of ewes that experience similar environmental conditions throughout their productive lives. The slight differences between the CG variance estimates by each model indicate that the hazard adjustments performed by different models are similar.

Although there are no previous studies regarding the effect of dam age on ewe LPL in sheep, daughters of ewe lambs were culled earlier than daughters of mature ewes (McLaren et al., 2020). There is a well-known effect of dam age on lamb survival (Nel et al., 2021; Odevci et al., 2021; Besufkad et al., 2024), where lambs born to young ewes have higher mortality than those born to mature ewes. Dam age also might have a direct association with the mature size of their daughters. Pettigrew et al. (2019) reported that daughters of ewe lambs were lighter over lifetime than daughters of mature ewes. Mature ewes are generally larger than ewe lambs, which may have an impact on the lifespan of their daughters. Asmad et al. (2014) reported that a greater proportion of ewes at 2,298 d of age were daughters of heavy dams as compared to light dams. These results suggest a potential effect of intrinsic dam features on daughter longevity, although a significant effect of ewe’s dam’s age on LPL was only detected when fitting model 1. In the present study, LPL depended on the ewe’s reproductive performance, because lambing record dates were used to calculate LPL. Non-significant effects of dam age on lifetime ewe’s reproductive performance, however, have been reported in other sheep breeds (Pettigrew et al., 2019; Vlahek et al., 2023). Therefore, our results suggest that Katahdin breeders have no reason to consider dam age when selecting replacement ewes to increase ewe longevity. However, it is essential to highlight that our LPL was recorded in ewes with 2 or more lambing records. Therefore, the EDA effect when ewes lamb only once remains unknown.

The present study has some differences from previous ones that evaluated LPL as survival data in sheep (Kern et al., 2010; Milerski et al., 2018). Direct comparisons of BR effect on LPL are, therefore, challenging to extrapolate. First, these previous studies did not evaluate rearing type, which probably grouped the ewes’ classes as 2/1 with 2/2, and 3/1 and 3/2 with 3/3. Moreover, Kern et al. (2010) evaluated LPL as the difference between the first lambing and the culling dates, while Milerski et al. (2018) evaluated 4 classes of birth type (1, 2, 3, and ≥4). Assuming only single, twin, and triplet birth classes, Milerski et al. (2018) and Kern et al. (2010) reported no significant effect on LPL. The birth type may affect the lamb size, where lambs from larger litters are frequently lighter and show smaller weight gain (Jucá et al., 2014; Chay-Canul et al., 2019). Ewe lambs’ reproductive performance depends on the body size, as heavier ewe lambs may have earlier puberty compared to the lighter ones (Ferra et al., 2010). Moreover, heavier ewe lambs may be more fertile and show a higher reproductive rate than lighter ewe lambs (Rosales Nieto et al., 2013). This might explain the longer productive life observed in ewes born from smaller litters observed by Hanna et al. (2023), but this previous study used a linear model and recorded productive life as ALL, which differs from the present study.

It is important to note that our LPL was calculated with ewes that had 2 or more lambing records, i.e., ewes that were not culled after the first lambing. Therefore, one can assume that all these ewes showed a satisfactory first lambing output. Then, the average prolificacy of 1/1 and 3/3 ewes over their lifetime were compared and lower (P < 0.05) average values for ewes 1/1 (1.74 ± 0.0075 lambs born and 1.60 ± 0.0077 lambs weaned) than 3/3 (1.82 ± 0.0144 lambs born and 1.70 ± 0.0147 lambs weaned) were found. Moreover, AWW for these BR classes were compared, as more prolific ewes are expected to produce lighter lambs, but ewes 1/1 produced slightly lighter lambs at weaning (19.2 ± 0.09 kg) than 3/3 ewes (19.9 ± 0.18 kg) (P < 0.05). Therefore, the higher survival probabilities observed for ewes 3/3 over lifetime may be associated with their slightly better reproductive performance compared to 1/1 ewes. Prolificacy is an intrinsic characteristic of the Katahdin breed, where a mean of 2 lambs born per ewe lambing was reported (Rastle-Simpson et al., 2017). Although lower birth weight is expected for lambs born in twin, triplet, or larger litters, Chay-Canul et al. (2019) reported a small difference in birth weights of single (4.1 ± 0.19 kg) and twin (3.8 ± 0.19 kg) Katahdin lambs. In the present study, ewes with progeny that weighed up to 3.8 kg on average at birth were in the quartile 1. Therefore, on average, the Katahdin ewes gave birth to adequate lamb size over their lifetimes even though producing a substantial number of twin and triplet litters. Our results showed that the AWW over lifetime is almost equivalent across BR classes, at least when considering ewes with 2 or more lambing.

The AFL is considered an essential maternal trait affecting profitability in the Katahdin breed (KHSI, 2020), as retained ewes only generate revenue once they first lamb. In the current study, AFL was fitted as a continuous covariate and no significant effect on LPL was detected. Previous studies analyzed AFL as a categorical factor and found significant effects on ewe survival. Riggio et al. (2009) evaluated the classes 10 to 18, 19 to 23, and 24 to 30 mo in Valle del Belice dairy sheep and reported a lower hazard for ewes that lambed before 19 mo, while Kern et al. (2010) analyzed the classes <395, 395 to <455, 455 to <730, and ≥730 d and observed a lower hazard for ewes that lambed before 395 d. On the other hand, other studies showed decreased risk in intermediate or older classes. Getachew et al. (2015) analyzed the classes < 725, 725 to 874, 874 to 928, and > 928 d in Ethiopian sheep breeds and reported lower hazard for the class 874 to 928 d, while Abdelqader et al. (2012) analyzed the classes ≤13, 14 to 16, 17 to 19, 20 to 22, and ≥23 mo in Awassi and Najdi ewes and observed a drop in risk as age increased. Therefore, the impact of AFL on ewe survival is probably dependent on the breed and production system, which can be explained by several factors. For instance, breeding season, age at puberty, and body weight are known factors affecting the AFL (Kenyon and Corner-Thomas, 2022). The puberty of ewe lambs is often observed when they have 50% to 70% of their mature weight (Dýrmundsson, 1981), while Katahdin breeders reported that females will cycle for the first time around 7 to 10 mo and should be approximately 70% of their mature weight before breeding (KHSI, 2020). Burke (2005) reported that the best breeding season for Katahdin in the southeastern U.S. is in late summer. Therefore, the variability of these factors across breeds may explain the different effects of AFL on ewe survival.

During the last 20 yr, NSIP has reported EBV for birth, weaning, and post-weaning body weights, which should be used to select replacement animals to improve growth rates. The NSIP suggests that breeders place positive selection emphasis on increasing weaning weight (Notter and Lewis, 2018). According to Notter and Lewis (2018), positive selection for birth weight may also be advantageous if a breed is prolific and the flock does not have issues with lambing difficulty, as a large birth weight is associated with better lamb survival. Moreover, NSIP also provides the maternal effects for both birth and weaning weights, and a maternal index used to select hair sheep breeds that aim to maximize the total weight of lamb weaned per ewe (Notter and Lewis, 2018). This selective process may be affecting the Katahdin ewe longevity, as a significant quadratic effect of ABW and AWW on LPL was observed in the current study. These results differ from Getachew et al. (2015), who observed no significant differences between ewes that weaned lighter (lamb weight less than 1 SD from the mean; HR = 1.07), intermediate (lamb weight ± 1 SD from the mean; HR = 1.00), and heavier (above 1 SD from the mean; HR = 0.97) lambs. This previous study used categorical classes of weaning weight. Although there are not many studies evaluating the impact of ewe productivity on ewe longevity based on the body weight of their lambs, one can expect earlier culling for lower- than higher-performing ewes due to the selection. The current study suggests that producing lambs with extreme weights (very low or very high) may result in lower LPL. A very low weight of the lambs at birth and at weaning can lead the breeder to cull the ewe early, as growth traits play an important role in the selection schemes of U.S. Katahdin sheep. On the other hand, low longevity in ewes that produce large lambs may be related to other factors. For instance, large lambs often lead to dystocia, which may cause ewe death (Jacobson et al., 2020). Moreover, body weight at birth and weaning generally decreases with the increased birth type (Burke, 2005; Chay-Canul et al., 2019). A number of lambs weaned with EBV has the greatest emphasis in the U.S. Hair Index (Notter and Lewis, 2018). Therefore, if there is a selective scheme to increase prolificacy, ewes that produce larger lambs from single births may be discarded early based on low prolificacy. Unfortunately, the number of lambs (born or weaned) as predictor variables in our Cox models was not evaluated, as these predictors presented a strong deviation from the Cox PH assumption.

While previous studies with other breeds (Kern et al., 2010; Abdelqader et al., 2012; Getachew et al., 2015; Milerski et al., 2018) addressed mainly HR, both survival and hazard functions were addressed in the current study. The survival function estimated survival probabilities that suggested a short median LPL for Katahdin ewes, with 50% of the ewes with 2 or more lambing events showing less than 3 yr of LPL. Moreover, approximately 33% of ewes were culled after a single recorded lambing event. These results should be interpreted with caution because disposal reasons were not recorded (and evaluated). Ewes of reproductive age are culled for voluntary or involuntary reasons (McLaren et al., 2020). Voluntary culling can be beneficial for the flock provided less productive ewes are replaced with ewe lambs of greater genetic merit. Although voluntary culling reduces the generation interval, it should not be so intense to avoid an extreme reduction in the number of replacement lambs. In this current Katahdin population, an average of 4.3 lambs weaned throughout a ewe’s lifespan was estimated. Considering that only half of these lambs are females, in the best scenario there would be 2 female lambs to replace each mature ewe. This number is probably lower, as there are factors such as post-weaning mortality, low fertility, and poor conformation that reduce the number of selection candidates (Kenyon and Corner-Thomas, 2022). Therefore, with the short median LPL observed in Katahdin sheep necessitating higher retention rates of ewe lambs to maintain flock size, the selection intensity in Katahdin females is probably limited by the number of ewe lambs available to be used as replacements.

An unknown portion of ewes culled in the present study were due to involuntary reasons such as diseases and reproductive issues as well as mortality. Involuntary culling varies across flocks but, independent of the proportion of involuntary culling in each flock, they are classified as ewe wastage. Farrell et al. (2019) reported that the ewe wastage rates ranged from 5% to 21% in New Zealand and a 10% reduction in this wastage could increase flock profitability by 17%. A study performed across the U.S. analyzed 147,560 ewes lost by nonpredator causes and identified the top 3 causes as old age (18.4%), internal parasitosis (15.9%), and lambing problems (10.1%) (USDA-APHIS, 2022). Of these 3 causes, only old age is a voluntary culling reason, which suggests a substantial percentage of ewe wastage. A great part of these data was collected on commercial sheep flocks, which may have less stringent culling practices than the seedstock flocks described in the present study. Seedstock flocks often use EBV in their selection schemes. Thus, voluntary culling is expected to be greater in seedstock than in commercial flocks. Regardless of the type of flock, a drop in involuntary culling can increase both ewe lifespan and the total offspring produced per ewe, allowing a more intense selection of females. Moreover, it can reduce the annual flock demand for replacement ewes lamb, which has an economic impact on the production system. Finally, we encourage breeders and NSIP to record both date and reason of culling, which can improve ewe longevity assessment and genetic evaluations in future studies. The culling date would allow the inclusion of data from ewes that had only one lambing record, while the culling reason would allow them to separate voluntary from involuntary culling data, consequently, survival curves for health issue, infertility issue, or production issue ewes could be estimated separately.

Conclusions

In the current study, the productive lifespan of Katahdin ewes in the US was described for the first time. The lack of information on the dates and reasons ewes died or were culled caused some limitations to our analyses, and breeders should be encouraged to collect such records. Still, based on our analyses, Katahdin ewes have a short median LPL, likely reflecting a considerable voluntary culling of younger ewes. A high annual replacement rate based on voluntary culling will reduce the generation interval, and consequently increase genetic gain per year. But this benefit may be offset in Katahdin sheep by lower selection intensities in females because of the reduced number of progeny per ewe during her lifetime. Furthermore, a high annual ewe replacement rate is costly and may impact overall flock profitability. These questions must be addressed to develop breeding programs that balance genetic gain and profitability in the U.S. sheep industry. In future studies, the rate of involuntary culling in Katahdin ewes with regard to annual genetic gain in females should be quantified for the traits currently under selection. Altogether, such information could be used to determine the extent longevity-related traits should be incorporated into breeding objectives in Katahdin sheep.

Glossary

Abbreviations

ABW

average lamb birth weight

AFL

age at first lambing

AWW

average lamb weaning weight

BR

birth-rearing type

BW

lamb birth weight

CG

contemporary group

Cox PH

Cox proportional hazard

CR

concordance rate

EBV

estimated breeding values

EDA

ewe’s dam’s age

HR

hazard ratio

K-M

Kaplan–Meier

LPL

length of productive life

LRT

likelihood ratio tests

NSIP

National Sheep Improvement Program

PH

proportional hazard

WW

lamb weaning weight

Conflict of interest statement

The authors declare no real or perceived conflict of interest.

Author contributions

Luis F. B. Pinto (Conceptualization, Formal analysis, Investigation, Methodology, Visualization, Writing—original draft, Writing—review & editing), Ronald M. Lewis (Conceptualization, Funding acquisition, Investigation, Writing—review & editing), Artur O. Rocha (Investigation, Writing—review & editing), Brad A. Freking (Resources, Writing—review & editing), Tom W. Murphy (Resources, Writing—review & editing), Carrie S. Wilson (Resources, Writing—review & editing), Sara M. Nilson (Investigation, Writing—review & editing), Joan M. Burke (Resources, Writing—review & editing), and Luiz F. Brito (Conceptualization, Investigation, Supervision, Writing—review & editing)