Effects of extending dairy cow longevity by adjusted reproduction management decisions on partial net return and greenhouse gas emissions: A dynamic stochastic herd simulation study

Prolonging dairy cattle longevity is regarded as one of the options to contribute to more sustainable milk production. Because failure to conceive is one of the main reasons for culling, this study investigates how adjustments in reproduction management affect partial net return at herd level and greenhouse gas emissions per unit of milk, using a dynamic stochastic simulation model. The effects of reproduction decisions that extend cattle longevity on milk yield, calving interval and pregnancy rate were derived from actual performance of Dutch commercial dairy cows over multiple lactations. The model simulated lactations, calving, and health status events of individual cows for herds of 100 cows. Scenarios evaluated differed in the maximum number of consecutive AI attempts (4, 5, or 6 services), or the production threshold (20, 15, or 10 kg of milk/d) at which cows that failed to conceive are culled (reproductive culling). Annual partial net return was computed from revenues of sold milk, calves, and slaughtered cows, and the costs from feed consumption, rearing replacement heifers, AI services, and treatment for clinical mastitis and lameness. Green-house gas emissions were computed for feed production, enteric fermentation, and manure management, and were expressed as total CO 2 equivalents (CO 2 -eq). Average age at culling increased with an increased maximum number of AI services. This increase was larger when going from a maximum of 4 to 5 AI attempts (108 d) than from a maximum of 5 to 6 attempts (47 d). Similarly, the average age at culling increased from 1,968 to 2,040 and 2,132 d when the threshold for reproductive culling decreased from 20, to 15 and 10 kg of milk/d, respectively. Average annual partial net return increased by 1.1% from €165,850 per 100 cows at a maximum of 4 AI to €167,670 per 100 cows at a maximum of 6 AI, and increased by 4.3% from €161,210 per 100 cows at a reproductive culling threshold of 10 kg/d to €168,190 per 100 cows at a threshold of 20 kg/d. Greenhouse gas emissions decreased by 1.2% from 0.926 to 0.915 kg CO 2 -eq per kg of fat-and protein-corrected milk (FPCM) with an increase in a maximum number of AI from 4 to 6 AI. Conversely, greenhouse gas emissions increased by 0.2% from 0.926 kg at a threshold of reproductive culling of 20 kg/d to 0.928 kg CO 2 -eq/kg FPCM at a threshold of 10 kg/d. Although lowering the threshold for reproductive culling has the potential to extend cattle longevity more than increasing the maximum number of AI services, only the increase in AI services benefits a farm’s partial net return, while reducing greenhouse gas emissions.


INTRODUCTION
On commercial dairy farms, failure to conceive is one of the primary reasons for culling cows, in addition to health disorders and low milk production (Dallago et al., 2021).Farmers' reproduction management involves decisions rules on the maximum number of artificial insemination (AI) attempts to get cows pregnant, as well as the production threshold below which cows that did not conceive after those maximum AI attempts are culled.Easing these reproduction management decision rules, will reduce reproductive culling and increase the average age at culling.
The average lifespan of a dairy cow in the Netherlands from birth to culling is around 5.8 years, with a range of 4.9 to 7.1 years across farms (Han et al., 2022), considerably shorter than the natural lifespan of dairy cows of approximately 20 years (De Vries et al., 2020).In Dutch dairy farming systems, the vast majority of culled dairy cows are slaughtered for human consumption and replaced by on-farm reared heifers.Prolonging Effects of extending dairy cow longevity by adjusted reproduction management decisions on partial net return and greenhouse gas emissions: A dynamic stochastic herd simulation study Ruozhu Han, 1 * Akke Kok, 2 Monique Mourits, 1 and Henk Hogeveen 1 the lifespan or longevity of dairy cattle could contribute to more sustainable milk production, from an economic, an environmental as well as a social perspective (Han et al., 2022;Schuster et al., 2020).
Extending cattle longevity through changes in reproductive decisions will inevitably affect farm profitability and greenhouse gas (GHG) emissions.A lower culling rate will reduce the demand for replacement heifers, reducing the associated rearing costs and GHG emissions.In addition, the milk yield of a herd might increase when longevity increases.Reduced reproductive culling increases the proportion of multiparous cows in a herd.Multiparous cows usually produce more milk than primiparous cows (Neave et al., 2017;Walter et al., 2022), resulting in a lower GHG emission per kg milk produced.However, the increase in herd yield potential due to a higher proportion of multiparous cows may not offset the milk loss due to higher disease risk for older cows (Gussmann et al., 2019;Rilanto et al., 2020).In addition, more AIs will directly increase AI costs, while a higher disease risk for older cows may increase treatment costs.The trade-offs between positive and negative impacts of extending longevity on farm economic and environmental performance make it difficult to advise on optimal longevity.The objective of this paper is to explore the effect of extending cattle longevity by assessing how different reproduction management decisions affect technical and economic results at herd level, and GHG emissions per unit of milk, using a dynamic stochastic simulation model.

MATERIALS AND METHODS
This study used a modified version of the bio-economic simulation model by Kok et al. (2017), developed to stochastically simulate Dutch dairy herds of 100 cows to evaluate the impact of varying dry period lengths.The original model of Kok et al. (2017) simulated individual lactations and calving intervals, while accounting for culling, either for fertility reasons (reproductive culling) or for other reasons (i.e., general culling).Model output was defined by partial cash flow at the herd and GHG emissions per kg of fat-protein-corrected milk (FPCM) production.To compute GHG emissions from 'cradle to farm gate', a life cycle approach was applied, which also accounts for the production of meat from surplus calves and culled cows, assuming that it substituted other meat on the basis of edible product, thus avoiding additional GHG emissions from meat production elsewhere (see Supplementary Material).
To evaluate the economic and environmental impact of alternative reproduction management strategies, the herd simulation model of Kok et al. (2017) was modified by accounting for i) the timing and success of AI and the resulting calving interval, ii) the impact of clinical mastitis and lameness, iii) the adjustment of the probability of disease for the time present in the herd, iv) the milk production losses and discarded milk due to lameness and clinical mastitis, v) the adjusted growth of first and second parity cows due to an increase in lactation length.and vi) the costs for AI and treatments for clinical mastitis or lameness (see Figure 1).
With the modified herd simulation model, the impact of alternative reproduction management decision rules were evaluated.In the default scenario, cows were inseminated a maximum of 4 times and culled if their milk yield dropped below a threshold of 15 kg/day.This default scenario was set to reflect typical reproduction management practices in Dutch dairy herds (Rutten et al., 2014).Alternative strategies were set by either increasing the maximum number of consecutive AI attempts per cow to 5 or 6 times or modifying the reproductive culling threshold (i.e., the threshold at which cows that failed to conceive are culled) to either 10 or 20 kg milk per day.
A sensitivity analysis was conducted to evaluate the impact of variations in average milk production on financial performance of the herd, GHG emissions and longevity, and the impact of changes in replacement heifer costs and milk prices on the financial performance of the herd.
The model was run for 500 herds of 100 cow places for each reproduction management strategy to obtain stable estimates for the average annual partial net return and GHG emission at herd level.Results are presented from year 7 when cattle longevity estimates reach model equilibrium for adjusted reproduction management strategies.
Details on the model updates and simulations are provided in the following sections.

Reproduction.
For each cow, the model randomly assigned several AIs (1-6) until conception at the start of each lactation, based on the proportion of cows getting successful AI per parity (Table 1) (Inchaisri et al., 2011).Subsequently, the length of the calving interval was determined by days between calving until conception and an assumed 280 d gestation period (Nogalski et al., 2011) (Table 1).Parity differences were estimated based on the mean proportion of successful AIs from parity 1 as reference, and the relative differences in probability of successful AI between parities (Inchaisri et al., 2011).
Health status.At the start of each lactation, each cow was stochastically assigned to one of 7 health events The probability of a cow remaining healthy was adjusted for the length of the calving interval.
Clinical mastitis was defined as an intramammary infection causing visibly abnormal milk (e.g., color, fibrin clots), and lameness was defined as a case of poor locomotion (suboptimal mobility score 4 or 5 on a scale of 5).
The incidence rate of clinical mastitis varied with parity (Table 2) and stage of lactation (before or after 100 d in milk (DIM)).To capture the distribution of mastitis incidence within lactation, 60% of clinical mastitis cases were assumed to occur before 100 DIM and 40% between 101 to 307 DIM, based on the interval between calving to dry period from first successful AI   (Steeneveld et al., 2008;Hertl et al., 2018).It was used to avoid mastitis occurring after the end of lactation.The moment of mastitis occurrence within these lactation periods was determined using a uniform distribution.Only cows with mastitis in the first 100 DIM were at risk of being culled for clinical mastitis 90 d after diagnosis.The probability of cows being culled due to clinical mastitis in each parity is stated in Table 2. Similar to mastitis, the incidence rate of lameness varied with parity.It was calculated based on the odds ratio between multiparous and primiparous cows and the incidence rate in parity 1 (Alban, 1995;Enting et al., 1997) (Table 2).Since the severity of lameness leads to varying degrees of milk loss, 80% of lameness cases was assumed to be mild and 20% to be severe (Randall et al., 2018).The probability of cows being culled due to lameness in each parity is stated in Table 2.The timing of culling due to lameness was determined using the data from the study of Edwardes et al. (2022).
The probability of reproductive culling varied with parity and the defined maximum number of AIs (Table 2).In addition, more AIs until conception resulted in a longer calving interval.Cows were assigned to reproductive culling when they did not become pregnant within the maximum number of AIs and when their milk production dropped below the defined threshold for reproductive culling.
To meet an overall cull rate in each parity, 'general culling' remained in the model besides reproductive culling, and culling for clinical mastitis, and lameness.Its probability was fixed per parity (Table 2) to approximate the overall annual culling rate of 30% in Dutch dairy farms.'General culling' occurred at a certain fraction of completion of a cow's assigned CI, drawn from a distribution with a positive skew and a median fraction of 0.17 (β distribution with parameter a = 1.3, b = 5 (Rutten et al., 2014)).
A culled cow was replaced by a heifer that was assumed to calve at the age of 24 mo and enters the herd the following day.
Milk production.Lactation curves were updated based on milk production recording data of 50 randomly selected Dutch herds collected by the Dutch Cooperative Cattle Improvement Organization CRV BV.Individual milk production (MP) in kg of cow i in parity j at each day in milk (DIM) was calculated as: where RPL i is the relative production level of cow i; ADY is the average daily yield based on 305-d yield in kg milk of a cow in parity j; a, b, c, and k model the shape lactation curve (Wilmink, 1987) (Table 3).To reflect the natural variation in milk production from about 80% to 120% of the average milk production, RPL was defined from a normal distribution with a mean of 0 and standard deviation of 0.1.Average milk protein, fat and lactose contents were calculated per parity class and used to parameterize the milk composition of the simulated lactation curves (Table 3).Time steps in the model were of variable length, starting and ending when a cow calved or was culled, and when a calendar year started or ended, thus allowing aggregation of herd data per calendar year.Milk yield was computed per cow per time step, using the integral of the milk production function.
Clinical mastitis was assumed to result in a yield reduction of 5% for the remaining lactation period from diagnosis until dry-off or culling (Seegers et al., 2003).Moreover, milk was assumed to be discarded for 6 d following the diagnosis due to assumed treatment with antibiotics.Mild lameness was associated with a milk yield loss of 1.6% in total lactation yield, and severe lameness was associated with a milk yield loss of up to Energy requirements and feed intake.Maintenance, milk production, gestation, and growth were included in the calculation of energy requirements (Kok et al., 2017(Kok et al., , 2019)).Subsequently, these requirements were used to compute feed intake of dairy cows, using a weighted average of fixed rations for the summer (170 d) and winter period (195 d).Roughage consisted of fresh grass (in summer only), grass silage and maize silage, and was supplemented with by-products and concentrate.
Greenhouse gas emissions.A life cycle approach was used to assess the impact of altered reproduction management strategies on greenhouse gas emissions.Emissions of carbon dioxide, methane, and nitrous oxide were computed for feed production, enteric fermentation, and manure management, and were expressed as total CO 2 equivalents.The model used a fixed value for GHG emissions per replacement heifer, that accounted for feed production, enteric fermentation, manure management and mortality in the rearing phase; and computed GHG emissions of the dairy cows from simulation results using the same methodology (Kok et al., 2017).Total GHG emissions were expressed as CO 2 equivalents per kg FPCM.
The CO 2 equivalent factors used in the original model (Kok et al., 2017) were updated to new IPCC values (100-year time horizon; Forster et al., 2021).With this update, the GHG emissions related to the rearing of young stock in the current model were estimated to be 4848 kg CO 2 equivalents per replacement heifer; and emissions related to feed production were 474 and 477 kg CO 2 / t dry matter for the summer and winter ration, respectively.
Partial net return.In accordance with a metric describing the economic performance of the simulated dairy farm from Kok et al. (2017), partial net return was estimated based on the modeled revenue from sold milk, calves and slaughter culled cows, and the costs from replacement heifer, feed, AI and treatment for clinical mastitis and lameness per case.Only variable costs were considered (Table 4).The regular cost of labor provided by the farmer and housing costs were assumed to be fixed in the short term, implying that these cost items were not affected by changes in cow longevity.
Partial net return = revenues (milk, calves and slaughter culled cows) -costs (replacement heifer, feed, AI, treatment cost of clinical mastitis and lameness) Annual partial net returns were computed per herd of 100 dairy cows for different reproduction management decision rules.The revenues consisted of revenues obtained from milk production, surplus calves and culled cows.Milk revenues were based on the Dutch payment system based on milk solids value (10:5:1 ratio of protein: fat: lactose) using the average Dutch prices from 2019 to 2021 (Table 4).
To estimate the revenues for surplus calf sales, it was assumed that 50% of the calves born was male and 50% was female.The number of female calves kept annually to be reared as a replacement heifer equalled 113.4% of the number of culled cows, to account for a 13.4% calf mortality rate during the rearing period.Female calves not needed for replacement as well as all male calves were sold at 2 weeks of age, adjusted for 10% mortality.
The weight of slaughtered cows was estimated by assuming a dressing percentage of 60%.Calf values as well as slaughter value (Table 1) were based on the yearly values of 2019-2021 (Table 4).
Costs consisted of rearing costs of replacement heifers, feed costs and costs for AI and for clinical mastitis and lameness treatment.Replacement heifer costs were based on the average market value of full grown heifers over the period 2019-2021, while feed costs were calculated from Dutch feed prices per feed stuff during that same time period (Kok et al., 2019).
The cost of AI included both the price of semen and the costs of the AI procedure (KWIN, 2022).Each case of clinical mastitis was assumed to be treated with antibiotics.The applied treatment costs were derived from Dutch survey results from 2009 (Lam et al., 2013).For the treatment of lameness, this study differentiated between mild and severe cases: the treatment costs for mild lameness were negligible and for severe cases, it was based on a weighted average treatment cost of multiple claw disorders.It was estimated by combining the cost for each type of claw disorder by its mean annual prevalence.These included sole ulcer and digital dermatitis, 2 of the most expensive disorders to treat (Edwardes et al., 2022;O'Connor et al., 2023).

Sensitivity analysis
Milk revenue is the paramount component of farm partial net return.Variation in milk production could directly lead to changes in partial net return of a farm and affects GHG emission and culling decisions.Besides milk yield, the milk price is directly associated with milk revenue.One of the benefits of extending cattle longevity is the reduced demand for replacement heifers.In the model, the market value of a replacement heifer is used to parametrise this cost.However, in the Netherlands most heifers are reared on farm.Rearing these heifers involves considerable costs that can vary widely between farms depending on available resources.Therefore, a sensitivity analysis was conducted to capture the variation of those factors by evaluating the impact of production level, replacement heifer price or milk price on the model's results.
To examine the effect of production level on model's results, the average daily milk production was adjusted by one SD to 22.75, 25.75, and 28.75 kg/day for, respectively, parity 1-3, 4 and parity 5 and more (Table 3).The effect of milk price variation on the partial net return of a dairy farm was estimated by analyzing the highest and lowest prices of milk between 2019 and 2021.Relative to the default price setting (Table 4), the maximum price was 20% higher and the minimum price was 10% lower.Lowest replacement heifer price of €861 was based on the total variable costs per successfully home reared heifer, excluding the costs of own rearing labor and barn costs.In turn, the highest price of €1567 was set on the total variable and fixed costs, where the fixed costs were valued by their full substitution (opportunity) value

RESULTS
The technical, economic and environmental results per herd of 100 cow places for all reproduction management strategies are presented in Table 5.
In the default scenario, based on a maximum of 4 attempts of AI and a milk yield drop below 15 kg as reproductive culling threshold, the average age at culling is 2,040 d or about 5.6 years.With an increase in the maximum number of AIs, all technical variables except for the culling rate show an upward trend.The impact on the age at culling is larger when shifting from a maximum of 4 to 5 AIs (108-d increase in age at culling) than from 5 to 6 AIs (47-d increase).Decreasing the threshold for reproductive culling from a milk yield of 20 to 10 kg/day increased age at culling but decreased all other technical indicators of performance.
Partial net return increased with an increase in maximum number of AIs, and decreased with less stringent thresholds of reproductive culling.Table 5 provides further insight into the effect of the various reproduction management decisions on components of the partial net return.While revenues from milk and calves increase with 0.7% and 5.7% respectively, with an increase of maximum number of AIs from 4 to 6, meat revenues decrease with 11%.All costs, except for replacement costs, are also higher with an increased maximum number of AIs, resulting in an overall increase in partial net return of 1.0%.With less stringent reproductive culling standards, all components of partial net return decrease, resulting in an overall decrease in partial net return of 4.0%.Within the strategy of increasing maximum number of AI, replacement costs are most strongly affected.As for changes in the reproductive culling threshold, milk revenues show the most prominent alterations among other economic components.
With increased maximum number of AIs, the CO 2equivalents per kg FPCM decreased from 0.926 to 0.915 (Table 5).In terms of the environmental consequences, there is no difference in GHG emissions per kg FPCM when the reproductive culling threshold is increased from 15 to 20 kg/day (Table 5).

Sensitivity analysis
A lower milk yield level led to lower partial net returns, earlier culling, and higher GHG emissions.Similarly, a higher milk yield led to higher partial net returns, later culling, and lower GHG emissions (Table 6).In the default scenario of maximum 4 AIs, one SD increase or decrease in ADY affected the partial net return with approximately 14%.The impact of one SD change on GHG emissions in the default scenario was relatively larger at the lower production level (+4.9%) than at the higher production levels (−4.0%).This contrasted with the impact on the age at culling, which decreased by 2.2% at the lower production level and increased with 3.7% at the higher production level.
The relative differences in partial net returns at alternative maximum of AIs increased with higher production levels, while the relative differences between culling age and GHG emissions reduced.Independent of the number of AI services, the partial net return altered proportionally with the relative changes in milk price and heifer price.

DISCUSSION
In recent years, research has been conducted to identify measures that enable a reduction of GHG emissions from dairy production, such as adjustments in feed ratios (e.g., Schils et al., 2006), feeding systems (O'Brien et al., 2010), the use of feed additives (Place and Mitloehner, 2010), manure management (Petersen et al., 2013) and breeding (e.g., De Haas et al., 2021;Richardson et al., 2021).Moreover, some studies focused on the impact of improved health and reproduction on GHG emissions (Gulzari et al., 2018;Mostert et al., 2018aMostert et al., , 2018bMostert et al., , 2019;;MacLeod et al., 2018;Kok Han et al.: Effects of extending dairy cow…  , 2017, 2019).One of the motivations behind these health and reproduction studies is the exploration of the impact of improved management on the culling rate of dairy cows and, consequently, their longevity, which is closely associated with GHG emissions (de Vries and Marcondes, 2020; Schuster et al.

, 2020).
There is a large variation in replacement rates among farms (Mohd Nor et al., 2015;Han et al., 2022), partly leading to considerable differences in GHG emissions across farms (Kristensen et al., 2011).Given the suboptimal replacement decisions commonly made by farmers (Mohd Nor et al., 2015), along with the substantial costs (Mohd Nor et al., 2012) and GHG emissions associated with the heifer rearing process (Schuster et al., 2020), we hypothesized that by adjusting the replacement rate, farmers could simultaneously reduce GHG emissions and enhance profitability, while taking into consideration that the age of cows is associated with disease incidence (e.g., Lean et al., 2023;O'Connor et al., 2019).
We explored the marginal effect of extending longevity of dairy cows (thus reducing replacement rate) on a typical Dutch farm by changing reproduction management decision rules (i.e., increasing AI attempts or lowering yield threshold for reproductive culling).The developed dynamic stochastic simulation model included these rules for reproductive culling, and simulated culling due to clinical mastitis, lameness or other reasons (i.e., general culling).By including parity as a risk factor for occurrence of mastitis and lameness, we were able to correct for the negative effects of an older herd on disease occurrence.
In the default scenario with a maximum of 4 inseminations and a minimum milk production of 15 kg/day as the reproductive culling threshold, the average age at culling was 2040 d (5.6 years).This corresponds reasonably well to the average of 5.9 years reported in an empirical study using census data of Dutch dairy farms (Han et al., 2022).The GHG-emissions under this default situation were 0.926 kg CO 2 -eq per kg FPCM.This estimation is relatively low compared with estimates of GHG emissions published in a recent review (Singaravadivelan et al., 2023), in which estimates varied from 0.92 to 13.8 kg CO 2 -eq per kg milk.However, the estimate is in line with estimates for relatively intensive dairy production systems, such as in Eastern Canada (0.92 kg CO 2 -eq per kg FPCM; McGeough et al., 2012), the US (0.46 -0.69 kg CO 2 -eq per kg milk; Rotz et al., 2010), the Netherlands (1.4 kg CO 2 -eq per kg FPCM; Thomassen et al., 2008) and Europe in general (1.3 kg CO 2 -eq per kg FPCM; Lesschen et al., 2011).However, please note that comparing these studies is challenging due to variations in timing and the use of different emission factors for converting methane (CH 4 ) and nitrous oxide (N 2 O) emissions to CO 2 -equivalents to estimate the global warming potential.
When comparing the default scenario with a situation allowing for AI services up to a maximum of 5 or 6 services, cattle longevity increased with 108 and 155 d, respectively.This increase in longevity was associated with a reduction in the culling rate from 0.28 to 0.25, and resulted in a decrease of GHG emissions of 0.008 (0.9%) and 0.011 (1.2%) kg CO 2 -eq per kg FPCM produced, respectively.These changes were caused by a slightly increased milk production per cow  6. Absolute changes within the default scenario of maximum of 4 Ais and relative changes of the scenarios on maximum AI of 5 and 6 services compared with the default scenario in average partial net return (€/herd of 100 cows per year), GHG emission (kg FPCM) and age at culling (days) for a variation in milk production level of one standard deviation (SD), a minimum and maximum (min, max) price of replacement heifer and milk given a reproduction strategy based on a maximum of 4, 5 and 6 inseminations (n = 500 herds) per year, lowering the GHG emissions per kg milk (e.g., Grandl et al., 2016), in combination with a reduction in the number of required replacement heifers, which reduced the GHG emissions from heifer rearing.Partial net returns increased by 13 and 18 euros per cow per year, respectively, mainly due to lower costs for rearing replacement heifers.The milk production per cow per year was slightly higher despite longer lactation lengths (Panthi et al., 2017), due to a higher average parity (Bokkers et al., 2014).In a study based on the lifetime performance data of 30 individual dairy cows, Grandl et al. ( 2019) also showed that the lifetime GHG emissions of dairy cows decreased with longer productive lifetime.In their study, the GHG emissions leveled out to approximately 1.1 kg CO 2 -eq per kg FPCM around a productive lifetime of 1600 d, while the net returns per cow increased and levelled out to approximately 0.17 Euro per kg FPCM.A productive lifetime of 1600 d is a longevity of approximately 2360 d (assuming a first calving age of 760 d), about 6 years and 6 mo, which is above the current average Dutch longevity.
In our study we did not account for a reduced genetic progress as a consequence of the increased calving intervals, which might have had an impact on the economic returns.However, this effect is not expected to be large (Schuster et al., 2020).Moreover, in studies aimed at genetic progress, it was concluded that the genetic progress in sires is not fast enough to warrant a high culling rate (De Vries, 2015) and consequently a reduced longevity.
When changing the reproductive culling rules of cows that failed to conceive (under the default setting of maximum 4 AI services) from a production threshold of 20 kg milk per day to 10 kg milk per day, the age at culling increased on average with 164 d.This change was associated with a reduction in culling rate of 0.04.Interestingly, in these scenarios, increased longevity was not associated with reduced GHG emissions.Moreover, when an improved longevity is reached by relaxing the reproductive culling rules on milk yield, the partial net returns reduced.Relaxing the threshold from 20 kg milk per day to 10 kg milk per day resulted in 69 Euros per cow per year lower partial net returns.The cost savings on replacement heifers did not outweigh the reduction in milk returns as a result of a lower milk production per year.
In this research, we explicitly modeled the effect of increased longevity on the disease occurrence.At the end, the incidence of mastitis and lameness was hardly affected by any of the evaluated longevity changes.The increased probability of production diseases because of older cows, was more or less compensated by the reduced number of transition cows as a result of the increased calving interval.
In our results, we observed a decreasing marginal effect when altering the rules for the maximum number of inseminations, comparable with the results of Grandl et al. (2019).The age at culling increased by 108 d when changing the maximum from 4 to 5 inseminations, whereas the changing the maximum number from 5 to 6 inseminations yielded only a 47-d increase.This discrepancy arises from a decline in the proportion of cows conceiving at each insemination attempt.Approximately 4% of all primiparous cows conceived at the 5th insemination attempt, compared with only 2% at the 6th attempt.Moreover, extending the maximum number of inseminations leads to a longer calving interval, eventually reducing milk production per cow per year.This reduction negatively affects both GHG emissions and farmers' income, suggesting an optimum number of inseminations, which most likely depends on the milk yield of the cow (e.g., Inchaisri et al., 2011;Kok et al., 2019;Stangaferro et al., 2018).
In this study we wanted to study the marginal effect of changes in longevity in dairy cows using a modeling approach.The association between dairy cattle longevity and profitability has also been studied using empirical data.While Adamie et al. (2013) showed a clear association between longevity and economic performance, this finding was not supported by the research conducted by Han et al. (2023) and Vredenberg et al. (2023).Establishing clear associations with empirical data poses challenges due to the presence of data noise, i.e., farm profitability is influenced by many other farm characteristics that may not always be possible to adjust for (Vredenberg et al., 2023).Therefore, we used a modeling approach allowing us to alter management variables while maintaining all other factors constant.
We modeled farmers' commonly used decision rules of thumb for determining when to cease inseminating cows (i.e., adhering to a maximum of 4 inseminations) and when to cull non-pregnant cows (i.e., when daily milk yield drops 15 kg a day).It is clear that the use of these straightforward decision rules is not optimal, which is not a novel observation.In the past much research has been carried out on optimizing insemination and culling decisions and specific metrics have been proposed to support these decisions such as the retention payoff value and insemination value (e.g., de Vries, 2006;Groenendaal et al., 2004;Cabrera 2010).These metrics are however based upon the assumption of unlimited availability of replacement heifers, which in the Dutch systems is not the case.Culling decisions are restricted by the number of available heifers at herd level, which is a result of the decision (made more than 2 years earlier) to keep and rear calves as replacement heifers (De Vries and Marcondes, 2020;Nor et al., 2015).Moreover, systemic barriers, as a consequence of the production system and the consisting ideas about replacement decisions, may also prevent an increase in productive lifetime (Roediger and Home, 2023).In practice farmers tend to stick to the rules of thumb that have proven themselves to be useful in the past (Kulkarni et al., 2023).A lack of practical decision tools for farmers to optimize the number of calves to be reared may hamper a more rational decision making regarding reproduction and culling decisions (De Vries and Marcondes, 2020).
Our results demonstrate that increased longevity by adjusted reproduction management decisions can benefit both farmers' income and GHG emissions.Moreover, it is not longevity itself that leads to a change in environmental and economic efficiency, but rather the method by which this extension of longevity is achieved.In contrast to merely adjusting the decision rule for the timing of reproductive culling, increasing artificial insemination attempts can enhance the sustainability of dairy farming from both economic and environmental perspectives.

CONCLUSION
The study shows that cattle longevity in the Netherlands can be extended by up to 5.5 mo by altering reproduction management decision rules in terms of the maximum number of AI services (from 4 to 6 attempts) or the production threshold after which a cow that failed to conceive was culled (from 20 kg to 10 kg milk per day).Although lower reproductive culling thresholds has the potential to extend cattle longevity more than increasing the maximum number of AI services, only the latter increases a farm's partial net return, while reducing greenhouse gas emissions.
Han et al.:  Effects of extending dairy cow… that could occur during the lactation (Figure1): staying healthy, recovering from clinical mastitis, recovering from lameness, being culled because of clinical mastitis, being culled because of lameness, being culled because of failure to conceive, or being culled for other reasons ('general culling').

Figure 1 .
Figure 1.Schematic representation of the simulation model reflecting the processes at cow level per cow place.Stochastics events are marked with an asterisk.
Han et al.: Effects of extending dairy cow…

1
ADY is the average daily yield based on 305-d milk yield; parameters a, b, c and k of the Wilmink lactation curves; and fat, protein and lactose content of the milk per parity class.(Wilmink lactation curve: Yield = a + b * DIM + c * exp(-k * DIM)).
Han et al.: Effects of extending dairy cow…Table

Table 1 .
The

Table 2 .
Han et al.:Effects of extending dairy cow… Incidence rates per parity of clinical mastitis and lameness and proportion of cows culled due to clinical mastitis, lameness or other reasons, and overall culling rate in each parity based on the default reproduction management decision rules of maximal 4 Ais and a reproductive culling production threshold of 15 kg/day

Table 3 .
Model inputs for individual lactation curves per parity

Table 5 .
Technical, economic and environmental simulation results per herd of 100 cows per year with a maximum of 4, 5 or 6 artificial insemination attempts per pregnancy (n = 500 herds per max number of Ais) with default reproductive culling standard (15 kg/day) and average milk production levels