Climate change and variability impacts on grazing herds: Insights from a system dynamics approach for semi‐arid Australian rangelands

Abstract Grazing livestock are an important source of food and income for millions of people worldwide. Changes in mean climate and increasing climate variability are affecting grasslands' carrying capacity, thus threatening the livelihood of millions of people as well as the health of grassland ecosystems. Compared with cropping systems, relatively little is known about the impact of such climatic changes on grasslands and livestock productivity and the adaptation responses available to farmers. In this study, we analysed the relationship between changes in mean precipitation, precipitation variability, farming practices and grazing cattle using a system dynamics approach for a semi‐arid Australian rangeland system. We found that forage production and animal stocking rates were significantly affected by drought intensities and durations as well as by long‐term climate trends. After a drought event, herd size recovery times ranged from years to decades in the absence of proactive restocking through animal purchases. Decreases in the annual precipitation means or increases in the interannual (year‐to‐year) and intra‐annual (month‐to‐month) precipitation variability, all reduced herd sizes. The contribution of farming practices versus climate effect on herd dynamics varied depending on the herd characteristics considered. Climate contributed the most to the variance in stocking rates, followed by forage productivity levels and feeding supplementation practices (with or without urea and molasses). While intensification strategies and favourable climates increased long‐term herd sizes, they also resulted in larger reductions in animal numbers during droughts and raised total enteric methane emissions. In the face of future climate trends, the grazing sector will need to increase its adaptability. Understanding which farming strategies can be beneficial, where, and when, as well as the enabling mechanisms required to implement them, will be critical for effectively improving rangelands and the livelihoods of pastoralists worldwide.


| INTRODUC TI ON
Climate change and variability is a major concern for grazing systems worldwide. Projected increases in the frequency and severity of extreme climate events (e.g. heat stress, drought and flooding) as well as drier conditions in part of the world, especially in arid and semiarid regions (Herrero et al., 2016;Kitoh & Endo, 2016;Warszawski et al., 2014), are expected to have significant negative consequences on herd populations as a result of decreases in feed and water quantity and quality, declined reproductive performance, heat stress, and increased disease incidence and mortality (as reviewed in Rojas-Downing, Nejadhashemi, Harrigan, & Woznicki, 2017;ThorntonSteeg, Notenbaert, & Herrero, 2009). These reductions in animal numbers threaten local livelihoods, especially in regions that are dependent on livestock as a source of food or income. Additional benefits that livestock can confer, such as non-food products and capital functions, may also be compromised and the conflicts over animal assets present in some regions may escalate, especially in Africa (e.g. Horn of Africa). Climate change may result in reduced land carrying capacity and associated overgrazing, which leads to losses in ecosystem goods and services. Some regions in high latitudes may, however, not suffer these negative impacts, with pasture and livestock productivities potentially increasing due to more suitable temperatures (Herrero et al., 2016).
Over the last century, inter-and intra-annual precipitation variability have generally increased across global grasslands (Sloat et al., 2018), although both positive and negative trends exist.
The rates of year-to-year variability increase appear to be largest in regions where livestock grazing is important for local food access and/or economies (e.g. Sahel, Somalia, Kenya, Zimbabwe, Australia; Sloat et al., 2018). Moreover, changes in climate variability may counterbalance the impacts of changes in mean variables alone (IPCC, 2012).
Despite the growing economic, social and environmental threats associated with such precipitation changes, climate change and variability impacts on short-and long-term herd dynamics have been understudied (Thornton, Ericksen, Herrero, & Challinor, 2014; Thornton et al., 2009). Field research often focuses on vegetation dynamics. When they do consider animal herds, these studies usually provide information related to specific management and weather patterns of relatively short duration, and do not necessarily detail climate mean and variability characteristics nor consider management effects.
Modelling studies, while being a simplified representation of actual systems, can provide additional insights by allowing impact analyses of a wide range of farming practices and short-and long-term climate scenarios. The level of details in herd-forage models to capture climate change effects vary. For example, some models do not represent the direct feedback of animal forage intake on forage availability (e.g. Hatch & Stafford Smith, 1997;Pulina, Salimei, Masala, & Sikosana, 1999). Some models run on an annual basis, thus do not allow the capture of seasonal climate variability effects (e.g. Bénié, Kaboré, Goïta, & Courel, 2005;Beukes, Cowling, & Higgins, 2002;Hahn et al., 2005;Hatch & Stafford Smith, 1997;Janssen, Walker, Langridge, & Abel, 2000;Perrings & Walker, 1997;Wu, Li, Stoker, & Li, 1996). Detailed models that run on a monthly or weekly time step have also been developed (e.g. models reviewed in Bryant & Snow, 2008). However, these models are complex in their pasture and animal dynamics and are constrained in their ability to assess the specific effects of a wide range of climate scenarios. In this study, we aim to provide novel insights into the potential impacts of climate change and variability on rangeland production systems by developing a purpose-built system dynamics model that allows the impacts of a wide range of climate scenarios on long-term herd dynamics to be assessed.
We also study the influence of intensification strategies and implications for enteric methane emissions. This study takes a case-study approach in a semi-arid Australian rangeland system, system constrained by high and increasing climate variability. We hypothesize that such an environment could be significantly impacted by a changing climate.

| Framework
To explore the dynamic behaviour of cattle herds under changing climate and farming scenarios, we constructed an integrated forage and herd model that links precipitation regimes to forage production, quality and herd dynamics (e.g. animal forage intake, liveweight gain, fertility and mortality rates) on a weekly basis (Figure 1).
We assessed the short-and long-term impacts (up to 30 years) of a wide range of climate scenarios on forage and herd dynamics. We also assessed the impact of farming intensification strategies that focussed on pasture improvement to increase forage production and carrying capacity, and animal feed supplementation. The production impacts of intensification strategies under climate scenarios also provide information as to their potential as a climate adaptation strategy. Climate and management impacts on enteric methane emissions were also assessed. These production, adaptation and mitigation considerations under a wide range of climate scenarios aimed at providing novel insights to key pillars of the climate-smart agriculture and United Nations Sustainable Development Goals frameworks (Lipper et al., 2014;United Nations, 2015).
Economic analyses were not the focus of this modelling study, which represents a subset of a beef enterprise and does not include farm revenues or costs. The herd was managed to ensure pasture utilization rates that are considered for the region as economically and environmentally sustainable and limit herd mortalities (~20%; Ash, Corfield, McIvor, & Ksiksi, 2011;Hunt, 2008;O'Reagain & Bushell, 2011;O'Reagain, Scanlan, Hunt, Cowley, & Walsh, 2014) rather than in a specific attempt to maximize profits. Farming practices modelled (pasture sowing and low-cost per head feed supplementation) were within the range observed in the region (McIvor & Gardener, 1995;McIvor & Monypenny, 1995;McLennan, Hirst, Shepherd, & McGuigan, 1991;Peck et al., 2011;Walker & Weston, 1990). Herd size rebuild after droughts was modelled through herd management (e.g. males were sold in priority as compared to females during droughts; young females were retained in the herd during the herd recovery phase). This allowed us to explore herd recovery periods in the absence of proactive rebuild through animal purchases.
In practice, pastoralists may try to rebuild their herd through animal purchases as this can restore profitability more quickly (Buxton & Smith, 1996). However, this option can be challenging due to increased cattle scarcity and associated high cattle prices after a widespread drought (Hatfield-dodds, Hughes, Cameron, Miller, & Jackson, 2018).

| Case study
A cattle operation (Wambiana Station) in northern Queensland, Australia (20.554666°S, 146.110317°E, Figure 2) was chosen as the case-study site for this modelling assessment, due to the availability of long-term historical forage biomass and stocking rates data as well as herd characteristics and stock management records, which were used to structure and parameterize the model. This region is also of interest as it has a high interannual precipitation variability (CVP-inter = 0.37) and a high climate seasonality with 80% of rain occurring between November and April (Bureau of Meteorology, 2018; Sloat et al., 2018), resulting in herds being sensitive to climate patterns. Increases or decreases in climate variability in this region could have significant implications for livestock production and its interaction with land condition. The meat production system modelled in this study is the one dominant in central and northern coastal Queensland, accounting for around 30% of the Australian herd (and 65% of the Queensland cattle; Meat & Livestock Australia, 2017). In this region, young males are castrated at 6 months, and steers are sold at an average liveweight of around 550 kg/head (2-3 years old). Females, when in excess of the requirement to replace breeding animals, are sold at 1-2 years old, whereas breeding animals are kept until about 9 years old. Bulls are either bred on farm or purchased at 2-3 years of age and are usually kept for around 5 years as this is considered their optimal productive lifespan for breeding.
The land used for beef operations in Australia is either freehold or leasehold, with leasehold dominating the more variable rangeland regions. Leasehold tenure is usually for many decades with F I G U R E 1 Simplified representation of key stocks, flows and causal linkages in the model. The model portrait includes stocks in which resources accumulate at a particular point in time (boxes) and flows which compute the rate of change into and out of the stock (thick arrows with valves). The rate at which flows enter or exit stocks as well as other technical relationships that indirectly affect this rate are influenced by parameters, also called converters. A positive (+) sign on the arrowheads indicates that a change in a source variable will change the destination variable in the same direction (e.g. an increase in animal sales contributes to a decreased herd stock). In contrast, a negative (−) sign indicates that the variables move in opposite directions (e.g. an increase in forage intake per animal contributes to a decrease in the forage biomass stock and vice versa). The figure was designed with Vensim software (Ventana Systems, 2017). A detailed description of the herd and forage components of the model, as well as underlying differential equations, are presented in Appendix S1) conditions that are not onerous which, in effect, confers private ownership of pastoral operations. Properties are usually family or company owned and can be held for many generations within family structures. Given this security of tenure, most operations aim for long-term sustainability, although the challenges in matching forage supply and forage demand in a highly variable climate with frequent droughts can lead to cycles of degradation and recovery. Total This conservative management, which aims at minimizing the risks of exhausting the forage resource, is not universally adopted within the region, where higher long-term stocking rates can be used, and contrasts with many grazing systems around the world where animals graze on communal land.

| Forage and herd model
The herd-forage model was developed using a system dynamics modelling approach and was run on a weekly basis over 30 years under different climate and farming scenarios ( Figure 2). A lead-in period of 60 years was used for each climate and farming practice combination to allow the model's stocking rates to stabilize in their spread of values: under very favourable climatic conditions, it takes some years for the stock numbers to increase from their initial stocking rate of 0.2 TLU/ha, as an input in the model, to values around 0.6-0.9 TLU/ha through natural replacement with no purchases, as for climate scenario S 15 ( Figure 5). The section below presents some of the key model components. Further details, including the model underlying differential equations, are provided in Appendix S1.
We considered forage production and intra-annual variations in forage quality as endogenous in the herd model, based on precipitation, to allow a direct and transparent representation of the feedback of animal consumption on forage availability (Figure 1).
A system dynamics approach is well suited to represent complex structures such as forage-herd interactions that include long feedback cycles between climate, forage production, animal reproduction, and growth and land condition-and often non-linear relations among herd and biomass components. The approach helps framing, understanding and discussing the complex issues by assessing key behaviours over time and facilitating the evaluation of constraints and leverage points (Forrester, 1961;Sterman, 2011Sterman, , 2002. In system dynamics models, profiling the evolution of the process has priority over finding a specific equilibrium or optimal solution. The basis of the method is that the complex relationships among the components of the system are just as important in determining the behaviour of the system as the individual component themselves. System dynamics has been recognized as an efficient method to represent animal population dynamics (e.g. Dahlanuddin, Henderson, Dizyee, Hermansyah, & Ash, 2017;Dizyee, Baker, & Rich, 2017;McRoberts, Nicholson, Blake, Tucker, & Padilla, 2013;Naziri, Rich, & Bennett, 2015;Rich, 2007;Rich et al., 2017;Rich & Roland-Holst, 2014;Stephens et al., 2012).
The dynamics in the model were captured by a series of stocks (e.g. herd or standing forage biomass stocks) and flows (e.g. birth rates or forage consumption rates over time) and their changing relationships and behaviours through time were modelled using integral and non-linear differential calculus (see Figure 1 for a simplified F I G U R E 2 Location of the Wambiana case study in Australia, states cattle numbers and study framework. Climate data from Jones, Wang, and Fawcett (2009) (mean over years 1981-2012). Cattle numbers in million head (M) from the Australian Bureau of Statistics (2016) representation of the model key dynamics). Forage availability and quality as well as herd fertility, liveweight gains, mortality and sales rates determine the size of these flows, and therefore, the size of the cattle stock at any given point in time. When the model is in equilibrium, the inflows (births) and outflows (deaths and sales) are equal and the population is steady. The model was programmed using Stella Architect software v1.5.1 (isee systems, 2017).

Forage biomass availability
The forage biomass stock is equal to the forage growth minus farmed cattle and wild animals' consumption and biomass senescence. We developed a simplified biomass growth model.
Precipitation has a 6 week lagged logarithmic-shaped effect on biomass growth (lag effect mentioned, e.g. in Bat-Oyun et al., 2016;Moran et al., 2014). Similar to the pasture growth model GRASP, weekly senescence rates are larger in December to represent detachment rate for carryover material, including the impact of storms (McKeon, Ash, Hall, & Stafford Smith, 2000).

Forage biomass quality
Intra-annual variations in forage quality were taken into account by estimating seasonal variations in voluntary food intake based on the approach used in producing Australia's National Greenhouse Gas Inventory (Commonwealth of Australia, 2016a).
In addition, cattle liveweight gain increases by 20% in summer, autumn and winter (December-August) if the annual number of growing weeks (precipitation >10 mm/week;McCown, Gillard, Winks, & Williams, 1981) is more than 13 weeks. If it is less than 13 weeks, no additional effect on liveweight gain was modelled as forage availability is the key limiting factor compared to forage quality. These rules contributed to represent the fact that precipitation distributed over the year was more favourable to grass quality over the year than precipitation regimes concentrated over a very limited number of weeks.

Herd structure
The cattle herd population was comprised of interlinked animal cohorts, grouped based on their age, purpose and gender ( Table 1) Table 1. Actual food intake. The actual food intake per animal is lower than the potential voluntary food intake when forage availability is low and animal competition for feed is high. We also account for the fact that the higher the competition for feed among animals, the less non-palatable parts are left ungrazed. The actual food intake influences forage availability and herd fertility, mortality, liveweight gains as well as emergency drought selling rules.

Breeding season
We assume seasonal mating. Bulls are allowed to mate with cows over a 4 month period, from the beginning of December until the end of March. Indeed, farmers aim to have calves from September to December, the period of the year when forage availability and quality is usually at its best (Rudder & Mccamley, 1972;Sutherland, 1961).

Steer liveweight gain
Steer liveweight gain depends on the actual food intake estimate.
This liveweight gain-intake relationship was developed from estimates of average liveweight, liveweight gains and voluntary intake for the different animal cohorts (Commonwealth of Australia, 2016b). Liveweight gain also depends on variations in forage quality and on the feed supplementation strategy.

Fertility
Fertility rate depends on the amount of forage available for intake per animal (sigmoid-shaped relationship). When forage is not limited, the maximum fertility rate is 75% (Table 1) (McGowan et al., 2014).
In this model, feed supplementation strategies prevent the fertility rate dropping below 50%. Once fertility rates drop below 50%, it becomes difficult to maintain a self-replacing breeding herd so this threshold was chosen.

Mortality
The model allows for 'normal' losses caused by a complex set of factors not directly related to nutritional status (Table 1). For animals over 0.5 years old (i.e. not milk-fed), these mortality rates increase with increases in nutritional stress. The implementation of feed supplementation suppresses this effect.

Herd sales
Conventional sales. In the model, steers were sold at an average liveweight of 567 kg/head (~3 years old). Females, when in excess of the requirement to replace breeding animals, were sold at 1-2 years old. Breeding females were kept until 9 years old. However, sales may happen earlier in the stage of life of the animals, as described below.
Sales to meet the desired stocking rate target. A desired stocking rate is indicated in the model and varies depending on the annual pasture utilization rate, the latest being defined as the percentage of annual pasture growth consumed by the herd. This desired stocking rate represents the fact that famers usually lower their stocking rate when long-term utilization rates are over 20% as they wish to prevent forage resource exhaustion and medium to longterm land degradation (Ash et al., 2011;Hunt, 2008;O'Reagain & Bushell, 2011;O'Reagain et al., 2014). If the actual cattle stocking rate is larger than the desired stocking rate, then a proportion of 1-to 2-year-old females is sold. The relationship between the stocking gap (actual cattle number minus desired number) and the proportion of females sold follows a square root curve shape.
Drought emergency sales. If forage resources available for grazing are limited, a proportion of the animals older than 0.5 year old are sold.
Males are sold in priority as compared to females, which are usually retained for as long as possible to maintain a viable reproductive herd.

Enteric methane emissions
We estimated methane emissions from grazing cattle enteric fermentation (excluding calves) based on Charmley et al. (2015) study who reported a close relationship between dry matter intake and methane production. This relationship was derived from an analysis of Australian data of dairy and beef cattle fed diets of over 70% forage. We considered methane from manure in grazing systems as negligible due to aerobic conditions (Commonwealth of Australia, 2016a). Biogenic methane emissions were expressed as CO 2 -eq using the 100-year Global Warming Potential value 34 from the IPCC Fifth Assessment Report and include climate carbon feedbacks, feedbacks which measure the indirect effects of changes in natural carbon reservoirs (e.g. ocean, atmosphere) due to changes in climate (IPCC, 2014).

| Model evaluation
Key forage and herd outputs of the model were evaluated by comparing the results from a baseline model simulation with a set of measured data for Wambiana and northern Queensland (see Figure 3 and Appendix S1 for evaluation results, Hunt et al., 2014;McGowan et al., 2014;O'Reagain & Bushell, 2011). Due to the limited amount of long-term forage and herd measurements available in the literature, we also compared our model outputs with the ones from the GRASP model, which has been extensively used for northern Queensland including Wambiana (Ash et al., 2015;McKeon et al., 2000;Scanlan, Macleod, & O'Reagain, 2013). Key outputs included temporal variations in forage growth, TSDM and stocking rates, as well as mean stocking rates, TSDM, fertility, mortality, calving and weaning rates, forage utilization rates, forage intake as a function of forage availability, animal liveweight gains and total methane emissions over the relevant time periods. The results showed agreement between the herd-forage model and the evaluation data sets for this climatically highly variable region. This gives confidence that the model adequately simulated these production systems.

| Farming scenarios
The farming scenarios tested in this study were different forage production levels and animal feed supplementation strategies ( Figure 2).

| Forage production level
Three levels of forage production (TSDM) were tested: (a) 2,000 kg/ha (default Wambiana productivity value for native pasture), (b) 3,000 kg/ha and (c) 4,000 kg/ha. The two higher levels of production, representing intensification strategies, are within the range observed for improved pastures grown on a low fertility soil in the region (McIvor & Gardener, 1995;Peck et al., 2011;Walker & Weston, 1990). The improved pastures are dominated by introduced grasses but can include oversown legumes and/or application of fertilizer. However, for these simulations, it was assumed that pasture quality remained constant across the different pasture productivities. These three forage production types, the values of which correspond to averages under historical climate baseline, were not fixed over time: TSDM fluctuated depending on weather, forage and herd dynamics.

| Feed supplementation
Tropical pastures across the world are usually of low quality in the dry season (i.e. low protein content and digestibility), especially so in Australia due to nutrient-poor soils. The seasonal pattern of rainfall where more than 80% of annual rainfall falls over a few months throughout the year is also key as much forage can be available but of poor nutritional quality during the long dry season. To mitigate the impacts of low forage quality, Australian farmers often provide cattle (especially females) with urea-type supplements, which have a high crude protein equivalent. They may also add, in fewer cases, molasses to the meal mix for its high energy content and to increase the palatability of the urea (McIvor & Gardener, 1995). To represent the impact of such intensification practices, three feed supplementation scenarios were tested: (a) no supplementation, (b) both females and males were supplemented during autumn and spring (March-November) and (c) only females were supplemented during autumn and spring. The feed supplementation effects considered were those of a combination of urea and molasses. These modest crude protein and energy supplements were provided to reduce mortality and minimize declines in female fertility and forage intake (Figure 1).

| Climate scenarios
We generated two sets of climate scenarios based on historical weather data, to provide insights from both isolated drought events (Set 1) and long-term trends in precipitation mean and variability (Set 2; Figure 2). Detailed precipitation characteristics of these scenarios are available in Appendix S2.

| Set 1-Drought period effect on herd stocking rate reduction and recovery time
The first set of climate scenarios represented different drought intensities and durations. We used the MarkSim weather generator (CIAT, 2001;Jones, Thornton, Díaz, & Wilkens, 2002;Thornton et al., 2002Thornton et al., , 2014 to produce 1,000 years of weekly precipitation data based on historical daily precipitation and temperature data from Charters Towers Post Office , 55 km north of Wambiana cattle station (Bureau of Meteorology, 2018; Table 2).
These generated years were then classified depending on their precipitation level. 'Very dry' years correspond to years statistically occurring in the data set once every 100 years (precipitation below 281 mm/year), 'dry' years to years occurring once every 10 years (281-432 mm/year) and 'non-dry' years to years that were neither 'very dry' nor 'dry' (>432 mm/year). We then selected years from this data set to generate 13 time series of 30 years. The baseline scenario included non-dry years only and was only used to estimate herd recovery times after drought events (see section 'Proxies to characterize the herd dynamics2.7'). The other scenarios included varying numbers of consecutive dry and very dry years ('drought period') which were imposed from year 6. The non-dry years in these other scenarios were the same as in the baseline. Figure 4 shows the list of these 13 scenarios. The 432 mm/year precipitation threshold that differentiated 'nondry' and 'dry' years was relatively consistent with the years considered in the region as drought years for livestock production. Indeed, the 'Queensland 1990s drought ' (1992-1996) was associated with precipitations below 437 mm/year in the Wambiana region (Stehlik, Gray, & Lawrence, 1999

| Set 2-Precipitation mean and variability effects on herd dynamics
As a complementary approach, we also generated a second set of scenarios to capture precipitation long-term trends. We used  (Table 3 and Appendix Figures S2-S7) aimed to cover the 'uncertainty space' as to how precipitation patterns may change in the future (Sillmann, Kharin, Zwiers, Zhang, & Bronaugh, 2013;Warszawski et al., 2014). For northern Australia, future precipitation changes are uncertain with some models showing a wetting trend although overall a drying trend is favoured (Watterson et al., 2015). Trends in variability are also uncertain, though there is a high level of confidence that heavy rainfall events will be more intense.

| Proxies to characterize the climate scenarios
The three variables used to characterize the climate scenarios were mean precipitation (mm/year), and inter-and intra-annual coefficient of variation of precipitation (CVP-inter and CVP-intra, respectively).

Variable Value
Mean annual precipitation (mm) 653 Standard deviation-annual precipitation 241 Interannual coefficient of variation of precipitation (CVP-inter)

| Proxies to characterize the herd dynamics
The main outputs described in this modelling study were time-series mean forage TSDM (kg/ha) and herd stocking rates (TLU/ha). We also considered time-series mean animal liveweight (kg), mortality (TLU ha −1 year −1 ), mortality rates (%), sales (TLU ha −1 year −1 ), sales rates (%), total enteric methane emissions (kg CO 2 -eq ha −1 year −1 ) and enteric methane emissions intensities (kg CO 2 -eq/kg liveweight sold). We also assessed TSDM and herd stocking rate reductions and recovery times under the first set of climate scenarios (Set 1).
These two variables provide information on the rangeland system ability to absorb and recover from the effect of droughts, which constitutes one of the components of the system's resilience concept (IPCC, 2012). In this study, the reduction in TSDM and stocking rates was defined as the percentage of drop from the year 5 variable's value to its lowest value. A recovery time was defined as the number of years it takes for a variable's value of a specific time series to reach the baseline value (stocking rate values rounded at two digits after the decimal point). Figure 4 shows a graphical representation of the reduction and recovery time variables.

| Statistical analyses
Given the complexities of the forage and herd system dynamics model (i.e. involving non-linear relationships as well as feedbacks), we undertook statistical analyses to describe some of the grazing system's response to climate and farming scenarios. Regression tables are provided in Appendix S3.
We used linear regressions to model the relationship between explained variables (e.g. mean TSDM for the time series) and explanatory variables related to climate and farming scenarios (e.g. mean precipitation, CVP-inter, CVP-intra, forage production type for the time series). The statistical model was: where Y is the response measurement, X i is the explanatory variable i, α is the intercept, β i is the slope or coefficient and ε the errors.
To summarize the contribution of the explanatory variables alone to the explained variable variance, we calculated the coefficient of determination (R 2 ) of the explanatory variable X i for the model including only the explanatory variable i: where Y is the response measurement, X i is the explanatory variable i, α is the intercept, β i is the slope or coefficient and ε the errors.

| Effect of drought period on herd stocking rate reduction and recovery time
The effect of droughts on herd dynamics was studied by imposing different drought intensities and durations (Set 1 of climate scenarios- Figure 4). The farming practices considered in this section were baseline practices (TSDM = 2,000 kg/ha, no feed supplementation).
TSDM and animal stocking rates were significantly affected by drought events. We found that the larger the intensity of the drought, the larger the reduction in stocking rates. Similarly, the longer the drought, the longer the recovery time, with herd recovery times longer than a couple of decades in some cases (see section 'Proxies to characterize the herd dynamics2.7' for stocking rate reduction and recovery time definitions).
Stocking rate recovery times were not only affected by Reductions in TSDM were proportionally larger than reductions in stocking rates. For instance, TSDM dropped by 74% and stocking rates by 29% when six consecutive very dry years were imposed.
However, the herd took up to three times longer to recover than pasture. For instance, recovery times were up to 24 years for stocking rates as compared to 7 years for TSDM.
Stocking rates were influenced by herd sales and mortality.
While mean sales rates under drought periods were not very different from the baseline, interannual variations in sales rates increased to a greater extent, highlighting the increased complexity of farmers selling routines during droughts. For instance, the coefficient of variation of sales rate was 0.37 under a six consecutive very dry years period (mean sales rate for that climate scenario: 23%), much more than the 0.06 estimated for the 6 year baseline (mean: 22%), and this due to most sales occurring in the first couple of years after which there were not many animals left to sell. Mortality rates and interannual variations in mortality rates also increased under drought periods. The coefficient of variation of mortality rate was 0.67 over a six consecutive very dry years period (mean mortality rate: 6%), much more than the 0.02 estimated for the 6 year baseline (mean: 1%).

| Effect of precipitation mean and variability on herd dynamics
In this section, we study forage and herd dynamics under a range of precipitation means and variabilities (Set 2 of climate scenarios, Figure 5). The farming management practices considered were baseline practices (TSDM = 2,000 kg/ha, no feed supplementation).
The 30 year long-term time series average for TSDM, stocking rates, sales and mortality were significantly correlated with the timeseries mean precipitation and CVP-intra (R 2 > 0.90, p < 0.05). High Note: Farming practices considered: baseline practices. The darker the shade of grey, the higher the variable value. Abbreviations: CVP-inter, interannual coefficient of variation of precipitation; CVP-intra, intra-annual coefficient of variation of precipitation.
F I G U R E 4 Mean annual total standing dry matter (a), animal stocking rates (b) and corresponding mean annual precipitation (c) under different imposed drought intensities and durations (Set 1 of climate scenarios). Farming practices considered: baseline practices. '1 dry year': one dry year imposed at year 6; '2 dry years': two consecutive dry years imposed at years 6 and 7, etc. See Appendix S2 for the climate scenarios mean annual precipitation, CVP-intra and CVP-inter. CVP-inter, interannual coefficient of variation of precipitation; CVP-intra, intra-annual coefficient of variation of precipitation; TLU, tropical livestock units R 2 indicated very small effects of the interactions between climate variables on the explained variables. Based on individual linear regressions, we found that a decrease of 20% in the time-series mean precipitation was associated with a decrease of 19% of mean TSDM (R 2 = 0.92, p < 0.05). A decrease of 20% of the time-series mean precipitation or an increase of 20% CVP-intra was associated with a decrease of 18% and 19% of mean stocking rates (R 2 = 0.30-0.51, p < 0.05). As for sales rates, they were significantly negatively related to CVP-intra and CVP-inter, and positively related to mean precipitation (R 2 = 0.94, p < 0.05). Animal liveweight was negatively related to CVP-inter (R 2 = 0.78, p < 0.05) and relationships for mortality rates were inconclusive (R 2 = 0.13).
To gain further insights as to the contribution of the different climate variables to forage and herd dynamics, we assessed their contribution to the variance of TSDM and stocking rates ( Figure 6a). Most of the variance in mean TSDM among the 15 climate scenarios was explained by mean precipitation of the time series (92%), followed by CVP-intra (12%) and CVP-inter (11%), when these explanatory variables were considered without their interaction with other variables. Most of the variance in mean stocking rates was explained by CVP-inter (58%), followed by CVP-intra (51%) and mean precipitation (30%).
The positive effects of higher mean precipitation on stocking rates could be reduced by increased climate variability and vice versa (Table 3). For example, for time series with mean precipitation over 1,067 mm/year (75th percentile-in that case, CVP-inter was 0.28-0.35), CVP-intra of 0.27-0.43 was associated with a mean stocking rate of 0.69 TLU/ha while CVP-intra of 1.22-1.38 was associated with a mean stocking rate of 0.22 TLU/ha.
Interannual variability in TSDM was significantly related to CVPinter and CVP-intra (R 2 = 0.87, p < 0.05) while interannual variability in SR was not significantly related to any variable (R 2 = 0.65).
Interannual variability in TSDM (from 0.27 to 0.45, mean: 0.36) was on average 6% higher than CVP-inter (from 0.27 to 0.44, mean: 0.34) for each of the time series, which is similar to findings from Le Houérou et al. (1988) for case studies with comparable CVP-inter.
Interannual variability in stocking rate (from 0.07 to 0.13, mean: 0.10) was on average 71% lower than interannual variability in TSDM and 72% lower than CVP-inter.

| Effect of intensification strategies on herd dynamics
In this section, we show the effects of forage and feed supplementation strategies on herd dynamics, taking into account model outputs averaged over the second set of climate scenarios (Set 2-same as in the section above). We also discuss how farming practices compare to climate variables in terms of their impact on forage and herd characteristics.
The combined intensification strategies (high forage productivity and feed supplementation) gave the greatest response in annual stocking rate, sales and sales rates, closely followed by F I G U R E 5 Mean annual total standing dry matter and animal stocking rates under 15 climate scenarios (Set 2 of climate scenarios). Farming practices considered: baseline practices. See Table 3 and Appendix S2 for the climate scenarios mean annual precipitation, CVP-intra and CVP-inter. CVP-inter, interannual coefficient of variation of precipitation; CVP-intra, intra-annual coefficient of variation of precipitation; TLU, tropical livestock units improved forages ( ation in animal stocking rates (from 0.10 to 0.03) and mortality rates (from 3.7% to 3.1%). The feeding strategy also resulted in lower mean TSDM (1,695 kg/ha) and higher interannual variation in TSDM (0.64) as compared to the baseline management (1,902 kg/ha, 0.36). This was driven by a higher total herd forage intake from reduced mortality rates, reduced declines in fertility rates and reduced declines in intake per animal, particularly during dry years.
Linear regressions including both climate and management variables showed that mean TSDM, sales rates, mortality rates and mortality during the time series were significantly related to mean precipitation, CVP-inter, CVP-intra, forage productivity type and feed supplementation (R 2 > 0.81, p < 0.05). Stocking rates and sales were significantly related to all variables, except feed supplementation strategies (R 2 > 0.81, p < 0.05). Liveweight and interannual variability in TSDM were significantly related to all variables except CVP-intra and forage productivity type (R 2 > 0.40, p < 0.05).
Interannual variability in stocking rate was significantly related to mean precipitation and feed supplementation strategies (R 2 = 0.84, p < 0.05). The differences in TSDM and SR between feed supplementing both males and females as compared to females only were inconclusive.
We also assessed how climate variables compared to farming scenarios in explaining the variance of TSDM and stocking rates Abbreviation: CVP-inter, interannual coefficient of variation of precipitation; CVP-intra, intra-annual coefficient of variation of precipitation; TLU, tropical livestock units.

TA B L E 4 Mean forage and herd characteristics under different intensification scenarios
F I G U R E 6 Contribution of climate and management variables to the variance in time-series mean total standing dry matter (light grey) and animal stocking rates (dark grey). In (a), only baseline farming practices were considered. In (b), both climate and management variables were considered. CVP-inter, interannual coefficient of variation of precipitation; CVP-intra, intra-annual coefficient of variation of precipitation ( Figure 6b). Most of the variance in TSDM among the 15 climate scenarios was explained by mean precipitation (61%), followed by forage productivity type (29%), CVP-inter (11%) and CVP-intra (4%), when these variables were assessed independent of interactions with other variables. Feed supplementation contributed to less than 1% of the variance. Most of the variance in mean stocking rates was explained by climate variables (CVP-inter: 38%, CVP-intra: 36%, mean precipitation: 21%), followed by forage productivity type (18%) and feed supplementation (<1%).
The positive effects of intensification strategies on stocking rates could be reduced by decreased mean precipitation or in-

| D ISCUSS I ON
In this semi-arid Australian rangeland case study, forage production and animal stocking rates were significantly impacted by drought events and long-term climate trends. Increases in precipitation means were favourable to grazing systems productivity while increases in climate variability negatively affected herd sizes. Although forage was proportionally more responsive to climate variability than the herd size, herds recovered more slowly after drought events, taking up to decades in some cases, in the absence of stock purchases to accelerate herd recovery. Farming intensification strategies increased long-term herd sizes but had less of an impact than climate on the variance in animal stocking rates. Similar to favourable climates, intensification also resulted in larger reductions in animal numbers during droughts and raised total enteric methane emissions.
Although the herd-forage model was developed to allow the testing of different potential scenarios, the current version of the model was not aimed at capturing the operational diversity and complexities of actual livestock enterprises in their entirety. In common with any model of a complex system, it was developed with a specific purpose and is underlined by a number of simplifying assumptions F I G U R E 7 Mean annual total standing dry matter (a) and animal stocking rates (b) under different climate and forage productivity scenarios. No feed supplementation was provided to the herd. See Appendix S2 for more details about Set 1 of climate scenarios. TLU, tropical livestock units (see below and Appendix S1). These simplifications could also in part explain the relatively high goodness-of-fit (R 2 ) of some of the  1992-1996, 2001-2004 and 2013-2015, which showed annual precipitations below 500 mm (see annual precipitation patterns since 1900 in Appendix S2, Bureau of Meteorology, 2018). The duration and frequency of these dry years, which are usually associated with El Niňo events, may also increase in the near future, although large climate uncertainties remain justifying the sensitivity approach undertaken in this study (Sillmann et al., 2013;Watterson et al., 2015, see example of projected climate uncertainties in Appendix S2). We found that with six consecutive years of very intense dryness, even with early decision-making in response to declining forage availability, the herd stocking rate decrease by 29%, and it took 24 years to fully recover herd numbers in the absence of additional animal purchases. In that case, the herd market liveweight value dropped by 31% (from 147AU$ to 101AU$ per hectare; prices from Meat & Livestock Australia, 2017). In this modelling study, the herd was managed to ensure pasture utilization rates that are considered for the region as economically and environmentally sustainable (Ash et al., 2011;Hunt, 2008;O'Reagain & Bushell, 2011;O'Reagain et al., 2014). While this is a strategy practised by a number of farmers in the region, other social and economic drivers can influence stocking decisions (Marshall, 2015). Some pastoralists may be in-  (Ellis & Swift, 1988). Other drivers of change in livestock systems and in broader development trends also add to future uncertainties and need to be further studied.
While this study focusses on a northern Australian beef system, other rangelands systems are also constrained by low precipitation and high and increasing climate variability (e.g. Namibia, north-east Kenya and south Argentina; Sloat et al., 2018). These regions are mainly located in developing countries where livestock is crucial for food access or the economy (Sloat et al., 2018).
Intensification strategies such as feed supplementation and improved pastures can be key strategies to adapt to climate change as they may result in farm production gains, greater herd size being carried with more animals being turned off for sale. While the current implementation of such strategies varies globally, examples are found around the world (FAO, 2007;Rao et al., 2015).
These changes in farming practices contribute, in different ways, to herd dynamics as compared to climate change. For instance, in this study, climate had the largest contribution to the stocking rates variance, followed by forage. Feeding practices had a negligible contribution. As highlighted in this study, intensification strategies may also increase the sensitivity of the herd to drought events as well as total enteric methane emissions and come at other costs that might not be offset by increased production levels. Detailed analyses of the economic, labour and environmental trade-offs of such interventions and enabling environments (markets, policies, social and human capital) need to be assessed within a context of increased climate pressures, complex financial market fluctuations and social environments (Godde, Garnett, Thornton, Ash, & Herrero, 2018;Stafford Smith et al., 2007). Low forage nutritional quality in extensive rangeland systems tend to result in high methane emission intensities as compared to other livestock production systems (Ash et al., 2015;Charmley, Stephens, & Kennedy, 2008;Herrero et al., 2013). Intensifying the production systems generally increases total methane emissions and can reduce emissions intensity (Ash et al., 2015;White, Snow, & King, 2010). Management decisions can be made along the intensification spectrum to balance productivity and profitability objectives versus environmental ones. For instance, Ash et al. (2015) found that modelled intensification practices such as protein supplementation or legume sowing improved pastures, genetics or rumen functions could increase farm enterprise profitability under historical climate in northern Queensland, while decreasing methane emission intensities. They also found that if some of the gains in profit from introducing technologies were foregone by reducing the herd size so that methane production per hectare does not increase over the baseline, then maximum net profit was reduced by about 10% but it was still considerably higher than the baseline management strategy. The profitability of intensification strategies can, however, vary among global rangelands. For instance, Hatch and Stafford Smith (1997) found that feed supplementation as a drought management strategy was not economically viable in a semi-arid South African rangeland modelling case study. Farmers may be required to adjust their practices and stocking rate targets on a more frequent basis to maximize both short-and long-term economic benefits while preventing land degradation. In Australia, farmers have been maintaining low stock numbers and pasture utilization rates to limit the effects of high climate variability (Landsberg, Ash, Shepherd, & McKeon, 1998). Moving livestock to take advantage of spatial heterogeneity in forage availability has also been a key adaptation strategy under high climate variability in many rangelands (e.g. southern Africa, Mongolia, China). However, this option is increasingly challenged as landscapes become frag- acknowledges the CGIAR Research Program on Climate Change, Agriculture and Food Security (CCAFS), which is carried out with support from the CGIAR Trust Fund and through bilateral funding agreements (for details, please visit https ://ccafs.cgiar.org/donors).
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