The single heterogeneous paddock (SHP) option within the dynamic biophysical model EcoMod [7,18] was used to allocate excreta (dung and urine together) to a grazed 1 ha area. For a full description of the model see [18]. The SHP approach allows a paddock’s soil nutrients, pasture production and species composition to be simulated independently within a defined proportion of the grazed area on a daily time-step. Options are available with regard to how nutrients are returned to the pasture i.e., to a defined area with a chance of repeat deposits or spread evenly to the whole paddock. This model incorporates daily climate data, soil properties, pasture species, livestock and management to describe the whole farm system. The climate data inputs include minimum and maximum temperature (°C), rainfall (mm), solar radiation (MJ/m²), vapour pressure (kPa) and minimum and maximum relative humidity (%). The climate data were obtained from the SILO database [19].

Simulations were based on climate data from the years 1901 to 2000 for the Ellinbank Research Farm in south-eastern Victoria (−38.25° N, 145.93° E). Ellinbank has a temperate climate (average daily minimum and maximum temperatures of 8.6 and 18.4 °C respectively) with a relatively high mean annual rainfall of 1054 mm during the study period. The soil type was a well-drained, basalt-derived, Red Mesotrophic Haplic Ferrosol [20]. The pasture system was a dryland (i.e., rainfed) perennial ryegrass (Lolium perenne L.) and white clover legume (Trifolium repens L. 1753) sward, which was grazed for a period of one day every 60 days (6 or 7 grazings per year) by 45 kg wethers, which were assumed to maintain their body weight. The model has previously been assessed to predict pasture growth rate at Ellinbank and has been found to give good agreement [8,18].

The animal module describes the animal’s energy requirements for maintenance (defined as 0.52 × body weight^{^0.75} MJ d⁻¹), feeding activity and body weight change (see [7], for details). The model assumes that the animal will try to eat enough food to meet its ME requirement, with ME intake constrained by the ME content of available feed and a constraint on the animal’s DM intake depending on its digestibility (1.8 kg/d at 80% dry matter digestibility). The sheep grazed the same paddock every 60 days to allow the pasture biomass time to recover from grazing and so that allocation of excreta was compared on the same days. Growth of each pasture species in the model is described by the plant’s photosynthesis and respiration response. In the model it was assumed that the optimum N content for photosynthesis was 4 and 4.5% for perennial ryegrass and white clover respectively.

Of the N consumed by the animal, a fixed proportion of 0.15 of N intake was assumed to be retained by the animal and not defecated (as assumed by [14]). In the model, the proportion of N excreted in dung (φ_F) depends on the N-energy density (ρ_I) of feed intake (kg N/MJ) and the proportion of N intake that is excreted (λ_N): where α and β were assumed to be 45 and 13% for values of φ_F at very low and very high λ_N respectively, and γ is an empirical coefficient, which was assumed to be 560 MJ/kg N.

No supplementary feed was fed to the sheep, which meant that the only true N input to the system was from fixation by legumes. Thus as stocking rates increased the pasture systems would become more N deficient. It was assumed that one animal would produce 0.5 m² of excreta (20 deposits of 0.025 m² including both dung and urine) each grazing day [3].

The model allows a minimum of 1% of the paddock to receive excreta and so a range of stocking densities from 200 to 2000 sheep/ha (increasing in 200 sheep/ha intervals) was used to allocate an increasing amount of excreta produced by the animals. Assuming that a 45 kg wether is 1 dry sheep equivalent (DSE; [21]), the range of stocking densities simulated would equate to a range in annual stocking rate of 3 to 33 DSE/ha. The model simulated the allocation of excreta produced by the range of stock densities to the grazed area either: randomly [22] over 1 to 10% of the grazed area per day representing an increase in excreta applied to the pasture by increasing the stocking density from 200 to 2000 sheep/ha (in 200 sheep/ha intervals) or uniformly spread to the whole 1 ha grazed area. The random and uniform allocation of dung with urine was applied so comparisons could be made between modelled N allocation methods—even though dung and urine would typically be excreted separately by the grazing animal.

Grazing system simulations were run for 100 years from 1901 to 2000 to allow for full expression of the nitrogen balance and its variability. A subset of 40 years from 1961 to 2000 was used for the analysis. The average annual N inputs (kg N/ha) to the grazing system by excreta and fixation by legumes were predicted by the model.

The model apportions predicted N losses (kg N/ha) from the system by volatisation, denitrification and leaching in this order. Ammonia volatisation from urine is influenced by temperature and rainfall. Temperature had a linear effect on volatilisation (0.20 × kg urine N × temperature °C/20) and rainfall greater than 5mm stopped volatilisation. Nitrification and denitrification in the model are influenced by temperature, water filled pore space (WFPS) and soil carbon status, using the same generic response functions as for other soil processes. The model includes a mechanistic treatment of the rate of nitrification as a function of available soil ammonium (NH₄⁺) and denitrification as a function of available soil nitrate (NO₃⁻). As the soil moisture increases above wilting point oxygen diffusion in the soil is hindered and thus slows the rate of nitrification, but promotes denitrification, due to increasing anaerobicity, with a consequent release of both N₂O and N₂ [23]. Modelled N₂O losses increase exponentially after 0.6 saturation of the WFPS, and decrease after saturation at 0.8, with cessation of N₂O loss at 0.95 saturation of the WFPS, with all products of denitrification being nitrogen gas (N₂) thereafter [23,24]. Nitrous oxide from nitrification was not predicted by the model, as nitrification was considered a minor source of N₂O in pasture systems in terms of total N loss [1]. Temperature, WFPS and soil carbon status influenced the rate of denitrification, with an assumed maximum rate of denitrification of 0.25 mg N kg⁻¹ soil. Full details of the model structure are given in [7].

The data were analysed using Genstat Version 12.1 [25]. The Mann-Whitney U-Test was used to evaluate any significant difference in total pasture intake (t DM/ha), N intake, total N inputs (excreta and legume fixation) to the system, amount of N fixed by legumes (all kg N/ha), total N losses, and proportion of N inputs lost by leaching, volatilisation and denitrification for an increasing stocking density of 200 to 2000 sheep/ha with their excreta distributed uniformly or randomly to the grazed area. Significance was attributed at a value of P < 0.05.

There was a consistent decline in soil N content over time in all simulations (Figure 1).

Figure 2 shows the average annual N in soil, plant matter, fixed by legumes and retained (removed) by the grazing animal, and losses by volatilisation, denitrification and leaching for each simulated pasture system. In the simulation in Figure 1 and in Figure 2, the grazing system with 2000 sheep/ha and a random distribution for excreta resulted in the lowest soil N content.

When excreta was distributed uniformly to the pasture at stocking densities of 1600 to 2000 sheep/ha the average pasture intake of the sheep was significantly greater than if excreta was distributed randomly (P < 0.05; Table 1). The concentration of N in the pasture ranged from 4.3% to 4.6% across the range of stocking densities applied. The N intake/ha of the sheep was also significantly greater at stock densities of 1200 to 2000 sheep/ha when excreta was distributed uniformly rather than randomly (P < 0.05).

Whilst N intake was significantly greater at high stock densities when the excreta were distributed uniformly, the total N return of excreta plus N fixed by legumes to the pasture system were not significantly different between the simulated grazing systems for both methods of distributing excreta (P > 0.05; Table 1). Even though the standard deviation in total N inputs (excreta + fixation) increased as stock density increased, the amount of N fixed by legumes meant there was no overall significant difference in these N inputs between the uniform and random distributions before accounting for N losses from the system. On its own, the amount of N fixed by legumes at >600 sheep /ha was significantly more when excreta was distributed randomly rather than uniformly (P < 0.05; Table 1).

Figure 3 shows that the average annual N leaching losses from the system ranged from 91 ± 62 to 67 ± 29 kg N/ha and 92 ± 60 to 95 ± 37 kg N/ha for low to high stocking densities and uniform and randomly distributed excreta respectively. Volatilisation N losses ranged from 3.1 ± 0.7 to 21 ± 4.7 kg N/ha and 3.1 ± 0.7 to 19 ± 4.7 kg N/ha for low to high stocking densities and uniform and randomly distributed excreta respectively. Whereas, denitrification losses were 5.4 ± 2.7 to 4.8 ± 1.2 kg N/ha and 5.1 ± 2.6 to 4.0 to 0.7 kg N/ha for low to high stocking densities and uniform and randomly distributed excreta respectively. On average, the N/ha lost by leaching remained at a similar level when excreta was distributed randomly to the grazed area but gradually reduced for the uniformly distributed excreta with increasing stock density. Volatilisation N losses increased with an increasing area of the grazing receiving excreta, and denitrification losses showed a similar pattern to leaching, however for both volatilisation and denitrification the losses were higher when excreta was distributed uniformly rather than randomly at higher stocking densities.

At the site simulated, the proportion of total N inputs (from excreta and N fixation by legumes) lost from the grazed area (Figure 4) declined as the stock density and pasture intakes increased (Table 1). Distributing excreta uniformly over the grazed area reduced the proportion of total N inputs lost (P < 0.05 to P < 0.001 for 1400 to 2000 sheep/ha) and in particular N lost by leaching (P < 0.01 to P < 0.001 for 1400 to 2000 sheep/ha). In some years, the N in the soil would start to build up in the soil and then be lost later in higher rainfall years (Figure 1). This resulted in the proportion of total N inputs in a year that were lost being more than one; hence for 200 sheep/ha the standard deviation was greater than one.

Figure 4 shows that the proportion of total N inputs lost by leaching averaged 0.75 at 200 sheep/ha to 0.21 and 0.29 at 2000 sheep/ha for uniform and random distributions of excreta respectively. In comparison, the proportion of N inputs lost by volatilisation ranged from 0.03 to 0.06 and 0.04 to 0.01 for denitrification losses across the range of stocking densities. The proportion of N inputs lost by volatilisation was not significantly different between uniformly and randomly distributed excreta across the range of stocking densities (P > 0.05). Even though the proportion of N inputs lost by denitrification each year was low, it was significantly greater at higher stocking densities when excreta was distributed uniformly rather randomly to the grazed area (P < 0.05 to P < 0.01 for 1200 to 2000 sheep/ha).