Equilibrium and non-equilibrium models of livestock population dynamics in pastoral Africa : their relevance to Arctic grazing systems

Equilibrium grazing systems are characterised by climatic stability that results in predictable primary producrion. Non-equilibrium grazing systems receive low and erratic rainfall that produces unpredictable fluctuations in forage supplies. In semi-arid Africa, these two types of environment present livestock owners with very different management problems. Identifying and maintaining optimal stocking rates is useful in equilibrium systems because livestock reproduce and produce at a rate determined by the availability of feed, which is an inverse function of stock density. The only problem is to determine what stocking rate is optimal. The correct stocking rate for a grazing system will vary depending on the production strategy and the social and economic circumstances of the rangeland user there is no single, biologically predetermined optimum density. Variable rainfall complicates the picture in non-equilibrium systems. Set stocking rates of any kind have little value if fluctuation in rainfall has a stronger effect than animal numbers on the abundance of forage. More useful in such an environment is the ability to adjust stocking rates rapidly to track sudden changes in feed availability. In semi-arid Africa, the distinction between equilibrium and non-equilibrium sysrems hinges on the reliability of rainfall. In northern latitudes, at least three primary variables important for plant growth and the survival of herbivores must be considered: rainfall, snow cover and temperature. It is probably not useful to consider arctic grazing systems as equilibrium systems; on the other hand, the non-equilibrium models developed in hot semi-arid environments do not capture the range of complexity which may be an inherent feature of plant-herbivore dynamics on the mountain and tundra pastures where reindeer are herded or hunted.


Introduction
Like many of the applied agricultural sciences, range management was developed to meet the needs of commercial producers in temperate climates.In the 1960s international aid agencies began to spend large amounts of money to transfer the new technologies to the open ranges of semi-arid Africa.The transplant did not work and -by the early 1980s when enthusiasm for the endeavour had worn offsub-Saharan range management projects earned a justified reputation as failures (Simpson & Sullivan, 1984;Swift, 1991;Baxter, 1994).In retrospect, it is clear that range management in Africa had been deprived of several of the prerequisites for its success in industrial countries: large-scale commercial producers, private land ownership and a temperate climate.Classical range management had packed its Rangi£er, 20 (2-3), 2000 standard conceptual tool bag, migrated south to equatorial latitudes but failed to take note of the particular socio-economic and ecological circumstances that confronted it there.
Like the tropics, the Arctic is a potential consumer of temperate notions of rational livestock production and resource management.A decade ago Beach (1990) identified a standard package of policies promoted by Scandinavian governments to rationalize traditional forms of reindeer herding.The package included the introduction of novel culling practices, selective breeding, grazing rotation and destocking -proven ingredients in the success of commercial livestock husbandry in most of Europe and North America.These techniques were either heavily modified or abandoned when they were applied to small holders in pastoral Africa; whether they will work in the Arctic is far from certain.
There has been little sustained communication by tesearchers across the latitudinal gradient that separates the tropics and the Arctic and sub-Arctic.This paper contributes to such a dialogue.It recounts a tale of lessons learned the hard way over the course of several decades in equatorial Africa and speculates briefly about the convergence of arctic and tropical range and livestock policy.My treatment of the arctic material is, at best, impressionistic.Real dialogue takes partners, but pastoral studies are still regionally compartmentalized and we have yet systematically to exploit the comparison between temperate, tropical and arctic forms of extensive livestock production.

The standard interpretation and alternative hypotheses
Many African rangelands are heavily stocked with domestic animals and have been for some time (Sandford, 1983).In a dry year, or after a run of dry years, the animals often yield very little output in terms of secondary production and occasionally die in large numbers (McCabe, 1987;Moris, 1988;Bernus, 1988;Fratkin, 1991;Scoones, 1992).The causes and consequences of such fluctuations have been poorly understood.The most common interpretation has been that the rangelands were overstocked, that they were used unproductively and that their long-term productivity declined with each crisis (reviewed in Sandford, 1983;Shackleton, 1993;Turner, 1993;Dahlberg, 1996).Inefficient land use practices were seen to be the problem and destocking was commonly recommended as the remedy (Brown, 1971;Lamprey, 1983;Jarvis, 1991).
In the last ten years this standard interpretation has been challenged by a number of alternative hypotheses about how grazing systems function in semi-arid environments.Central to these arguments is a distinction between equilibrium grazing systems, in which annual rainfall is relatively high and reliable from year to year, and non-equilibrium systems in which it is low and erratic.These two kinds of environments present herd owners with different kinds of management problems and environmental risks.
Equilibrium grazing systems are characterized by relatively high climatic stability resulting in predictable primary production.In this setting, 'fine 142 tuning' for optimal output is possible because livestock renew themselves -reproduce, grow and produce meat and milk -at a rate determined by the availability of feed, which is an inverse function of stock density.Provided with a reliable feed supply, livestock populations can grow to the point where they have considerable impact on the species composition and density of the vegetation on which they depend.The opening sections of this paper summarize some of the evidence for, and policy implications of, the equilibrium/non-equilibrium dichotomy as it has been applied to semi-arid grazing systems.The last part of the paper discusses the relevance of this dichotomy for management regimes for ungulates in the Arctic and sub-Arctic.commercial ranchers, the economically optimal stocking density -MP or maximum profit -is the stocking rate which maximizes the differential between total revenue and variable costs.This economic optimum can be identified by inspection; it occurs at the point of greatest vertical distance between the revenue and variable cost curves.Finally, MO -the density beyond which rising costs exceed revenue -represents the outer margin of viable economic operation on the rangeland in question.Beyond MO net revenue is nil, rendering insolvent any unsubsidized herd owner who persistently operates at these densities.

Carrying capacity in equilibrium systems
In Figs. 1 and 2, livestock and plant populations are closely coupled by density-dependent negative feedback -more livestock result in more pasture eaten, therefore less pasture available and consequently fewer livestock (Caughley, 1987: 168) Fig. 2 addresses this issue.It identifies at least six distinct management objectives and associated stocking densities at which different observers -or producers -might conclude that the system contained the correct number of animals: optimal individual animal performance (MN), profit maximization (MP), yield maximization (MY), maximization of the number of herding operations supported by the resource (MO) and, finally, the maximum total number of livestock which could be supported on a permanent (K) or temporary basis (K+, not shown in Fig. 2).With the exception of K+ all these stocking densities are potential equilibria at which the rate of growth of plants equals the rate at which plants are consumed by herbivores.With the exception of K, all these potential optima are managed equilibria sustained by alternative culling rates.Although all are technically feasible, each of these different 'equilibrium' densities is appropriate to a particular management and production system or is advocated by different sets of professional observers.
In contrast to large-scale market-oriented ranching, however, open-range African herding is characterized by different livestock breeds, species and product combinations, variable levels of market involvement and different systems of land tenure.Fig. 3 presents hypothetical revenue or physical product curves for fenced beef ranching systems and subsistence-oriented African husbandry systems using communal rangelands.These curves illustrate some of the principal differences between commercial and pastoral productivity and the likely impact of these differences on stocking policy.The altered shape of the pastoral output curve combined with a 'flat' variable cost curve for subsistence producers minimizes the difference between MP, MY, MO and K; it also positions these thresholds at very high stocking densities compared to commercial ranching.Maximum yield at MY is higher in the pastotal system than in the ranch system as a result of the combined effects of a broader product mix, exploitation of live rather than terminal animal products, and the greater physiological resilience of indigenous breeds.These factors help explain why African pastoral producers can achieve their production goals at stocking rates near ecological carrying capacity.semi-arid regions of Africa.Mixed-product output per hectare from subsistence-oriented pastoralism is routinely several orders of magnitude higher than beef output from commercial ranching in comparable environments (Prins, 1989;Behnke & Abel, 1996).In climatically stable environments these economic benefits are achieved at the cost of lowered plant density and destocking would immediately make many people poorer (Abel, 1993).
That subsistence-oriented producers can meet their production targets at much higher stocking rates than commercial producers does not mean that the land they occupy is more resilient (Stafford Smith, 1996).On the contrary, it implies that there are strong incentives for African herd owners to stock heavily for their immediate benefit but with potentially disastrous long-term environmental consequences.This is not, unfortunately, a problem that most stocking experiments are equipped to examine because they rarely continue long enough to pick up the lagged effect of high stocking densities on output levels (Ash & Stafford Smith, 1996).For African husbandry systems, reliable data on the long tetm sustainability of highly productive and highly stocked systems are virtually non-existent.

The population dynamics of non-equilibrium systems
Semi-arid grazing systems are arrayed along a continuum ranging from non-equilibrium to equilibrium, with most African grazing systems probably lying somewhere between the extremes (Wiens, 1984;Ellis & Swift, 1988;Coppock, 1993;Scoones, 1993).For purposes of comparison, the following account ignores the intermediate forms and presents a simplified picture of several important features of strongly non-equilibrium grazing systems.
At low rainfall levels, semi-arid grazing systems are driven by one dominant input -water -which arrives in discontinuous pulses some of which are large enough to send waves of biological activity cascading through the system (Noy-Meir, 1973).Biotic activity is regulated by a sporadic aboitic variable.In these environments, predictable seasonal fluctuations in rainfall are compounded by stochastic annual variations.Since annual variability in rainfall is inversely correlated with mean annual rainfall levels, the supply of water becomes more erratic as the total amount declines (Nicholson et al, 1986;Nicholls & Wong, 1990) & Swift, 1988).If droughts are frequent and severe enough, differential die-back and recovery rates will ensure that livestock populations will be almost continuously out of synchronization with their food supply in a particular year.In extreme instances, the herbivores are 'ambushed when at high density by a drought that cuts the food from under them, and ... trapped inappropriately at low density when a burst of pasture growth provides enough food to maintain a hundred times their number' (Caughley, 1987: 179, referring to kangaroos).In these systems, any equilibrium between the supply and demand of feed is largely coincidental -a fortuitous match between forage production and rainfall in one year and livestock population levels generated by rainfall and forage production in past years (Ellis & Swift, 1988).
• Weak habitat saturation.If herds die off in droughts more quickly than they tecover in good years, mean stocking rates in environments subject to stochastic rainfall variation will be lower than they would be under comparable but constant conditions (Caughley, 1987;Scoones, 1993).
If livestock densities that are in theory sustainable under stable conditions are equated with 'carry¬ ing capacity', then these systems will maintain mean stocking densities below carrying capacity (Ellis & Swift, 1988;McLeod, 1997;Hary et al., 1997).

It is also possible that droughts may 'focus the impact of animals on the vegetation into intense episodes' thereby precipitating sudden, discontinuous changes in plant species composition over wider areas (Illius & O'Connor, in press
).The extent to which this happens or is likely to happen is unknown.Numerous experiments show that the species composition of vegetation in semi-arid areas changes in response to constant high grazing pressure.But these results are not pertinent to nonequilibrium dynamics, which are characterized by alternating periods of high and low stocking densities and recurrent imbalances in the supply and demand for forage.Field studies that document the negative consequences of pastoral land use are more compelling but are contradicted by case material that suggests little widespread rangeland degradation even in the Sahel, long presumed to be the locus classicus of desertification (Tucket et al, 1991;Hiernaux, 1996).

The relevance of the equilibrium/nonequilibrium dichotomy for arctic ungulates
In their comparison of kangaroos and caribou, Caughley & Gunn (1993) noted parallels between semi-arid and arctic grazing systems in terms of structural simplicity, exposure to uncertain weather extremes and the instability of herbivore populations.Their analysis suggests that non-equilibrium grazing systems comparable to those in the semiarid tropics may exist in the Arctic.In both settings the 'components of climate that determine plant growth...vary prodigiously from year to year' (Caughley & Gunn, 1993: 52), forage availability rather than herbivore density drives changes in herbivore populations and does so quickly: 'Populations of both red kangaroos and caribou appear to be buffeted, and occasionally hammered, by changes in the availability of food mediated entirely by capricious weather' (Caughley & Gunn, 1993: 53, 54).As Caughley (1987)  • Additional evidence has emerged that insular caribou populations are 'loosely regulated by food at low populations density' due to 'the impact of frequent density independent factors', a conclusion that could be sustained despite the possibility that the index of winter severity used in the study was 'too simplistic' and that one of the study islands had no weather station (Ouellet et al, 1996; see also Nagy et al., 1996 for Peary caribou on Banks Island; Tyler et al., 1999 for Svalbard reindeer).• Whitten's (1996) analysis of the demography of the Porcupine caribou herd in Alaska has moved on from a presentation of census results (Fancy et al., 1994) to an analysis of the mechanisms of population regulation, summarized as follows: The Porcupine Herd undergoes population fluctuations of variable amplitude and period because weather setbacks come at irregular intervals.Recovery rates under normally prevailing conditions are slow enough and weathet setbacks occur frequently enough that the population tends to stay within a fairly narrow range of densities and seldom, if ever, reaches levels where there would be population regulation through food competition if access to forage were never restricted.There is no true equilibrium in this system.• Similar conclusions apply to the population dynamics of a mountainous caribou herd in the Alaskan interior: 'The size of a caribou herd in a given year is likely to be largely a function of its size during the previous population low and the number of years of favorable weather in the interim' (Valkenburg et al., 1996).There are, however, also likely to be consistent differences in the way semi-arid tropical and arctic climates stress animals, differences that complicate simple comparison between unstable, weather-driven population dynamics in these two types of systems.In semi-arid Africa and Australia weather affects livestock viability in a remarkably simple way: either it rains or it does not.Plant growth and senescence, livestock malnutrition and recovery all hinge on the presence or absence of a single physical input.No other climatic factor comes close to having the importance of rainfall, which can be exceedingly unstable in areas where it is scarce.This means that the character of an entire year is established by rainfall in the preceding wet seasons.
The situation is more complex at higher latitudes where fluctuations in both temperature and precipitation influence both the growth and the availability of forage in summer or winter, respectively.At northern latitudes, one set of weather variablessuch as rainfall or the timing of the onset of warmer weather in spring -may cause fluctuations in the quality and quantity of feed production, while a second set of weather factors -such the prevalence of ground ice or the depth of snow cover -determine how much of total primary production is accessible to herbivores in winter (Mech et al., 1987;Tyler 1987;McRobertse^/., 1995;Langvatnetal., 1996;Post et al., 1997;Forchhammer et al, 1998) The picture is further complicated by the way different kinds of arctic vegetation respond to weather and to grazing.Herbaceous vegetation in semi-arid Africa and Australia responds quickly to rainfall.In the arctic green biomass production may also react rapidly to fluctuating weather stimuli, but at least one kind of forage -lichens -does not.Lichen recovery from fire or heavy grazing is measured in decades (Thomas et al, 1995;Arseneault et al., 1997).Depending on the relative availability of winter and summer ranges in an area, reindeer/caribou populations may be constrained by vegetation resources that fluctuate either annually or across decades.Because they ate grazed in different seasons, these feed sources may also influence different vital rates (Sasther, 1997) with different levels of variance and elasticity (Walsh et al., 1995;Gaillard et al., 1997).Just this sort of complexity is suggested by the dynamics of the George River caribou herd which may be regulated by winter or summer feed availability, or both (Messier et al., 1988;Crete & Huot, 1993;Manseau et al, 1996;Arseneault et al, 1997).What initially looked like a simple system now looks rather complicated.
Constrained by forage resources that respond to grazing pressure on different time scales and influence different vital rates, reindeer/caribou grazing systems appear to exhibit locally specific patterns of population regulation depending on the relative abundance of winter and summer forage in an area.For example, marked yearly fluctuations in herd size are not apparent in the data on Norwegian wild reindeer summarized by Skogland (1990) who emphasized density-dependent population regula¬ tion and attributed large crashes to over-hunting: The primary factor in population regulation of wild reindeer herds is density-dependent food limitation in winter, and...density-independent effects are most likely to be a contributory factor only at high population density (Skogland, 1985).
In Africa and I suspect in the Arctic as well, these debates have practical implications for the design of public policy.Our perception of the resource management capacities of local communities, the relationship between rural communities and regulatory authorities and pastoral development priorities all turn on the extent to which grazing systems are nat-urally homeostatic and subsequently perturbed, or intrinsically non-equilibrial.There are several reasons for suspecting that these questions can be usefully investigated for arctic and sub-arctic pastoral systems.To an extent rare in sub-Saharan Africa, circumpolar real-estate is controlled by powerful industrial states that possess the means to enfotce their will.It is unlikely that the official policies promulgated by these states will be so inadequately funded or erratically implemented as to be irrelevant to the daily lives of reindeer herders.Even in theit hinterlands, central government policies make a difference, as will any contributions that science makes to the formulation of better policies.
Recent advances in the understanding of semiarid tropical grazing systems resulted from a reexamination of agricultural problems from an ecological perspective.Ecological analyses provided an alternative to the prescriptive formulae of the applied agricultural sciences, formulae that were better suited fot temperate rather than tropical environments and for commercial rather than subsistence producers.The ecological sciences are well qualified to fulfill a similar role with respect to debates on reindeer pastoralism.Because they reside in the industrialized north, reindeer/caribou have been extensively studied.We probably already know more about Rangifer than we will ever, unfortunately, be able to discover about the agro-ecology of African cattle breeds managed under subsistence conditions on Africa's open ranges.Domesticated reindeer share both their geographical range and their genetic constitution with caribou which facilitates comparison between the ecology of wild and domesticated populations.Despite the inevitable shortcomings, the empirical record on Rangifer ecology is robust enough to enable ecologists usefully to scrutinize the development of grazing management policy.Routine ecological studies, clear synthesis of results and vigorous engagement may contribute a great deal.

Fig. 2 Fig
Fig. 2 converts physical outputs in Fig. 1 into cash equivalents and compares the returns with operating costs at different stocking densities.For

Figs. 1
Figs. 1-3 also illustrate why carrying capacity has proved such a slippery concept.Within the limits of what is biologically feasible, the correct stocking rate for a grazing system must be determined in relation to the production strategy and the social and economic circumstances of the rangeland user.There is no single, biologically predetermined optimum equilibrium density and, hence, little point in simply characterizing an area as 'overstocked'.This analysis explains why outside observers commonly perceive African rangelands as chronically overstocked.Due to the historical association of range management with commefcial beef ranching, many of the standard botanical indicators used to assess 'carrying capacity' have actually been implicitly derived to identify economically profitable stocking rates for commercial ranchers which is shown as the density MP in Fig. 2. Subsistence producers are likely to target an alternative density, MY, situated along an entirely separate production function depicted in Fig. 3.Here we have an explanation of how livestock numbets in some parts of Africa have continued to grow, in some instances for decades, beyond the purported limits of carrying capacity.What was being estimated were not ecological but economic carrying capacity levels and, moreover, economic carrying capacity levels for kinds of production systems that did not exist in the areas being assessed (Behnke & Scoones, 1993) Fig. 3 also demonstrates why the controversy over pastoral overstocking has been so intractable in Rangifer, 20 (2-3), 2000 Density independence.Shortfalls in feed supply are a consequence of periods of plant senescence that result in declines in the quality and quantity of forage.If forage quality routinely declines below maintenance levels as the vegetation cures, most animals begin to starve at the start of the dry season(Coppock et al., 1986 a;b).The rate at which animals die will depend more on the length of the dry period than on the number of animals subjected to it.To an extent that is remarkably independent of their density, livestock in semi-arid Africa lose weight in normal dry seasons, recruitment and reproduction suffer in poor years and adult animals die in severe multi-year droughts(Coughenour et al, 1985;McCabe, 1987;Homewood & Rodgers, 1991).•Spatial heterogeneity.Despite the loose overall coupling between livestock populations and their feed resources, there may be intense, densitydependent competition for the limited amount of high quality forage that is available to livestock in key resource areas in the dry season(Scoones, 1993;1995).In general, we might expect the impact of livestock on vegetation to diminish with increased distance from water and key resource areas, during the wet season, and in the early years of post-drought herd recovery when livestock populations are low.There is ample evidence that the reverse also holds true: that livestock impacts on vegetation can be intense in 'sacrifice' areas around watering points and in riparian areas that are key dry-season grazing resources (references in Illius & O'Connor, in press).
showed for kangaroos, major changes in herbivore population size can be generated simply by compounding frequent but less extreme perturbations.Long term fluctuations in caribou/reindeer populations could therefore be 'essentially a mathematical artifact of year-to-year fluctuations in weather...even when the weather has no time trend' (Caughley & Gunn 1993: 54).Subsequent to the publication of Caughley & Gunn (1993) there has accumulated additional evidence that sustains their interpretation, as follows: • More complete data have been assembled on population trends for the major barren-ground caribou herds in Northwest Territories, Canada, and this material makes an even stronger case for population instability than the data initially summa . With multiple factors determining the outcome, weather-induced stress is a function of the impact of individual factors, their correlation, and their additive or offsetting consequences.Multiple confounding factors could dampen or exacerbate climatic instability.Caughley & Gunn (1993) documented high coefficients of vatiation for important individual climate factots.How this variability is 'packaged' in individual years will present analytical problems and is likely to have impacts on herbivore dynamics that are not apparent in semi-arid grazing systems.

. Stable densities of plants and herbivores and pre- dictable levels of herd output are made possible by this feedback and because these systems are not unduly buffeted by the vagaries of climate. It only remains for the manager to decide what level and what kind of output is required from the system and what densities of plants and animals will deliv- er this output. African cattle breeds can survive, produce and repro- duce under nurritional conditions that are inadequate by the standards of commercial breeds in temperate cli- mates. • In pastoral systems, herd output falls precipitately from the point of MY to zero yield at ecological carrying capacity, reflecting a non-linear relationship between stocking density and live animal outputs such as fibre, milk or manure. If production and reproduction can conrinue during periods of weight loss, stocking rates that maximize live animal outputs will be higher than those that maximize meat output (Donnelly
et al.,  1983;Donnelly et al., 1985;

Behnke & Abel, 1996) • Pastoralists can obtain over 2.5 times more energy from combined meat and milk production than from meat production alone, because of the greater efficiency of conversion of both feed energy and nutrients -princi- pally nitrogen -from pasture into milk (Western, 1982; Western & Finch, 1986; Blaxter, 1962; King, 1983; Spedding, 1971). •Operating costs for inputs other than labour are very low for many subsistence-oriented herders, giving a gently sloping variable cost curve. When variable costs are minimal, MP, the stocking rate that maximizes net revenue, shifts to the right, effectively eliminating for subsistence-oriented systems the distinction between those stocking rates that optimize economic profits
(Tapson, 1990oss output (MY)(Tapson, 1990).

. This combina- tion of a harsh and unstable climate has several con- sequences for the relationship between livestock and vegetation: • Seasonality. In semi-arid areas livestock popula- tions are commonly limited by the abundance and quality of forage in the dry season. It may be difficult to maintain livestock in sufficiently high numbers through the dry season to challenge the vegetation in the wet season when it is growing, vulnerable to damage but abundant relative to feed requirements. Conversely, when grazing pressure is high -i.e. in dry seasons or during droughts when demand for feed often outstrips supply -the plants are relatively impervious to abuse, the living bits having retreated behind thorns, inside woody structures, below ground or been stored in seeds.
• Stochastic disturbance.Seasonal

1986) 148 and Tyler (1987) describe island grazing systems in which seasonal and inter-annual fluctuations in feed availability create intriguing parallels with semi- arid Africa grazing systems. Reindeer/caribou are not limited by summer nutrition and populations can be severely reduced by icing; winter nutrition is limited and stocking rates may be maintained below summer carrying capacity. Substitute 'dry season' for 'winter', 'wet season' for 'summer' and 'drought' for 'ice' and we could be talking about African livestock-vegetation interactions rather than island reindeer/caribou. Non-equilibrium dy- namics caused by stochastic disturbance may repre- sent an appropriate model. Policy implications for reindeer manage- ment Two decades ago Ingold (1980: 27, 47, 211) argued that reindeer pastoralism destabilised arctic grazing systems by encoutaging violent oscillations in ungulate numbers and pasture availability in a 'vicious circle' in which 'impoverishment results ftom a cultural failure to impose effective limits to [herd] growth, just as the impetus for growth derives from the prospect of impoverishment'. For Ingold, reindeer pastoralism destroyed natural bal- ances or exacerbated natural imbalances. In the semi-arid tropics, remarkably similar arguments were part of what Sandford (1983) has called the 'Mainstream view' -the assertion that contemporary pastoralism upset natural homeostasis, degraded the environment and impoverished those who practiced it. The work summarized in the first two sections of this paper was an attempt to dismantle parts of the ecological rationale that underpinned Mainstream perceptions of semi-arid Africa. A similar debate is underway in the Arctic, with some scholars arguing that the flexibility and opportunism characteristic of indigenous production systems are appropriate responses to an erratic and harsh environment
Adamczewski et al. (