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A simple population viability analysis of the Critically Endangered Euphorbia clivicola R.A. Dyer under four management scenarios
Biological Conservation 96 (2000) 263±270
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A simple population viability analysis of the Critically Endangered Euphorbia clivicola R.A. Dyer under four management scenarios M.F. Pfab *, E.T.F. Witkowski Restoration and Conservation Biology Research Group, Department of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Private Bag X3, PO Wits, Johannesburg 2050, Gauteng, South Africa Received 14 March 2000; received in revised form 6 June 2000; accepted 13 June 2000
Abstract This paper describes a population viability analysis (PVA) for Euphorbia clivicola R.A. Dyer, a threatened succulent con®ned to only two known populations in the Northern Province of South Africa, one of which is protected in a nature reserve. The PVA explicitly compared the relative eectiveness of four management scenarios in bringing about the recovery of the protected population that had shown a 91% decline over the decade during which the population was monitored. Demographic monitoring data as well as autecological data collected in 1996 were used to determine the temporal variation in observed demographic and reproductive parameters. The model parameters were allowed to vary randomly over the observed ranges in order to incorporate stochasticity of the environmental factors ®re, herbivory and rainfall. If future management practices remain unchanged, the model predicted that there is an 88% probability of the protected population becoming extinct within the next 20 years. The population should recover under a management scenario involving a ®re frequency of every 3 years, the exclusion of herbivores and augmentation. The model has since been validated with data collected in 1999. Such analyses are useful for adaptive management purposes. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Adaptive management; Demography; Environmental stochasticity; South Africa; Threatened plant
1. Introduction Population viability analysis (PVA) has traditionally been used to estimate minimum viable populations for threatened taxa. However, the greatest strength of PVA is the opportunity to evaluate the ecacy of various management options (Burgman et al., 1988; Shaer, 1990; Boyce, 1992; Lindenmayer et al., 1993; Ruggiero et al., 1994; Mills et al., 1996), the objectives of which are to build populations up to adequate sizes and to reduce the risks of extinction (Given, 1994). Although a few recent PVAs have explicitly included management (Haig et al., 1993; Lindenmayer and Possingham, 1996; Drechsler, 1998), such applications have been especially lacking for threatened plants (but see Drechsler et al., 1999). Management recommendations for threatened plants have been mainly developed from deterministic matrix models (e.g. Manders, 1987). These models are however * Corresponding author at present address: Gauteng Directorate of Nature Conservation, PO Box 8769, Johannesburg 2000, Gauteng, South Africa. Tel.: +27-11-355-1480; fax: +27-11-337-2292.
static, a major weakness since they do not take account of the random or unpredictable changes in environmental conditions, or any other factors resulting in stochastic extinctions. Stochastic computer simulation models, based on the temporal variation in observed demographic parameters, are considered valuable for PVA investigations (Shaer and Samson, 1985; Menges, 1992). Variations in these parameters may be obtained from long-term demographic monitoring data and are in¯uenced by an extensive range of ecological and genetic factors. In¯uential factors include environmental variability, intraspeci®c density, interspeci®c competition, herbivory, mutualisms, pathogens, pollen limitation and dispersal, while in¯uential genetic factors incorporate both heterozygosity and allelic diversity (Schemske et al., 1994). This paper describes a simple stochastic computer simulation model for Euphorbia clivicola R.A. Dyer, a Critically Endangered (CR A1a) plant species, which explicitly evaluates the consequences of four dierent management scenarios involving burning, control of herbivores and population augmentation.
0006-3207/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(00)00088-4
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Euphorbia clivicola is endemic to the Northern Province of South Africa and is con®ned to only two known populations approximately 38 km apart. One population occurs in a nature reserve while the other occurs on the extremities of an urban area. Demographic monitoring data collected for the protected population by the Transvaal Provincial Administration (Division of Nature Conservation) from 1987 to 1993 and again in 1996 indicated a drastic decline from 173 seedlings, 288 juveniles and 1460 adult plants in 1987 to zero seedlings, ®ve juveniles and 160 adults in 1996. The urban population decline, from an original estimate of 3000 individuals to 382 plants in 1996, was directly due to loss of habitat and habitat fragmentation. Detailed investigations of the population biology and ecology of both populations during 1996 revealed that the probable cause of the protected population decline was an unsuitable ®re management programme implemented within the nature reserve. An 8-year absence of ®re and the consequent accumulation of a dense moribund grass layer was probably the cause of the severe herbivory pressure observed in the population (Pfab and Witkowski, 1999a). The E. clivicola plants, due to their relatively high nutritional value and accessibility in the thick moribund grass layer, were selectively grazed by small antelope such as mountain reedbuck (Redunca fulvorufula), signi®cantly reducing the regenerative output of the population (Pfab and Witkowski, 1999b). Euphorbia clivicola is a dwarf spiny perennial succulent. The main stem and root merge to form a subterranean tuberous body (Bruce et al., 1951) that probably acts as a storage organ allowing for adults to exhibit dormancy, observed during monitoring years, and rendering the species ®re tolerant through the protection of meristems (Pfab and Witkowski, 1999a). Only the young ultimate branches appear above ground, congested into a dense mass (Bruce et al., 1951). The branches bear minute deciduous leaves and during June sessile solitary cymes, while the three-seeded fruit are produced predominantly during August (Raal, 1986). Ballistic release of seed occurs as the tension in the constricting, drying fruit walls increase. Simple germination trials in 1996 indicated that seeds germinate immediately after release, essentially explaining the absence of seed banks. 2. Methods 2.1. Model parameters The model was constructed using a spreadsheet package (Microsoft Excel Version 5.0) and formulated as a Lefkovitch matrix incorporating demographic and reproductive parameters (Table 1). Demographic parameters represented transitions between stage classes,
seedling and juvenile persistence, adult survival and transitions between adult and dormant stages (Table 1). All adults that did not persist were assumed to become dormant. Monitoring data indicated that between 10 and 25% of dormant adults resprouted again two years later on average, thus essentially being incorporated back into the adult stage class. It was assumed that all adults that did not resprout had perished, a simplifying assumption forced by the lack of available data on dormancy in this species. The number of seedlings recruited was obtained by multiplying the number of adults by the percentage of reproductive adults (producing fruit) at each annual time step (frep), which was in turn multiplied by the reproductive parameter, fa,se (the number of seedlings produced by an average reproductive adult). The parameter fa,se was calculated from ®eld data collected in 1996 from which a multiple regression equation, relating fruit number to plant size, herbivory damage and grass competition (Pfab and Witkowski, 1999b), and a regression relationship, relating the percentage of viable seeds to plant size, were developed [Eqs. (1) and (2) in the Appendix]. 2.2. Environmental stochasticity An operational view was adopted whereby the measurement of environmental stochasticity was simpli®ed by focusing its measurement on population responses (Menges, 1992). Thus environmental stochasticity was simulated by allowing the matrix elements (Table 1) to vary randomly between the observed minimum and maximum demographic (Fig. 1) and reproductive (Fig. 2) parameters calculated from monitoring data.
Table 1 Stage matrix and population vector for calculating the numbers of plants in each stage class at each time stepa 2
ase;se 6 ase;j 6 4 0 0 a
0 aj;j aj;a 0
frep fa;se 0 aa;a aa;d
32 3 0 se 6 7 0 7 76 j 7 ad;a 54 a 5 0 d
The population vector lists the number of plants in each stage class at time t, where se refers to seedlings, j to juveniles, a to adults and d to dormant plants. This is multiplied by the stage matrix, incorporating demographic and reproductive parameters, to obtain the number of plants in each stage class at each annual time step (t+1), where ase,se is the probability of a seedling remaining a seedling, ase,j is the probability of a seedling growing into a juvenile, aj,j is the probability of a juvenile remaining a juvenile, aj,a is the probability of a juvenile growing into an adult, aa,a is the probability of an adult surviving, aa,d is the probability of an adult becoming dormant, ad,a is the probability of a dormant plant emerging from dormancy into the adult stage class, fa,se is the number of seedlings produced per reproductive adult and frep is the percentage of reproductive adults (producing fruit).
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Of the four components of stochasticity, environmental, genetic, demographic and natural castrophes, the only category of variability incorporated into the model was that of environmental stochasticity. This should be regarded as a weakness of the model, although modeling of genetics is not likely to be as important as modeling demographic and environmental processes (Boyce, 1992) and environmental stochasticity is considered to be more important than demographic stochasticity (Burgman et al., 1988). Furthermore, if
Fig. 1. Variation in observed demographic parameters for the protected population of Euphorbia clivicola over monitoring years, where se,se is the probability of a seedling remaining a seedling, se,j is the probability of a seedling growing into a juvenile, j,j is the probability of a juvenile remaining a juvenile, j,a is the probability of a juvenile growing into an adult and a,a is the probability of an adult surviving. Time since the last ®re event is indicated. Since monitoring occurs in July and ®re events in September, the eects of the ®re in 1988 would only have been observed from the 1988±1989 transition onwards.
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genetic changes were present in the E. clivicola population, they would have produced changes in the observed demographic parameters such as reproduction and survival (Ewens et al., 1987; Shaer, 1987; Caswell, 1989; Menges, 1992; Schemske et al., 1994) and therefore would be inherent in the model. Since natural catastrophes are essentially extremes of environmental stochasticity (Shaer, 1987), they could be incorporated into the model by increasing the strength of environmental stochasticity thus increasing the probability of critically unfavourable years (Menges, 1992). In an attempt to understand population responses to environmental stochasticity, the variation in ecological data recorded during the monitoring period, including rainfall, herbivory and the incidence of ®re, was closely examined alongside the observed variation in the demographic and reproductive parameters. Temporal variation in ecological and monitoring data suggested that: 1. A ®re in the spring of 1988 resulted in a delayed increase in adult survival from 1989 to 1990 (Fig. 1) and a reduced grass biomass along with the associated decrease in shading of adult plants as well as lower levels of competition with graminoids. 2. The low adult survival immediately after the 1988 ®re was probably due to severe herbivory immediately prior to the ®re in the winter of 1988 (Fig. 3). Herbivory may promote dormancy in E. clivicola, a response documented in other species (EhrleÂn, 1995) or in fact may lead to mortality through rendering the plants more susceptible to stresses such as drought, insect attack and competition (Hendrix, 1988; Given, 1994). The low adult survival immediately after the 1988 ®re could not have been caused by ®re-induced mortality since the species is ®re tolerant, ®re damage stimulating vegetative regrowth (Pfab and Witkowski, 1999a). 3. Reduction of herbivory occurred for a number of years subsequent to the ®re in 1988 (Fig. 3), supporting the hypothesis that resource availability and accessibility for grazers was higher after a recent ®re (Pfab and Witkowski, 1999b). As such, the monitoring data suggest that a ®re every 3 years would maintain high adult survival by maintaining low levels of herbivory and competition with graminoids. 4. Drought conditions from 1991 to 1993 (Fig. 4) resulted in low adult survival over the same period. This could not have been attributed solely to herbivory since herbivory pressure was relatively low during 1991 and 1992 (Fig. 3). 5. Since high rainfall (e.g. 1987/1988 season; Fig. 4) did not have favourable eects on adult survival when ®re had been absent for longer than three years, it was assumed that rainfall modi®ed the
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6. 7.
8. 9.
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primary eects of ®re and herbivory on adult survival. The variation in seedling persistence could not be explained by the incidence of ®re (Fig. 1) or the variation in herbivory (Fig. 3) and rainfall (Fig. 4). Variation in juvenile persistence (Fig. 1) seemed to re¯ect the variation in rainfall (Fig. 4). The incidence of ®re did not appear to aect juvenile persistence while monitoring data indicated that herbivory rarely aected juvenile plants. Growth of seedlings into juveniles and juveniles into adults (Fig. 1) reached a peak during the rainy seasons of 1989/1990 and 1990/1991 (Fig. 4). The variation in the percentage of reproductive adults (frep) (Fig. 2) closely re¯ected variation in rainfall (Fig. 4). However, this eect was delayed one season.
2.3. Correlation among parameters Demographic parameters generally do not vary as statistically independent quantities (Burgman et al., 1993). It is most likely that the environment aects all stages in a similar way, severe environmental conditions
Fig. 2. The percentage of adult Euphorbia clivicola plants in a reproductive state during the months of July in monitoring years. Data were adjusted to account for ¯ower/fruit abortion by assuming 16% of the population (calculated from ®eld data collected in 1996) became nonreproductive during the period from July to August, August being the month during which the species is predominantly fruiting.
Fig. 3. The percentage of adult plants of Euphorbia clivicola that were found to be grazed by herbivores during the years of monitoring. Grazing was not recorded in 1989.
resulting in low parameters in all stages and vice versa. If each matrix parameter was assumed to vary independently of all other matrix parameters, environmental stochasticity would be dampened resulting in an underestimation of extinction probabilities (Burgman et al., 1993). Conversely, the estimation of correlation coecients to be used in models is dicult, requiring a large amount of data and underlying assumptions (Burgman et al., 1993). Since all demographic parameters were aected in a similar way (increasing or decreasing together) by variation in rainfall, with the exception of seedling survival, perfect correlation among all demographic and reproductive parameters, except ase,se was assumed. In order to re¯ect the delayed eect of rainfall on reproduction, frep was assumed to be correlated with all other parameters of the previous year. All parameters were calculated within the relevant range from the same random number that was generated at each annual time step. In general, evidence of distribution statistics of demographic parameters over time is sparse (Menges, 1992). As such, random numbers were drawn from a uniform distribution as opposed to a normal distribution. A uniform distribution would simulate greater variation than a normal distribution since the latter would dampen environmental variation. The use of the uniform distribution would result in more conservative estimates of extinction probabilities and thus the desired `worst-case' scenario (Gilpin and SouleÂ, 1986). Since knowledge of autocorrelation in environmental stochasticity is dicult to ascertain from empirical data (Menges, 1992), zero autocorrelations were assumed. In other words, the eects of adverse environmental conditions were not carried over from one year to another. Despite the analytical convenience of zero autocorrelation, it should be regarded as a simplifying assumption (Caswell, 1989). 2.4. Management scenarios The population viability analysis under each of four dierent management scenarios involved 500 simulations
Fig. 4. Mean annual rainfall and total seasonal rainfall recorded from 1984 to 1996 for the site of the protected population of Euphorbia clivicola. Seasons elapse from July to June.
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over suitable time periods. A population consisting of less than 10 adults was considered extinct. An expected time to extinction for each scenario was calculated (Caughley and Gunn, 1996). Management actions under scenario 1 are essentially the same as those implemented over the past 10 years. The vegetation is burnt every 3±5 years, and during drought years as much as every 8 years. Favourable years, re¯ected by high adult survival and resulting from the occurrence of ®res, took place with a frequency of 0.33 under past burning practices. Up to 5 years of unfavourable conditions, with low adult survival could occur under this management. Thus under management scenario 1 adult survival was set to vary randomly between 0.78 and 0.94 at a frequency of 0.33, otherwise it was set to vary between 0.62 and 0.66 (Table 2) with the number of unfavourable years not exceeding 5. Similarly, higher values of fa,se were intended to re¯ect favourable conditions with maximum safe sites for seedling establishment after recent ®re, while lower values were intended to re¯ect unfavourable conditions with the incidence of safe sites for seedling establishment reduced in the absence of ®re (Table 2 and Appendix). Under scenario 2, management actions involve burning the vegetation every third year. If the vegetation would be burnt every 3 years, reducing grass cover and maintaining herbivory at low levels, adult survival should remain between 0.78 and 0.94. Thus adult survival was set to vary between these two values (Table 2). Similarly, the values of fa,se (Table 2) were intended to re¯ect the increase in available sites for seedling establishment attributed to sparser grass conditions (Appendix).
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Management actions under scenario 3 involve burning the vegetation every third year and excluding herbivores from the population to eliminate herbivory damage. In the absence of herbivory, the number of seedlings produced per average reproductive plant would increase to range between 13.46 and 23.51 [Table 2 and Eq. (1) in the Appendix] seedlings. In addition to the management practices outlined in scenario 3, scenario 4 additionally involves augmenting the population with juvenile plants grown in a greenhouse from seeds harvested from the population 3 years previously. Harvesting of fruit was incorporated into the model, set to occur as soon as the number of adults in the population dropped lower than 200 individuals. Ten fruit collected from 15 plants would yield 450 seeds on average. According to greenhouse germination trials, these seeds would germinate and establish as 210 juveniles on average. At small population sizes, if less than 20% of the population is fruiting, there may not be a sucient number of reproductive plants to harvest the required number of fruit. In these cases, all mature fruit could be picked. This possibility was incorporated into the model. Juvenile plants introduced to the juvenile stage class were immediately aected by juvenile survival and growth rates. 3. Results The population viability analysis predicted that if future management actions remain unchanged from those of the past, the protected population of E. clivi-
Table 2 The range between which the demographic and reproductive parameters were allowed to vary under the four management scenarios for the protected Euphorbia clivicola populationa Range of variation Parameter
Scenario 1
Scenario 2
Scenario 3
Scenario 4
ase,se ase,j aj,j aj,a aa,a
0.13±1 0±0.12 0.32±1 0±0.33 0.62±0.66u 0.78±0.94f 0.1±0.25 0.02±0.48 0.11±6.56u 6.56±11.46f
0.13±1 0±0.12 0.32±1 0±0.33 0.78±0.94
0.13±1 0±0.12 0.32±1 0±0.33 0.78±0.94
0.13±1 0±0.12 0.32±1 0±0.33 0.78±0.94
0.1±0.25 0.02±0.48 6.56±11.46
0.1±0.25 0.02±0.48 13.46±23.51
0.1±0.25 0.02±0.48 13.46±23.51
Extinction Probability
885% within 20 years
587% within 50 years
427% within 100 years
22% within 100 years
Mean time to extinction
10 years
58 years
184 years
4950 years
ad,a frep fa,se
a Scenario 1 involves no change from past management, scenario 2 burning every third year, scenario 3 burning every third year and herbivore exclusion while scenario 4 involves all management actions under 3 but augmentation is additional. For scenario 1, values re¯ecting unfavourable years (absence of ®re) are indicated by u while those re¯ecting favourable years (recent ®re) are indicated by f. Extinction probabilitystandard deviation and the mean time to extinction (Caughley and Gunn, 1996) under each scenario are indicated.
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cola has an 88% probability of becoming extinct within the next 20 years with a mean time to extinction of 10 years (Table 2). The model predicted that the likelihood of persistence of the population increased as the management actions became more complex, the extinction probability and mean time to extinction decreasing with the implementation of a more suitable ®re management programme under scenario 2 and decreasing further under scenario 3 with the exclusion of herbivores in addition to alterations in ®re management (Table 2). Predictions for management scenario 4 indicated that the population would only be viable (Mace and Lande, 1991) when augmentation of the population with juveniles is combined with appropriate ®re management and herbivore exclusion. Under this scenario the population would have a 2% probability of becoming extinct within the next 100 years with a mean time to extinction of 4950 years (Table 2). 4. Discussion The explicit comparison of the relative eectiveness of dierent potential management actions to induce the recovery of the protected population of E. clivicola, which had shown a 91% decline from 1987 to 1996, is the greatest advantage of the PVA described in this paper. This has been previously recognized as a major strength of population viability analyses (Boyce, 1992; Lindenmayer and Possingham, 1996). It is clear that the protected population of E. clivicola will require intensive management to prevent its extinction. A more appropriate ®re management programme will have to be implemented which should involve burning at least every third year depending on rainfall (Pfab and Witkowski, 1999a). In addition, herbivores must be excluded from the population to eliminate the detrimental eects of herbivory damage (Pfab and Witkowksi, 1999b). However, the PVA indicated that the population should also be augmented with juvenile plants grown from seeds harvested from the population 3 years previously. Harvesting fruit from 15 plants (10 fruit per plant) would yield an estimated 210 juveniles for augmentation purposes. Augmentation of an extant population may be regarded as the simplest management option available for threatened plant species, where plant material is collected from the site itself so as to prevent the introduction of foreign genetic material (Falk, 1992). Herbivory damage is known to increase the mortality risk of individual plants (Watkinson, 1986; Raal, 1988; Doak, 1992; Bossard and Rejmanek, 1994; EhrleÂn, 1995), induce dormancy in plants (EhrleÂn, 1995) and eliminate species from plant communities (Hendrix, 1988; Moolman and Cowling, 1994). It is likely therefore that excluding herbivores from the E. clivicola population would result in higher adult survival than
those observed during favourable monitoring years (a possible eect not included in the model due to the uncertainty associated with it), essentially re¯ecting adult survival characteristics expected of succulents (Nobel, 1994; Witkowski et al., 1997). If this occurs, augmentation would seldom be necessary since the number of adults should increase and remain above 200 individuals. It is unfortunate that, since 1996, the nature reserve managers responsible for the protected population have been reticent in implementing the management actions recommended under scenario 4, only conceding implementation of scenario 2 by burning the area in the spring of 1996. This has, however, provided an opportunity to validate the model. A full population count three years later in 1999 indicated that the protected population now totals 110 adults, 13 juveniles and three seedlings. The model prediction for the 1999 population was 10211 adult plants, 2222 juveniles and 255186 seedlings. Therefore, the actual population size for all stage classes, except seedlings, falls well within one standard deviation of the model output. In fact, nine adult plants were found to be senescent, in that all above-ground branches were dead, indicating that these adults had died or become dormant. Thus the total number of living adults in the 1999 population is 101, almost an exact match with the model prediction. It is not surprising that only three seedlings had been found. At emergence, seedlings are extremely small and inconspicuous in thickly vegetated conditions and are thus located with extreme diculty. Of more importance than an accurate prediction of the stage structure of the population, the model correctly predicted (1) an increase in seedling and juvenile numbers (from zero seedlings and ®ve juveniles in 1996) and (2) a continuing decline in the number of adult plants. In the event that co-operation is achieved with the natural resource manager, a PVA such as described in this paper could become an indispensable tool for the conservation of threatened species. The process of adaptive management could be successfully applied whereby the application of the proposed management actions could develop a better understanding of the dynamics of the population, while monitoring of the population could provide data to validate and/or re®ne the PVA model (Boyce, 1992), as done, for example, by Maschinski et al. (1997). 5. Conclusions The application of population viability analysis for the explicit comparison of potential management actions has proven to be extremely useful. However, in order to be successful such an analysis is dependent on a reliable set of long-term demographic monitoring data
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that indicate the temporal variation in population dynamics. It is essential that key ecological factors aecting the population are recorded over the monitoring period. Detailed autecological information on the species is also vital (Burgman et al., 1988) to identify the key factors. Furthermore, the construction of a PVA model may be achieved simply by using a spreadsheet package, rendering this valuable conservation tool directly available to ®eld biologists working closely with natural resource managers. Population viability analysis no longer has to be the exclusive domain of mathematicians and expert modelers.
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Acknowledgements We would like to thank the Department of Environmental Aairs and Tourism, Northern Province, for the supply of monitoring data and our ®eld assistants JoAnne Aingworth and Anthony Stewien. Rhett Smart is thanked for his valuable follow-up study on E. clivicola in partial ful®llment of his Honours Degree at the University of the Witwatersrand. The Richard Ward Endowment Trust, the Botanical Society of South Africa and the University of the Witwatersrand are thanked for ®nancial assistance.
Appendix A Calculation of the number of seedlings produced per reproductive adult (fa,se) in relation to the availability of safe sites for seedling establishment.
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reevaluation of IUCN threatened species categories. Conservation Biology 5, 148±157. Manders, P.T., 1987. A transition matrix model of the population dynamics of the Clanwilliam Cedar (Widdringtonia cedarbergensis) in natural stands subject to ®re. Forest Ecology and Management 20, 171±186. Maschinski, J., Frye, R., Rutman, S., 1997. Demography and population viability of an endangered plant species before and after protection from trampling. Conservation Biology 11, 990±999. Menges, E.S., 1992. Stochastic modelling of extinction in plant populations. In: Fiedler, P.L., Jain, S.K. (Eds.), Conservation Biology Ð The Theory and Practice of Nature Conservation Preservation and Management. Chapman and Hall, New York and London, pp. 253±275. Mills, L.S., Hayes, S.G., Baldwin, C., Wisdom, M.J., Citta, J., Mattson, D.J., Murphy, K., 1996. Factors leading to dierent viability predictions for a grizzly bear data set. Conservation Biology 10, 863±873. Moolman, H.J., Cowling, R.M., 1994. The impact of elephant and goat grazing on the endemic ¯ora of South African succulent thicket. Biological Conservation 68, 53±61. Nobel, P.S., 1994. Remarkable Agaves and Cacti, Oxford University Press, New York. Pfab, M.F., 1997. Population biology and ecology of Euphorbia clivicola R.A. Dyer, an endangered plant endemic to the Northern Province of South Africa. Master of Science Research Report. The University of the Witwatersrand. Pfab, M.F., Witkowski, E.T.F., 1999a. Fire survival of the Critically Endangered succulent, Euphorbia clivicola R.A. Dyer Ð ®re-avoider or ®re-tolerant? African Journal of Ecology 37, 249±257. Pfab, M.F., Witkowski, E.T.F., 1999b. Contrasting eects of herbivory on plant size and reproductive performance in two populations of the Critically Endangered species, Euphorbia clivicola R.A. Dyer. Plant Ecology 145, 317±325. Raal, P.A., 1986. Conservation Plan. Euphorbia clivicola, Transvaal Provincial Administration, Nature Conservation Division. Raal, P.A., 1988. Ecology and population biology of Euphorbia perangusta (Euphorbiaceae) in the Transvaal, South Africa. Bothalia 18, 105±110. Ruggiero, L.F., Hayward, G.D., Squires, J.R., 1994. Viability analysis in biological evaluations: Concepts of population viability analysis, biological population, and ecological scale. Conservation Biology 8, 364±372. Schemske, D.W., Husband, B.C., Ruckelshaus, M.H., Goodwillie, C., Parker, I.M., Bishop, J.G., 1994. Evaluating approaches to the conservation of rare and endangered plants. Ecology 75, 584±606. Shaer, M.L., 1987. Minimum viable populations: coping with uncertainty. In: SouleÂ, M.E. (Ed.), Viable Populations for Conservation. Cambridge University Press, Cambridge, pp. 69±86. Shaer, M.L., 1990. Population Viability Analysis. Conservation Biology 4, 39±40. Shaer, M.L., Samson, F.B., 1985. Populations size and extinction: A note on determining critical population sizes. The American Naturalist 125, 144±152. Watkinson, A.R., 1986. Plant population dynamics. In: Crawley, M.J. (Ed.), Plant Ecology. Blackwell Scienti®c publications, Oxford, pp. 137±184. Witkowski, E., Knowles, L., Liston, R.J., 1997. Threatened plants in the northern provinces of South Africa: case studies and future approaches. In: Hale, P. (Ed.), Conservation Outside Nature Reserves. Surrey Beatty, Brisbane, pp. 446±451.
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A simple population viability analysis of the Critically Endangered Euphorbia clivicola R.A. Dyer under four management scenarios M.F. Pfab *, E.T.F. Witkowski Restoration and Conservation Biology Research Group, Department of Animal, Plant and Environmental Sciences, University of the Witwatersrand, Private Bag X3, PO Wits, Johannesburg 2050, Gauteng, South Africa Received 14 March 2000; received in revised form 6 June 2000; accepted 13 June 2000
Abstract This paper describes a population viability analysis (PVA) for Euphorbia clivicola R.A. Dyer, a threatened succulent con®ned to only two known populations in the Northern Province of South Africa, one of which is protected in a nature reserve. The PVA explicitly compared the relative eectiveness of four management scenarios in bringing about the recovery of the protected population that had shown a 91% decline over the decade during which the population was monitored. Demographic monitoring data as well as autecological data collected in 1996 were used to determine the temporal variation in observed demographic and reproductive parameters. The model parameters were allowed to vary randomly over the observed ranges in order to incorporate stochasticity of the environmental factors ®re, herbivory and rainfall. If future management practices remain unchanged, the model predicted that there is an 88% probability of the protected population becoming extinct within the next 20 years. The population should recover under a management scenario involving a ®re frequency of every 3 years, the exclusion of herbivores and augmentation. The model has since been validated with data collected in 1999. Such analyses are useful for adaptive management purposes. # 2000 Elsevier Science Ltd. All rights reserved. Keywords: Adaptive management; Demography; Environmental stochasticity; South Africa; Threatened plant
1. Introduction Population viability analysis (PVA) has traditionally been used to estimate minimum viable populations for threatened taxa. However, the greatest strength of PVA is the opportunity to evaluate the ecacy of various management options (Burgman et al., 1988; Shaer, 1990; Boyce, 1992; Lindenmayer et al., 1993; Ruggiero et al., 1994; Mills et al., 1996), the objectives of which are to build populations up to adequate sizes and to reduce the risks of extinction (Given, 1994). Although a few recent PVAs have explicitly included management (Haig et al., 1993; Lindenmayer and Possingham, 1996; Drechsler, 1998), such applications have been especially lacking for threatened plants (but see Drechsler et al., 1999). Management recommendations for threatened plants have been mainly developed from deterministic matrix models (e.g. Manders, 1987). These models are however * Corresponding author at present address: Gauteng Directorate of Nature Conservation, PO Box 8769, Johannesburg 2000, Gauteng, South Africa. Tel.: +27-11-355-1480; fax: +27-11-337-2292.
static, a major weakness since they do not take account of the random or unpredictable changes in environmental conditions, or any other factors resulting in stochastic extinctions. Stochastic computer simulation models, based on the temporal variation in observed demographic parameters, are considered valuable for PVA investigations (Shaer and Samson, 1985; Menges, 1992). Variations in these parameters may be obtained from long-term demographic monitoring data and are in¯uenced by an extensive range of ecological and genetic factors. In¯uential factors include environmental variability, intraspeci®c density, interspeci®c competition, herbivory, mutualisms, pathogens, pollen limitation and dispersal, while in¯uential genetic factors incorporate both heterozygosity and allelic diversity (Schemske et al., 1994). This paper describes a simple stochastic computer simulation model for Euphorbia clivicola R.A. Dyer, a Critically Endangered (CR A1a) plant species, which explicitly evaluates the consequences of four dierent management scenarios involving burning, control of herbivores and population augmentation.
0006-3207/00/$ - see front matter # 2000 Elsevier Science Ltd. All rights reserved. PII: S0006-3207(00)00088-4
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Euphorbia clivicola is endemic to the Northern Province of South Africa and is con®ned to only two known populations approximately 38 km apart. One population occurs in a nature reserve while the other occurs on the extremities of an urban area. Demographic monitoring data collected for the protected population by the Transvaal Provincial Administration (Division of Nature Conservation) from 1987 to 1993 and again in 1996 indicated a drastic decline from 173 seedlings, 288 juveniles and 1460 adult plants in 1987 to zero seedlings, ®ve juveniles and 160 adults in 1996. The urban population decline, from an original estimate of 3000 individuals to 382 plants in 1996, was directly due to loss of habitat and habitat fragmentation. Detailed investigations of the population biology and ecology of both populations during 1996 revealed that the probable cause of the protected population decline was an unsuitable ®re management programme implemented within the nature reserve. An 8-year absence of ®re and the consequent accumulation of a dense moribund grass layer was probably the cause of the severe herbivory pressure observed in the population (Pfab and Witkowski, 1999a). The E. clivicola plants, due to their relatively high nutritional value and accessibility in the thick moribund grass layer, were selectively grazed by small antelope such as mountain reedbuck (Redunca fulvorufula), signi®cantly reducing the regenerative output of the population (Pfab and Witkowski, 1999b). Euphorbia clivicola is a dwarf spiny perennial succulent. The main stem and root merge to form a subterranean tuberous body (Bruce et al., 1951) that probably acts as a storage organ allowing for adults to exhibit dormancy, observed during monitoring years, and rendering the species ®re tolerant through the protection of meristems (Pfab and Witkowski, 1999a). Only the young ultimate branches appear above ground, congested into a dense mass (Bruce et al., 1951). The branches bear minute deciduous leaves and during June sessile solitary cymes, while the three-seeded fruit are produced predominantly during August (Raal, 1986). Ballistic release of seed occurs as the tension in the constricting, drying fruit walls increase. Simple germination trials in 1996 indicated that seeds germinate immediately after release, essentially explaining the absence of seed banks. 2. Methods 2.1. Model parameters The model was constructed using a spreadsheet package (Microsoft Excel Version 5.0) and formulated as a Lefkovitch matrix incorporating demographic and reproductive parameters (Table 1). Demographic parameters represented transitions between stage classes,
seedling and juvenile persistence, adult survival and transitions between adult and dormant stages (Table 1). All adults that did not persist were assumed to become dormant. Monitoring data indicated that between 10 and 25% of dormant adults resprouted again two years later on average, thus essentially being incorporated back into the adult stage class. It was assumed that all adults that did not resprout had perished, a simplifying assumption forced by the lack of available data on dormancy in this species. The number of seedlings recruited was obtained by multiplying the number of adults by the percentage of reproductive adults (producing fruit) at each annual time step (frep), which was in turn multiplied by the reproductive parameter, fa,se (the number of seedlings produced by an average reproductive adult). The parameter fa,se was calculated from ®eld data collected in 1996 from which a multiple regression equation, relating fruit number to plant size, herbivory damage and grass competition (Pfab and Witkowski, 1999b), and a regression relationship, relating the percentage of viable seeds to plant size, were developed [Eqs. (1) and (2) in the Appendix]. 2.2. Environmental stochasticity An operational view was adopted whereby the measurement of environmental stochasticity was simpli®ed by focusing its measurement on population responses (Menges, 1992). Thus environmental stochasticity was simulated by allowing the matrix elements (Table 1) to vary randomly between the observed minimum and maximum demographic (Fig. 1) and reproductive (Fig. 2) parameters calculated from monitoring data.
Table 1 Stage matrix and population vector for calculating the numbers of plants in each stage class at each time stepa 2
ase;se 6 ase;j 6 4 0 0 a
0 aj;j aj;a 0
frep fa;se 0 aa;a aa;d
32 3 0 se 6 7 0 7 76 j 7 ad;a 54 a 5 0 d
The population vector lists the number of plants in each stage class at time t, where se refers to seedlings, j to juveniles, a to adults and d to dormant plants. This is multiplied by the stage matrix, incorporating demographic and reproductive parameters, to obtain the number of plants in each stage class at each annual time step (t+1), where ase,se is the probability of a seedling remaining a seedling, ase,j is the probability of a seedling growing into a juvenile, aj,j is the probability of a juvenile remaining a juvenile, aj,a is the probability of a juvenile growing into an adult, aa,a is the probability of an adult surviving, aa,d is the probability of an adult becoming dormant, ad,a is the probability of a dormant plant emerging from dormancy into the adult stage class, fa,se is the number of seedlings produced per reproductive adult and frep is the percentage of reproductive adults (producing fruit).
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Of the four components of stochasticity, environmental, genetic, demographic and natural castrophes, the only category of variability incorporated into the model was that of environmental stochasticity. This should be regarded as a weakness of the model, although modeling of genetics is not likely to be as important as modeling demographic and environmental processes (Boyce, 1992) and environmental stochasticity is considered to be more important than demographic stochasticity (Burgman et al., 1988). Furthermore, if
Fig. 1. Variation in observed demographic parameters for the protected population of Euphorbia clivicola over monitoring years, where se,se is the probability of a seedling remaining a seedling, se,j is the probability of a seedling growing into a juvenile, j,j is the probability of a juvenile remaining a juvenile, j,a is the probability of a juvenile growing into an adult and a,a is the probability of an adult surviving. Time since the last ®re event is indicated. Since monitoring occurs in July and ®re events in September, the eects of the ®re in 1988 would only have been observed from the 1988±1989 transition onwards.
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genetic changes were present in the E. clivicola population, they would have produced changes in the observed demographic parameters such as reproduction and survival (Ewens et al., 1987; Shaer, 1987; Caswell, 1989; Menges, 1992; Schemske et al., 1994) and therefore would be inherent in the model. Since natural catastrophes are essentially extremes of environmental stochasticity (Shaer, 1987), they could be incorporated into the model by increasing the strength of environmental stochasticity thus increasing the probability of critically unfavourable years (Menges, 1992). In an attempt to understand population responses to environmental stochasticity, the variation in ecological data recorded during the monitoring period, including rainfall, herbivory and the incidence of ®re, was closely examined alongside the observed variation in the demographic and reproductive parameters. Temporal variation in ecological and monitoring data suggested that: 1. A ®re in the spring of 1988 resulted in a delayed increase in adult survival from 1989 to 1990 (Fig. 1) and a reduced grass biomass along with the associated decrease in shading of adult plants as well as lower levels of competition with graminoids. 2. The low adult survival immediately after the 1988 ®re was probably due to severe herbivory immediately prior to the ®re in the winter of 1988 (Fig. 3). Herbivory may promote dormancy in E. clivicola, a response documented in other species (EhrleÂn, 1995) or in fact may lead to mortality through rendering the plants more susceptible to stresses such as drought, insect attack and competition (Hendrix, 1988; Given, 1994). The low adult survival immediately after the 1988 ®re could not have been caused by ®re-induced mortality since the species is ®re tolerant, ®re damage stimulating vegetative regrowth (Pfab and Witkowski, 1999a). 3. Reduction of herbivory occurred for a number of years subsequent to the ®re in 1988 (Fig. 3), supporting the hypothesis that resource availability and accessibility for grazers was higher after a recent ®re (Pfab and Witkowski, 1999b). As such, the monitoring data suggest that a ®re every 3 years would maintain high adult survival by maintaining low levels of herbivory and competition with graminoids. 4. Drought conditions from 1991 to 1993 (Fig. 4) resulted in low adult survival over the same period. This could not have been attributed solely to herbivory since herbivory pressure was relatively low during 1991 and 1992 (Fig. 3). 5. Since high rainfall (e.g. 1987/1988 season; Fig. 4) did not have favourable eects on adult survival when ®re had been absent for longer than three years, it was assumed that rainfall modi®ed the
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6. 7.
8. 9.
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primary eects of ®re and herbivory on adult survival. The variation in seedling persistence could not be explained by the incidence of ®re (Fig. 1) or the variation in herbivory (Fig. 3) and rainfall (Fig. 4). Variation in juvenile persistence (Fig. 1) seemed to re¯ect the variation in rainfall (Fig. 4). The incidence of ®re did not appear to aect juvenile persistence while monitoring data indicated that herbivory rarely aected juvenile plants. Growth of seedlings into juveniles and juveniles into adults (Fig. 1) reached a peak during the rainy seasons of 1989/1990 and 1990/1991 (Fig. 4). The variation in the percentage of reproductive adults (frep) (Fig. 2) closely re¯ected variation in rainfall (Fig. 4). However, this eect was delayed one season.
2.3. Correlation among parameters Demographic parameters generally do not vary as statistically independent quantities (Burgman et al., 1993). It is most likely that the environment aects all stages in a similar way, severe environmental conditions
Fig. 2. The percentage of adult Euphorbia clivicola plants in a reproductive state during the months of July in monitoring years. Data were adjusted to account for ¯ower/fruit abortion by assuming 16% of the population (calculated from ®eld data collected in 1996) became nonreproductive during the period from July to August, August being the month during which the species is predominantly fruiting.
Fig. 3. The percentage of adult plants of Euphorbia clivicola that were found to be grazed by herbivores during the years of monitoring. Grazing was not recorded in 1989.
resulting in low parameters in all stages and vice versa. If each matrix parameter was assumed to vary independently of all other matrix parameters, environmental stochasticity would be dampened resulting in an underestimation of extinction probabilities (Burgman et al., 1993). Conversely, the estimation of correlation coecients to be used in models is dicult, requiring a large amount of data and underlying assumptions (Burgman et al., 1993). Since all demographic parameters were aected in a similar way (increasing or decreasing together) by variation in rainfall, with the exception of seedling survival, perfect correlation among all demographic and reproductive parameters, except ase,se was assumed. In order to re¯ect the delayed eect of rainfall on reproduction, frep was assumed to be correlated with all other parameters of the previous year. All parameters were calculated within the relevant range from the same random number that was generated at each annual time step. In general, evidence of distribution statistics of demographic parameters over time is sparse (Menges, 1992). As such, random numbers were drawn from a uniform distribution as opposed to a normal distribution. A uniform distribution would simulate greater variation than a normal distribution since the latter would dampen environmental variation. The use of the uniform distribution would result in more conservative estimates of extinction probabilities and thus the desired `worst-case' scenario (Gilpin and SouleÂ, 1986). Since knowledge of autocorrelation in environmental stochasticity is dicult to ascertain from empirical data (Menges, 1992), zero autocorrelations were assumed. In other words, the eects of adverse environmental conditions were not carried over from one year to another. Despite the analytical convenience of zero autocorrelation, it should be regarded as a simplifying assumption (Caswell, 1989). 2.4. Management scenarios The population viability analysis under each of four dierent management scenarios involved 500 simulations
Fig. 4. Mean annual rainfall and total seasonal rainfall recorded from 1984 to 1996 for the site of the protected population of Euphorbia clivicola. Seasons elapse from July to June.
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over suitable time periods. A population consisting of less than 10 adults was considered extinct. An expected time to extinction for each scenario was calculated (Caughley and Gunn, 1996). Management actions under scenario 1 are essentially the same as those implemented over the past 10 years. The vegetation is burnt every 3±5 years, and during drought years as much as every 8 years. Favourable years, re¯ected by high adult survival and resulting from the occurrence of ®res, took place with a frequency of 0.33 under past burning practices. Up to 5 years of unfavourable conditions, with low adult survival could occur under this management. Thus under management scenario 1 adult survival was set to vary randomly between 0.78 and 0.94 at a frequency of 0.33, otherwise it was set to vary between 0.62 and 0.66 (Table 2) with the number of unfavourable years not exceeding 5. Similarly, higher values of fa,se were intended to re¯ect favourable conditions with maximum safe sites for seedling establishment after recent ®re, while lower values were intended to re¯ect unfavourable conditions with the incidence of safe sites for seedling establishment reduced in the absence of ®re (Table 2 and Appendix). Under scenario 2, management actions involve burning the vegetation every third year. If the vegetation would be burnt every 3 years, reducing grass cover and maintaining herbivory at low levels, adult survival should remain between 0.78 and 0.94. Thus adult survival was set to vary between these two values (Table 2). Similarly, the values of fa,se (Table 2) were intended to re¯ect the increase in available sites for seedling establishment attributed to sparser grass conditions (Appendix).
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Management actions under scenario 3 involve burning the vegetation every third year and excluding herbivores from the population to eliminate herbivory damage. In the absence of herbivory, the number of seedlings produced per average reproductive plant would increase to range between 13.46 and 23.51 [Table 2 and Eq. (1) in the Appendix] seedlings. In addition to the management practices outlined in scenario 3, scenario 4 additionally involves augmenting the population with juvenile plants grown in a greenhouse from seeds harvested from the population 3 years previously. Harvesting of fruit was incorporated into the model, set to occur as soon as the number of adults in the population dropped lower than 200 individuals. Ten fruit collected from 15 plants would yield 450 seeds on average. According to greenhouse germination trials, these seeds would germinate and establish as 210 juveniles on average. At small population sizes, if less than 20% of the population is fruiting, there may not be a sucient number of reproductive plants to harvest the required number of fruit. In these cases, all mature fruit could be picked. This possibility was incorporated into the model. Juvenile plants introduced to the juvenile stage class were immediately aected by juvenile survival and growth rates. 3. Results The population viability analysis predicted that if future management actions remain unchanged from those of the past, the protected population of E. clivi-
Table 2 The range between which the demographic and reproductive parameters were allowed to vary under the four management scenarios for the protected Euphorbia clivicola populationa Range of variation Parameter
Scenario 1
Scenario 2
Scenario 3
Scenario 4
ase,se ase,j aj,j aj,a aa,a
0.13±1 0±0.12 0.32±1 0±0.33 0.62±0.66u 0.78±0.94f 0.1±0.25 0.02±0.48 0.11±6.56u 6.56±11.46f
0.13±1 0±0.12 0.32±1 0±0.33 0.78±0.94
0.13±1 0±0.12 0.32±1 0±0.33 0.78±0.94
0.13±1 0±0.12 0.32±1 0±0.33 0.78±0.94
0.1±0.25 0.02±0.48 6.56±11.46
0.1±0.25 0.02±0.48 13.46±23.51
0.1±0.25 0.02±0.48 13.46±23.51
Extinction Probability
885% within 20 years
587% within 50 years
427% within 100 years
22% within 100 years
Mean time to extinction
10 years
58 years
184 years
4950 years
ad,a frep fa,se
a Scenario 1 involves no change from past management, scenario 2 burning every third year, scenario 3 burning every third year and herbivore exclusion while scenario 4 involves all management actions under 3 but augmentation is additional. For scenario 1, values re¯ecting unfavourable years (absence of ®re) are indicated by u while those re¯ecting favourable years (recent ®re) are indicated by f. Extinction probabilitystandard deviation and the mean time to extinction (Caughley and Gunn, 1996) under each scenario are indicated.
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cola has an 88% probability of becoming extinct within the next 20 years with a mean time to extinction of 10 years (Table 2). The model predicted that the likelihood of persistence of the population increased as the management actions became more complex, the extinction probability and mean time to extinction decreasing with the implementation of a more suitable ®re management programme under scenario 2 and decreasing further under scenario 3 with the exclusion of herbivores in addition to alterations in ®re management (Table 2). Predictions for management scenario 4 indicated that the population would only be viable (Mace and Lande, 1991) when augmentation of the population with juveniles is combined with appropriate ®re management and herbivore exclusion. Under this scenario the population would have a 2% probability of becoming extinct within the next 100 years with a mean time to extinction of 4950 years (Table 2). 4. Discussion The explicit comparison of the relative eectiveness of dierent potential management actions to induce the recovery of the protected population of E. clivicola, which had shown a 91% decline from 1987 to 1996, is the greatest advantage of the PVA described in this paper. This has been previously recognized as a major strength of population viability analyses (Boyce, 1992; Lindenmayer and Possingham, 1996). It is clear that the protected population of E. clivicola will require intensive management to prevent its extinction. A more appropriate ®re management programme will have to be implemented which should involve burning at least every third year depending on rainfall (Pfab and Witkowski, 1999a). In addition, herbivores must be excluded from the population to eliminate the detrimental eects of herbivory damage (Pfab and Witkowksi, 1999b). However, the PVA indicated that the population should also be augmented with juvenile plants grown from seeds harvested from the population 3 years previously. Harvesting fruit from 15 plants (10 fruit per plant) would yield an estimated 210 juveniles for augmentation purposes. Augmentation of an extant population may be regarded as the simplest management option available for threatened plant species, where plant material is collected from the site itself so as to prevent the introduction of foreign genetic material (Falk, 1992). Herbivory damage is known to increase the mortality risk of individual plants (Watkinson, 1986; Raal, 1988; Doak, 1992; Bossard and Rejmanek, 1994; EhrleÂn, 1995), induce dormancy in plants (EhrleÂn, 1995) and eliminate species from plant communities (Hendrix, 1988; Moolman and Cowling, 1994). It is likely therefore that excluding herbivores from the E. clivicola population would result in higher adult survival than
those observed during favourable monitoring years (a possible eect not included in the model due to the uncertainty associated with it), essentially re¯ecting adult survival characteristics expected of succulents (Nobel, 1994; Witkowski et al., 1997). If this occurs, augmentation would seldom be necessary since the number of adults should increase and remain above 200 individuals. It is unfortunate that, since 1996, the nature reserve managers responsible for the protected population have been reticent in implementing the management actions recommended under scenario 4, only conceding implementation of scenario 2 by burning the area in the spring of 1996. This has, however, provided an opportunity to validate the model. A full population count three years later in 1999 indicated that the protected population now totals 110 adults, 13 juveniles and three seedlings. The model prediction for the 1999 population was 10211 adult plants, 2222 juveniles and 255186 seedlings. Therefore, the actual population size for all stage classes, except seedlings, falls well within one standard deviation of the model output. In fact, nine adult plants were found to be senescent, in that all above-ground branches were dead, indicating that these adults had died or become dormant. Thus the total number of living adults in the 1999 population is 101, almost an exact match with the model prediction. It is not surprising that only three seedlings had been found. At emergence, seedlings are extremely small and inconspicuous in thickly vegetated conditions and are thus located with extreme diculty. Of more importance than an accurate prediction of the stage structure of the population, the model correctly predicted (1) an increase in seedling and juvenile numbers (from zero seedlings and ®ve juveniles in 1996) and (2) a continuing decline in the number of adult plants. In the event that co-operation is achieved with the natural resource manager, a PVA such as described in this paper could become an indispensable tool for the conservation of threatened species. The process of adaptive management could be successfully applied whereby the application of the proposed management actions could develop a better understanding of the dynamics of the population, while monitoring of the population could provide data to validate and/or re®ne the PVA model (Boyce, 1992), as done, for example, by Maschinski et al. (1997). 5. Conclusions The application of population viability analysis for the explicit comparison of potential management actions has proven to be extremely useful. However, in order to be successful such an analysis is dependent on a reliable set of long-term demographic monitoring data
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that indicate the temporal variation in population dynamics. It is essential that key ecological factors aecting the population are recorded over the monitoring period. Detailed autecological information on the species is also vital (Burgman et al., 1988) to identify the key factors. Furthermore, the construction of a PVA model may be achieved simply by using a spreadsheet package, rendering this valuable conservation tool directly available to ®eld biologists working closely with natural resource managers. Population viability analysis no longer has to be the exclusive domain of mathematicians and expert modelers.
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Acknowledgements We would like to thank the Department of Environmental Aairs and Tourism, Northern Province, for the supply of monitoring data and our ®eld assistants JoAnne Aingworth and Anthony Stewien. Rhett Smart is thanked for his valuable follow-up study on E. clivicola in partial ful®llment of his Honours Degree at the University of the Witwatersrand. The Richard Ward Endowment Trust, the Botanical Society of South Africa and the University of the Witwatersrand are thanked for ®nancial assistance.
Appendix A Calculation of the number of seedlings produced per reproductive adult (fa,se) in relation to the availability of safe sites for seedling establishment.
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