Two study sites (Dankbaar site and Grootkolk site) were surveyed on numerous occasions; however, survey methods used at these two sites differed. In 1978, all V. erioloba trees were marked in a 1 ha plot at the Dankbaar site. Tree height and stem circumference were recorded for each of the 18 permanently marked trees at irregular intervals from 1978 to 2016 (survey years 1978, 1980, 1983, 1985, 1988, 1989, 1991, 1994, 1998, 1999, 2008 and 2016). In 2016, for the first time since the original survey in 1978, all additional trees within the plot were measured and permanently marked.

At the 1 hectare (ha) Grootkolk site, height and stem circumference of all V. erioloba individuals were measured at irregular intervals from 1979 to 2016 (survey years 1979, 1984, 1986, 1989, 1994, 1996, 1999, 2008 and 2016). The stem circumferences of all dead trees were also recorded at Grootkolk in the year of the survey when the tree was found to have died.

Because of the different survey methods used at the two sites; the data collected could not be analysed in the same manner for both the sites. For example, only the 18 marked trees at Dankbaar were surveyed throughout the 38-year period; thus an analysis of the population structure is inappropriate as the entire population in the 1 ha plot was not surveyed.

An estimate of the growth rate per year over the entire study period (38 years) was calculated for each marked tree at the Dankbaar site by subtracting the first measured stem diameter (1978 survey) from the last live measured stem diameter and dividing by the number of years between these two measurements. Similarly, this method was used to calculate changes in height of a tree. A linear regression using GraphPad 7.02 (GraphPad Software, www.graphpad.com) of stem diameter versus annual growth rate was used to investigate the relationship between these two variables. Additionally, stem diameter growth rates over the first 10-year period (1978–1988), second 10-year period (1988–1998) and third 10-year period (1988–2008) were calculated for each marked individual. This was calculated in the same way as for the entire period, but using the first and last measured diameters for the appropriate periods and calculating a mean across all the individuals. Dead and coppiced individuals were excluded from the calculations from the survey year in which the death or coppicing was recorded for the first time.

The mean stem diameter in 1978 and 2016 of all marked trees was used to estimate the average age using the growth rate determined in the current study. The average age of all the marked trees in 1978 and in 2016 were calculated by dividing the mean stem diameter for the particular year by the growth rate determined in the current study. For comparative purposes the mean age of the trees was also calculated by the same method using the mean diameter growth rate for only the interior duneveld (3.2 mm/year) and for the interior duneveld and riverbed combined (3.6 mm/year) reported by Steenkamp et al. (2008). Age was also determined using the growth rate for the interior duneveld and riverbed combined (5.1 mm/year) based on the equation derived for the relationship between radiocarbon age and stem circumference (Steenkamp et al. 2008). These calculations were made using the mean stem diameter of the live trees in 2016 as well as the last ‘alive’ measured stem diameter for the dead trees. These calculations were also performed for the Grootkolk population using the mean stem diameter of the stem circumference classes.

The stem circumferences for trees at the Grootkolk 1 ha plot were classified into 12 equal stem circumference classes (0–20, > 20–40, > 40–60, > 60–80, > 80–100, > 100–120, > 120–140, > 140–160, > 160–180, > 180–200, > 200–220, > 220–240 starting with class 1 and ending with class 12) for each of the survey years. The size class distribution was examined visually to classify the population into one of four population structure types (Gaugris & Van Rooyen 2007; Figure 3). In this model, Type I size class distribution represents a growing population and follows an inverse J-shaped curve, which represents the ideal curve shape for a growing population in a natural environment. There is a constant decrease in the number of individuals as the size classes increase, and the curve spans the whole range of size classes described for the species. Populations with a Type II curve have a near ideal population structure that differs from a Type I only by having a lower abundance of smaller size classes. Populations with Type III size class distributions are typically associated with disturbance. The Type IIIa curve broadly resembles a Type I size class distribution but applies to populations where a section of the curve spanning one or several size classes is missing or where abundance is lower than expected. The typical large pool of small individuals is generally missing in Type IIIb and the size class distribution shows a succession of minor peaks, even with some gaps where one or several size classes may be missing altogether. In the Type IV curve, one or two peaks are observed over a restricted range of size classes, and this curve thus represents an abnormal size class distribution. The curve is either bell-shaped with a peak more or less in the middle of the size class range, or it shows a high frequency of large size classes, with little or no representation of smaller classes.

For the 1 ha Grootkolk site the number of individuals recorded per stem circumference size class was calculated in order to obtain the density of trees per size class. Regressions were performed on the density (Di) of individuals against size class (Mi) (Gaugris & Van Rooyen 2007). The diameter class midpoint (Mi) was calculated as the mean of the upper and lower limit of each size class (Condit et al. 1998). Logarithmic transformations, ln (Di + 1) and ln (Mi), were used to standardise the data (Lykke 1998; Niklas, Midgley & Rand 2003) before performing least square linear regressions, that is, ln (Di + 1) for the y-axis and ln (Mi) for the x-axis. The value of +1 was added because some size class bins were empty (Lykke 1998). The linear regressions were evaluated in terms of their slopes and y-axis intercepts (Gaugris, Vasicek & Van Rooyen 2012; Van der Merwe & Geldenhuys 2017). Strongly negative slopes typically represent regenerating populations (Condit et al. 1998), and a high y-axis intercept indicates many small individuals in the population. A y-axis intercept near to zero indicates that few small individuals are present (Everard, Midgley & Van Wyk 1994). Both slopes and y-axis intercepts of regressions were compared statistically across years by means of an analysis of covariance using GraphPad 7.02 (GraphPad Software, www.graphpad.com).

Two additional mean values were calculated for the stem diameter distribution for each survey year: (1) the ‘centroid’ was calculated as the arithmetic mean of all stem diameters recorded; and (2) the ‘midpoint of stem diameter range’ was calculated as the mean of the upper and lower limits of the diameter range included in the size class distribution. Niklas et al. (2003) found a relationship between the position of the centroid and the diameter class range midpoint for a species. If a centroid value is smaller than the midpoint value, the population is young and growing. When the centroid value is larger than the midpoint value, the population is mature to old. In general, as the mean stem diameter increases in a population, self-thinning occurs and the density decreases, in such a way that an increasing part of the biomass is found in fewer individuals (Niklas et al. 2003; Silvertown & Charlesworth 2001). As self-thinning occurs the centroid of a population shifts towards the right within the size class distribution.

Over the period of 38 years, 6 of the 18 originally marked trees at the Dankbaar site died (33%) and three showed coppice regrowth following substantial dieback because of a fire (Table 1-A1). In 1978 the mean height of the 18 trees was 5.1 m and mean stem diameter 235.85 mm. In 2016 the mean height of the remaining nine originally marked trees that had not experienced dieback was 6.8 m and mean stem diameter 282.7 mm. The mean height for the six dead individuals at the onset of the study was 6.1 m and at the time of last measurement before death 6.8 m. A mean height increase of 60 mm/year was calculated. The 2016 survey measured the remaining 12 originally marked trees as well as 12 additional trees now present; thus, after 38 years, the population increased by six trees in the 1 ha plot.

A linear regression of growth rate against stem diameter (Figure 4) indicated that growth rate decreases significantly as stem diameter increases, that is, as the individuals age (p = 0.022). The mean growth rate for the first 10-year period (1978–1988) was 2.99 mm/year, the second 10-year period (1988–1998) 1.01 mm/year and the third 10-year period (1998–2008) 2.84 mm/year, indicating a variable growth rate over time. Stem diameter growth rate per year varied widely between the nine remaining trees (0.91 mm – 4.86 mm/year), with a mean value of 2.5 mm/year. Depending on the choice of mean annual growth rate or application of the regression between stem circumference and age, the mean age of the six dead trees could be estimated at between 71 and 142 years (Table 1).

At the Grootkolk site, 61 live and 14 dead individuals were recorded in the initial survey in 1979. The number of live individuals at Grootkolk in the Nossob riverbed gradually decreased over the survey period (Figure 5). Initially the size class distribution of the trees from 1979 to 1999 could visually be classified as Type IIIb curves; however, there was a gradual transition to a Type IV curve from 2008 to 2016 (Figures 3 and 5). In spite of the decreasing tree numbers and the change of curve shape, linear regressions on the density of individuals against the diameter class midpoint (Figure 1-A1) revealed no significant differences between the slopes (Table 2-A1) or intercepts (Table 3-A1) of the fitted lines.

Using calculations from Steenkamp et al. (2008) for the interior duneveld and riverbed, the largest live tree at Grootkolk was aged between 195 and 212 years, while the relationship between stem circumference and radiocarbon age for the interior duneveld and riverbed combined aged the tree between 136 and 148 years (Table 2). When using the same two methods of calculation, most of the dead trees fell in the age categories 25–53, 37–71 and 49–89 years.

In all survey years the position of the centroid (arithmetic mean of all stem diameters recorded per site) was to the left of the midpoint of the size class distribution. However, the difference between these two values decreased over time and in 2016 the two values were nearly the same (Table 4-A1), indicating that the population was changing from a young and growing population to a mature to old population.

Marked V. erioloba tree stem diameters at Dankbaar in the interior duneveld increased at a mean rate of 2.50 mm/year (range 0.91 mm – 4.86 mm/year) over the monitored period. This mean annual diameter increase is less than the 3.6 mm/year established by Steenkamp et al. (2008) and substantially lower than the 12 mm – 14 mm/year previously reported for Acacia species growing in arid and semi-arid environments (Gourlay 1992). The Steenkamp et al. (2008) study used annual growth ring and radiocarbon ageing to determine growth rates. A mean growth rate was derived from individuals in the interior duneveld as well as in the Nossob riverbed. If only the individuals in the interior duneveld in the Steenkamp et al. (2008) study are considered, then the mean annual diameter increment is 3.2 mm/year. Although Steenkamp et al. (2008) concluded that the growth rate did not differ significantly between trees growing in the dry Nossob riverbed and those growing in the interior duneveld, growth rate varied substantially between individual trees. Variability in the growth rates of other tree species has been reported and the suggested underlying causes for this phenomenon include microsite conditions and/or genetic potential of individual trees (Stahle et al. 1996).

Depending on the equation used to determine the age of the dead trees there could be a twofold or greater difference in calculated age at both the Dankbaar (Table 1) (71 years as opposed to 142 years) and Grootkolk (Table 2) (25 years as opposed to 127 years) sites. The high variability in estimated age at which 6 of the 18 marked trees died (48, 103, 163, 178, 181 and 191 years, using the mean annual diameter increase of 2.5 mm/year calculated for this current study) was unexpected. Moustakas et al. (2008), using a combination of aerial photographs and satellite images covering a period of 61 years to provide spatial data on mortality, found that V. erioloba mortality risk was greatest for trees of intermediate size. This does not seem to be the case for the Dankbaar population, where mortality was found to be predominantly among the large trees. At Grootkolk, the data seem to indicate that mortality was highest in smaller size classes and gradually declined for larger size classes. The density of trees at Grootkolk was low, and consequently self-thinning (Silvertown & Charlesworth 2001) is unlikely to have occurred.

On the basis of the position of the centroid in relation to the midpoint of the stem diameter class range, the Grootkolk population could be considered as a population gradually changing from young and growing to mature to old. This is supported by a visual assessment of the size class distribution, which showed a gradual transition from a Type IIIb to a Type IV curve shape over the 38 years. The large peak of young individuals in size class 4 that was evident at the first survey gradually became smaller and shifted to size class 5, and a prominent second peak emerged at size class 8 at the last survey.

At Grootkolk, few seedlings were recorded and few individuals appeared to be recruiting into the population. The low survival of size class 2, 3 and 4 individuals over the monitored period could possibly be ascribed to individuals progressing to larger size classes over the monitored period without being replenished. This is supported by the fact that size classes 5 and 8 had more individuals at the end of the monitoring period than when monitoring commenced. Overall, the survival of individuals in the larger size classes (e.g. size classes 6, 7 and 9) exceeded that in the smaller size classes (e.g. size classes 1, 2 and 3). In spite of the fact that the Grootkolk population was almost halved over the 38-year period, the slopes and intercepts of the size class distribution regressions showed no differences between years (Figure 1-A1).

In their study, Steenkamp et al. (2008) reported an ageing size class distribution with poor recruitment at some sites in the Nossob riverbed. At other sites, many young individuals were found with only a few mature or dying trees in these populations. The Grootkolk site situated in the same riverbed illustrated an ageing population with few young individuals. It has been suggested that flooding of the Nossob River and/or consecutive years of above-average rainfall were necessary for regeneration of V. erioloba. Steenkamp et al. (2008) were, however, unable to find support to substantiate the need for flooding.

Seed germination of V. erioloba is best after good rain events, and seedling survival depends on the availability of moisture during the next few seasons. Mortality rates during seedling establishment are generally higher than during the adult stages (Silvertown & Charlesworth 2001). Seedlings and saplings suffer high mortality in dry years (Barnes 2001; Theron, Van Rooyen & Van Rooyen 1985; Van Rooyen & Van Rooyen 1998; Van Rooyen et al. 1984). The high density of wildlife in the Nossob riverbed could also have contributed to the ageing of the Grootkolk population, with losses in young individuals because of trampling and browsing by herbivores and occasional toppling and breaking of larger trees by wind. Likewise, insects and rodents that impact on the seed pool may be more numerous in the riverbed habitat (Steenkamp et al. 2008). Furthermore, competition from a well-established grass layer may inhibit tree seedling establishment and growth in the riverbed (Steenkamp et al. 2008); however, this was not evident at the Grootkolk site. Fire also significantly impacts V. erioloba populations. After good rainfall, sufficient fuel accumulates and enables fire to spread through the landscape. In general, up to one-third of individuals in an area that experiences a fire are killed by the fire, with most of the individuals subsequently resprouting from the base (Van der Walt & Le Riche 1984). Large old trees, especially those with hollow stems, are most sensitive to fire (Milton & Dean 1995). During the study period, fire only occurred at the Dankbaar study site (large fires in 1995 and 2012). No tree mortality resulting from the fire was evident at the site; however, three of the individuals displayed coppiced growth subsequent to fire. Vachellia erioloba population dynamics differed at the two study sites over the last 38 years. Considering all tree mortalities and recruitments, the Dankbaar population can be considered a self-sustaining population with an increase of 12 new individuals (net increase of six trees) at the site over the 38-year period. The density (number of individuals per the 1 ha plot) of the Grootkolk population is declining and the size classes of the remaining individuals increasing as the population ages.