Long-Term Population Dynamics of Namib Desert Tenebrionid Beetles Reveal Complex Relationships to Pulse-Reserve Conditions

Simple Summary Rain seldom falls in the extremely arid Namib Desert in Namibia, but when a certain amount falls, it causes seeds to germinate, grass to grow and seed, dry, and turn to litter that gradually decomposes over the years. It is thought that such periodic flushes and gradual decay are fundamental to the functioning of the animal populations of deserts. This notion was tested with litter-consuming darkling beetles, of which many species occur in the Namib. Beetles were trapped in buckets buried at ground level, identified, counted, and released. The numbers of most species changed with the quantity of litter, but some mainly fed on green grass and disappeared when this dried, while other species depended on the availability of moisture during winter. Several species required unusually heavy rainfalls to gradually increase their populations, while others the opposite, declining when wet, thriving when dry. All 26 beetle species experienced periods when their numbers were extremely low, but all had the capacity for a few remaining individuals to repopulate the area in good times. The remarkably different relationships of these beetles to common resources, litter, and moisture, explain how so many species can exist side by side in such a dry environment. Abstract Noy-Meir’s paradigm concerning desert populations being predictably tied to unpredictable productivity pulses was tested by examining abundance trends of 26 species of flightless detritivorous tenebrionid beetles (Coleoptera, Tenebrionidae) in the hyper-arid Namib Desert (MAP = 25 mm). Over 45 years, tenebrionids were continuously pitfall trapped on a gravel plain. Species were categorised according to how their populations increased after 22 effective rainfall events (>11 mm in a week), and declined with decreasing detritus reserves (97.7–0.2 g m−2), while sustained by nonrainfall moisture. Six patterns of population variation were recognised: (a) increases triggered by effective summer rainfalls, tracking detritus over time (five species, 41% abundance); (b) irrupting upon summer rainfalls, crashing a year later (three, 18%); (c) increasing gradually after series of heavy (>40 mm) rainfall years, declining over the next decade (eight, 15%); (d) triggered by winter rainfall, population fluctuating moderately (two, 20%); (e) increasing during dry years, declining during wet (one, 0.4%); (f) erratic range expansions following heavy rain (seven, 5%). All species experienced population bottlenecks during a decade of scant reserves, followed by the community cycling back to its earlier composition after 30 years. By responding selectively to alternative configurations of resources, Namib tenebrionids showed temporal patterns and magnitudes of population fluctuation more diverse than predicted by Noy-Meir’s original model, underpinning high species diversity.

. Clockwise from top left: (a) bare gravel plain with a distant fog cloud during an interpulse year, (b) effective rainfall driving the production of ephemeral grasses, (c) which dries, (d) becomes detritus, (e) and is consumed by tenebrionid beetles such as Zophosis moralesi.
Initial ballpark figures derived from the grass productivity and decomposition studies mentioned above are applied to derive a crude index of the detritus pool to reflect its general size, notwithstanding rainfall, productivity, and decomposition being heterogeneous at multiple spatial scales [63], partly allochthonous, and different between habitats. This index allows tracking the effect of rainfall over time through its effects on grass productivity and the decay of detritus. The quantity of detritus was calculated as the sum of annual productivity and decomposition rates, assuming a linear relationship: where D is the index of the grass detritus pool, j is the current year, and j − 1 the previous year, P is the productivity of grass following effective rainfall [23,24]: 10.93) and a is the fraction of previous detritus remaining after annual decomposition, being 84% without rainfall [20] and decreasing with rainfall: a = 0.84 − (annual rainfall/100).
Pitfall traps 15 cm in diameter were deployed in March 1976 (the project is ongoing). At the gravel plain study site (23 • 32.628 S, 15 • 02.973 E), 15 traps were placed in five groups of three, 0.4-6.75 m apart within groups, and 50-200 m between [59,64]. Traps were monitored twice or thrice weekly for 90.5% of the time (221,355 trap-days). Solifugids, scorpions, spiders, lizards, and geckos, amounting to 4.3% of captures, could have preyed on trapped beetles, as could have transient birds and gerbils, but their impact on the results is unknown, and is assumed not to have biased the relative records of tenebrionid species over time. Live trapped tenebrionids were usually identified at the traps, alternatively in the laboratory, and then released a short distance from the traps. During the first 25 years, taxonomically verified voucher specimens guided the identification of species. Later, when this project was incorporated into the institutional training program, a photo album of dorsal or lateral images was used as an identikit. Previous records guided the final identification [26,59,[64][65][66][67][68]. Data analyses were performed only on the most regularly trapped species, recorded >120 times [69], referred to as focal species (Appendix A, Table A1).
"Abundance", here, refers to the capture rate, a function of trappability, density, and activity. The annual time scale encompasses weather related fluctuations of activity. Annual abundance data were standardised to captures per full trap-years to analyse trends, rounded to whole numbers, keeping singletons constant.
Following Wolda [70], arithmetic differences in annual abundance (N) between successive years were expressed by the gradation coefficient (GC): where Nj is N + 1 2 in year j and Nj − 1 for the year before year j. At low annual abundance (N < 20), caution is necessary when interpreting GC values, as trapping becomes increasingly sporadic. The annual variation coefficient, AV, is the variance of all GC values. GC and AV were determined for all study species and all successive years. Abundance fluctuations were tested for cyclicity by autocorrelation (lagged 3-22) of log(N + 1 2 ) and GC. Finally, species were compared by correlation (Pearson's r), which formed the basis of the distance measures for a cluster analysis, using Ward's method of hierarchical grouping attained by minimising the sum of squares [71]. Species that correlated and clustered most closely (p < 0.001) were assigned to distinct groups.
The years when the populations of each species began to increase were examined for rainfall events in that and the previous year to identify any connection between abundance and rainfall. Then, monthly trends [69] were examined for details of responses. A population was identified as having responded to rain ("triggered") when GC increased by >0.05 (≈10% increase in N), provided that N increased by >10 (i.e., fluctuations at very low abundance, such as a doubling from 1 to 2, were discounted). Population irruptions are here defined as year to year increases in abundance by over 200% (GC > +1. 3), and population crashes as year to year decreases over 200% (GC < −1.3). The initial response time is the period (months) that elapsed before a sustained population increase was detectable after a rainfall event.
One-year lags were tested in the same way to account for larval maturation in seasonally active species. Rainfall over a week that triggered population increases was categorised as follows: heavy rainfall (>40 mm per annum), effective rainfall (>10.9 mm per week), light rainfall (<10.9 mm per month), summer, and winter rainfall. Decreases in abundance over an order of magnitude from maxima marked the end of responses.
Changes in the annual composition of communities at each site were determined on square-root transformed abundance data of each focal species. From the yearly abundance table of species, a resemblance matrix was calculated based on Bray-Curtis similarities between all the pairwise combinations of years for each ecosystem. This matrix was processed with the nonparametric Mantel tests (Spearman R) [72] with 9999 permutations against two null model matrices: (1) the seriation matrix codes for equidistant steps between consecutive years (e.g., 1978 vs. 1979 = 1 year distance, 1978 vs. 1980 = 2 years distance . . . ); (2) the cyclicity matrix codes for the resemblance of community structure at different times of the sampling period.
Insects 2021, 12, x FOR PEER REVIEW 6 of 25 rainfall was 1 mm or less (Table A2). Seasonal rainfall was not correlated (r = 0.12, p > 0.05), with most (59%) rain falling in late summer (January-March) and 27% in early winter (April-May) ( Figure A1). Winter rainfall was weakly cyclical at 5 y intervals (r = 0.35). Effective rainfall pulses were recorded in 23 of the 58 years, occurring at intervals of 2.3 ± SD 2.0 y (Table A2, Figure 2b) and were correlated with annual rainfall (r = 0.81), as well as summer (r = 0.69) and winter (r = 0.39) rain, with no autocorrelation. Three intervals between pulses before 1997 were 7-8 years long, while all other intervals were <3 y (Table A2). Seven heavy effective rainfalls (Q4, >40 mm) occurred in three groups, 1976-1978, 1997, and 2006-2011. The pitfall trapping of tenebrionids began in the year (1976) of the first heavy rainfall. During the first 21 years of trapping, there were seven effective rainfall events (MAP = 19.6 mm), compared to 15 in the 24 years that followed (MAP = 35.3 mm). The longest interval between heavy rainfalls during the first period was 19 years (6838 days between the last rain of the 1978 event and the first rain of the 1997 event).
Fog precipitation was measured in 47 of the years, annually recording 118 ± SD 56 Juvik units. Annual fog and rain precipitation were not correlated (r = 0.085), but fog was weakly autocorrelated at 21-year intervals (r = 0.24). Annual fog precipitation was significantly higher in the 18 years, 1979-1996, between heavy rainfall events than in the other 20 years, during periods with more rain (150 ± SD 52 vs. 96 ± SD 57 Juvik units, t = 3.044, Effective rainfall pulses were recorded in 23 of the 58 years, occurring at intervals of 2.3 ± SD 2.0 y (Table A1, Figure 2b) and were correlated with annual rainfall (r = 0.81), as well as summer (r = 0.69) and winter (r = 0.39) rain, with no autocorrelation. Three intervals between pulses before 1997 were 7-8 years long, while all other intervals were <3 y (Table A1). Seven heavy effective rainfalls (Q4, >40 mm) occurred in three groups, 1976-1978, 1997, and 2006-2011. The pitfall trapping of tenebrionids began in the year (1976) of the first heavy rainfall. During the first 21 years of trapping, there were seven effective rainfall events (MAP = 19.6 mm), compared to 15 in the 24 years that followed (MAP = 35.3 mm). The longest interval between heavy rainfalls during the first period was 19 years (6838 days between the last rain of the 1978 event and the first rain of the 1997 event).
Fog precipitation was measured in 47 of the years, annually recording 118 ± SD 56 Juvik units. Annual fog and rain precipitation were not correlated (r = 0.085), but fog was weakly autocorrelated at 21-year intervals (r = 0.24). Annual fog precipitation was significantly higher in the 18 years, 1979-1996, between heavy rainfall events than in the other 20 years, during periods with more rain (150 ± SD 52 vs. 96 ± SD 57 Juvik units, t = 3.044, p < 0.005; Figure 2c).
The calculated detritus reserve reflected large productivity pulses following heavy rainfalls, with the highest increases in 1976, 1997, 2006, 2011, and 2018 (Figure 2d). The reserve gradually declined between 1978 and 1996, besides a minor increase in [1989][1990]. After a boost in 1997, detritus declined until 2006. It reached an overall peak in 2011, with a subsequent small increase in 2018 (Figure 2d).

Trapping Data Characteristics
In total, 63,291 captures of tenebrionids were made at a rate of 0.31 ± SD 0.43 trap −1 day −1 (annual range 0.0016-2.4644 trap −1 day −1 ). The lowest rate was one tenebrionid captured in 15 continuously deployed traps during 309 days in 1994, while the maximum captured in a single trap in three days was 134 in 2011. Peak trap rates were recorded in 1976 /77, 2000, 2006, 2008, 2011, and 2018, with each peak associated with several years of high numbers ( Figure 3). The annual abundance of tenebrionids was not autocorrelated but tracked the annual detritus index (r 2 = 0.80), while it did not match any other annual rain or fog related measure (r 2 < 0.19, p > 0.05).

Trapping Data Characteristics
In total, 63,291 captures of tenebrionids were made at a rate of 0.31 ± SD 0.43 trap −1 day −1 (annual range 0.0016-2.4644 trap −1 day −1 ). The lowest rate was one tenebrionid captured in 15 continuously deployed traps during 309 days in 1994, while the maximum captured in a single trap in three days was 134 in 2011. Peak trap rates were recorded in 1976 /77, 2000, 2006, 2008, 2011, and 2018, with each peak associated with several years of high numbers ( Figure 3). The annual abundance of tenebrionids was not autocorrelated but tracked the annual detritus index (r 2 = 0.80), while it did not match any other annual rain or fog related measure (r 2 < 0.19, p > 0.05). The tenebrionid community of 54 species (Table A1) showed a high Shannon diversity (H' = 2.551) and evenness (J' = 0.639), with 17 species accounting for 95% of the trapped individuals and the 26 focal species for 98.96%.

Abundance Variation
Year to year changes in the abundance of focal species (GC > 0.05 or <−0.05) occurred every year (Figure 4). In the gravel plain, the largest numbers of species increased in abundance during 1978, 1984, 1988, 1997, 2006-2008, 2011, 2013-2014, and 2018, all but one (1984) being in the same or the next year following effective rainfalls ( Figure 2b). AV, which took both increases and decreases into account, followed different patterns over time. Species differed in terms of the time of population growth and decline, and there were few years when all species had the same trend. Abundance changes were gradual in some species and extremely variable in others (quartile 0-4 AV: 0.182, 0.525, 0.851, 1.586, 4.979; Table 1). The tenebrionid community of 54 species (Table A1) showed a high Shannon diversity (H' = 2.551) and evenness (J' = 0.639), with 17 species accounting for 95% of the trapped individuals and the 26 focal species for 98.96%.

Abundance Variation
Year to year changes in the abundance of focal species (GC > 0.05 or <−0.05) occurred every year (Figure 4). In the gravel plain, the largest numbers of species increased in abundance during 1978, 1984, 1988, 1997, 2006-2008, 2011, 2013-2014, and 2018, all but one (1984) being in the same or the next year following effective rainfalls ( Figure 2b). AV, which took both increases and decreases into account, followed different patterns over time. Species differed in terms of the time of population growth and decline, and there were few years when all species had the same trend. Abundance changes were gradual in some species and extremely variable in others (quartile 0-4 AV: 0.182, 0.525, 0.851, 1.586, 4.979; Table 1).
All but one of the 26 focal species was recorded in at least 22 years, one in every year ( Table 1). The abundance tracks of the 26 focal species could be allocated to six clusters (p < 0.001, Ward's method-Pearsons-r, Figure 6). Group partners matched each other, with one species, Cauricara eburnea being unique, not matching any other species (p > 0.05, Figure 6). (1984) being in the same or the next year following effective rainfalls ( Figure 2b). AV, which took both increases and decreases into account, followed different patterns over time. Species differed in terms of the time of population growth and decline, and there were few years when all species had the same trend. Abundance changes were gradual in some species and extremely variable in others (quartile 0-4 AV: 0.182, 0.525, 0.851, 1.586, 4.979; Table 1). Autocorrelation revealed that population fluctuations were not cyclical, except for Zophosis devexa and Cauricara velox cycling over 9-10 year ( Figure 5), although only the former was significant (r = 0.33, p < 0.05).  All but one of the 26 focal species was recorded in at least 22 years, one in every year ( Table 1). The abundance tracks of the 26 focal species could be allocated to six clusters (p < 0.001, Ward's method-Pearsons-r, Figure 6). Group partners matched each other, with one species, Cauricara eburnea being unique, not matching any other species (p > 0.05, Figure 6).  Zophosis moralesi was the most abundant species, accounting for 20.1% of the overall total. This species belongs to group A, whose five members accounted for 40.9% of the total abundance and tracked the detritus index (r 2 = 0.31 to 0.83). The three group B species (18.0%) were influenced immediately by effective rainfall (r 2 = 0.32 to 0.53), with the populations irrupting in years with effective rainfall events and crashing a year later ( Figure 6). Group C (14.8%) comprised eight gravel plain species that gradually increased populations over several years following heavy rainfall events, then gradually declined. The annual abundance of group C members did not correlate with any of the environmental factors considered here, as their gradual rates of increase and decrease varied. Two group D species (19.7%) tracked detritus (r 2 = 0.10 to 0.38), with Zophosis amabilis consistently present every year, even across the extremely dry period of 1990-1996, when many other species were not recorded. One species, Cauricara eburnea, that was allocated to group E (0.4%), correlated negatively with all the other gravel plain species (r < −0.57) and with the detritus index (r = −0.36). During 1980-1990, when populations of other species were declining, this species slowly increased its numbers before gradually declining during the period following 2006 ( Figure 6). Most of the seven group F species (5.3%) were first recorded during the second part of the study period ( Figure 6). All members of this group were typical riverbed residents and occasionally dispersed across the plains, especially after 2006.

Rhammatodes subcostatus F
When examining the population attributes against other characteristics of each species (Table 1), it is notable that all abundant species (>median) were diurnal, belonging to the tribes Adesmiini or Zophosini, but there was no relationship with size (r = −0.26) or seasonality (r = −0.03). The three species with the highest AV were strictly winter active, but AV bore no relationship with any other characteristics. The only characteristics associated with particular groups were that six of the eight group C members were nocturnal or crepuscular, as were two of the three group B species, while other groups comprised diurnal species (Table 1). Table 1. Abundance measures of focal species [69]: average and maximum trap rate per 1000 trap days, the number of years in which species were recorded and populations increased (GC > 0.05) or decreased (GC < −0.05), annual variation (AV), the number of population irruptions (GC > 1.3) recorded over the study period. The next set of columns describes which kind of rainfall triggered population increases (S = effective rainfall in summer, Oct-Mar; W = effective rainfall in winter, April-September; H = heavy rainfall, >40 mm; L = light rainfall, <11 mm), the number of months for the population to show first consistent response, the number of years to reach a peak and the number of years until the end of a response. The right columns are characteristics of the species: dry body mass (mg) [73], diel activity (D = diurnal, N = nocturnal, C = crepuscular) [64,68], and the principal season of activity according to winter records (<33% = summer (S), >66% = winter (W), 33-66 = aseasonal (A)).  All but one of the 26 focal species was recorded in at least 22 years, one in every year ( Table 1). The abundance tracks of the 26 focal species could be allocated to six clusters (p < 0.001, Ward's method-Pearsons-r, Figure 6). Group partners matched each other, with one species, Cauricara eburnea being unique, not matching any other species (p > 0.05, Figure 6).   Total Tenebrionidae   1976  1978  1980  1982  1984  1986  1988  1990  1992  1994  1996  1998  2000  2002  2004  2006  2008  During 1990-1996, abundances of all species dropped extremely low, with only 0.38% of the total captures made during this entire period. Population densities were so low that few species were recorded (Figures 4 and 6), and even the otherwise abundant species of group A were no longer recorded. This drop was less severe for Zophosis amabilis (0.83%). Another exception was Cauricara eburnea, a generally uncommon species (maximum annual abundance 29). Through the 1990s, its annual abundance averaged 23% of the maximum, being the most abundant species during several of these dry years ( Figure 6). Protracted periods of population lows for this species were before 1984 and after 2006. A period of extremely low density began for group C members between 1988 and 1990 through to 2002, when trapping effort was increased from 15 to 75 traps for eight months, confirming that these species were still present. After 2006, they were again recorded in the regular traps. Nearly all focal species appeared in considerable numbers after 2006, including two group B and all the group F members previously recorded seldom, or not at all, during the initial 30 years (Figure 6).

Responses to Trigger Events
In years when abundance began to increase (GC > 0.05), monthly abundances indicated the onset of responses by focal species relative to the month of rainfall events. Sometimes, adults became active and were detected during the month or months immediately following a rainfall event. Most population responses were initiated within six months, but some species responded only 10-24 months after a trigger event (Table 1). Most population peaks occurred during the year of the event or a year after, but four peaks occurred after 3-7 years, following steady population increases after the trigger event.
Specific rainfall schedules and amounts triggered the population responses of different tenebrionid species (Table 1). The timing and magnitude of irruptions and declines differed among species and groups. Sixteen of the 26 focal species responded to heavy rainfalls, while most of the erratic range expansions of the group F members occurred in the years following heavy rainfalls. Five species responded only to winter rainfall, not summer rain, even when this was heavy. Summer rain of 11-40 mm triggered six species, including the three most abundant. Three species responded to light rainfalls, such as 8.5 mm in the winter of 1983, and some of these responses were cued seasonally, e.g., the summer active Zophosis amabilis increased six months following light winter rainfall events. No species responded to every rainfall event.
Short pulses of population irruption, typically lasting 1-3 years (Table 1), were interspersed with long intervals of population decline, usually 5-10 years. There were fewer years with abundance increases than decreases (Wilcoxon matched pairs: t = 60, z = 2.16, n = 26, p < 0.05). The number of irruptions balanced crashes (>200% increase and decrease, respectively), the maximum being the seven irruptions and eight crashes experienced by Eustolopus octoseriatus during 45 years. All but four species had GC values signifying irruptions, but effective irruptions and crashes could be registered erratically at generally low abundance, e.g., Cauricara eburnea disappearing in 1994 and reappearing a year later without responding to a trigger event ( Figure 6). The sequence of heavy rainfall years 1997,2006,2008,2009,2011,2013, and 2018 primed most species to irrupt and crash, even those that otherwise changed slowly. The most pronounced irruptions followed by crashes a year later were by Eustolopus octoseriatus (AV > 3.5), with the most extreme fluctuation occurring from 2010 to 2012, when its annual abundance first increased from 34 to 7909 then crashed to 30 a year later.

Population Responses to Rainfall
Long term studies of insects in arid America, Australia, and the Middle East [55,56,[74][75][76][77][78][79][80] report that population fluctuations and their differences among species are largely attributable to rainfall variations. The current study follows this conclusion, with the caveats that population responses are also strongly modified by rainfall timing and the life history characteristics of the component species. Patterns of population responses to precipitation were either species specific or were characteristic of clusters of species, independent from phylogeny and biogeography. Furthermore, some responses were complex, with variable lag times placing them beyond the reach of conventional statistics [56,81], requiring case by case examination of population increases relative to the occurrence of trigger events.
Rainfall, the most important trigger of Namib Desert tenebrionid population irruptions, acts on populations in various ways. First, it increases primary production, generating detritus, the basis for detritivore productivity [45]. Effective rainfall briefly stimulates ephemeral grass growth on the previously bare gravel plains (Figure 1) [23], whereas perennial plants in nearby habitats require heavy rainfall to become established and grow [17,[82][83][84][85][86][87]. In the current study, total tenebrionid abundance tracked the calculated increases in detritus biomass after effective rain, and its gradual decrease. The detritus index, incorporating rapid increases and gradual decreases in resources, extends the effects of rainfall across years. The model needs empirical confirmation and refinement, especially in terms of the decay of this reserve, adjusted for different habitats. Nevertheless, the principle of using such a model was vindicated by the outcome. Conversely, it can be argued that the total tenebrionid population should be an indicator of the relative availability of detritus over time, which can serve to guide investigations of detritus stocks and their decomposition, to improve modelling.

Population Responses to Rainfall
Long term studies of insects in arid America, Australia, and the Middle [55,56,[74][75][76][77][78][79][80] report that population fluctuations and their differences among specie largely attributable to rainfall variations. The current study follows this conclusion, the caveats that population responses are also strongly modified by rainfall timing the life history characteristics of the component species. Patterns of population respo to precipitation were either species specific or were characteristic of clusters of spe independent from phylogeny and biogeography. Furthermore, some responses were plex, with variable lag times placing them beyond the reach of conventional stat Effective rainfall in summer, especially when heavy, appears to be the principal driver of the populations of the dominant perennially active species (group A), as well as of the ephemerally active tenebrionid species (group B) and uncommon beetles (group C). The latter only attained sufficient numbers to be recorded in years following heavy rains, gradually increasing in abundance until they could be the most abundant species in the community eight years later (Figure 8). These three groups constituted more than three-quarters of tenebrionid numbers, explaining the aforementioned relationship to the detritus index.
Rainfall also increases soil moisture for several weeks [43,44,88], favouring reproductive success and recruitment [52,89]. For the group B species, with quick and short responses to rainfall, the population peak occurred while shallow soil moisture was suitable for larval development and there was green grass for consumption [26]. In winter, even relatively light rainfall triggered responses by several species (groups D-E, Table 1), probably because soil moisture lasted longer in winter due to reduced evaporation from 3-9 • C cooler soil [43,60].
Rainfall in early winter (April and May) was a principal driver of the group D populations. Zophosis amabilis was active throughout the year, peaking in summer. This species, however, showed no strong population responses to summer rains, even if heavy. Its adult population increased six months after winter rainfalls of >5 mm. Cauricara velox was strictly winter active, with its population responding only to effective winter rains in either the same season or a year later. Besides these species, Zophosis cerea and Rhammatodes tagenesthoides of group C and Cauricara eburnea of group E were also cued to winter rains. Furthermore, responses to light winter rains were prevalent even with other species, e.g., in 1984, eight species increased in abundance a year after 8.5 mm winter rain in 1983. The mechanisms by which winter rainfall drives populations are unknown. In the Central Namib, rains falling in April and May ( Figure A1) are normally the last of the summer monsoons (therefore, conventionally considered part of a summer rainfall regime), but the resultant lingering moisture in the cool months of early winter probably resembles the effects of the winter rainfall fronts of the southern Namib and Western Cape [90,91]. The lingering moisture would also affect plants, perhaps explaining the conflicting interpretations concerning winter and summer rainfall zones in the Namib [92]. In arid areas elsewhere, it has been noted that the significance of soil moisture changes with seasons, facilitating the enhanced growth of some plants during cool months [91]. Different species partition their access to water over time [93]. We could be seeing a similar process with the tenebrionids, explaining the diverse population patterns between response groups and, to a lesser extent, within groups. The current recognition of high species diversity enabled by complex time niches elucidate Barrows' [94] hypothesis that relationships to hydrological patterns could explain the high diversity of tenebrionids he found in the Coachella Valley dune field in California.

Population Responses to Fog
The increase in Namib fog from low, in the 1970s, to high, during the 1990s (Figure 2c), allowed the separation of the effects of fog and rainfall. Particularly during the high fog years of the early 1990s, when all indices related to rainfall were low and most species' populations were declining, associations of beetle populations with fog were implicated for the eight Namib species that declined more gradually than other species [49]. Fog directly benefits tenebrionids [39,[95][96][97], but it also enables some perennial plants that take up fog water [98][99][100][101][102] to constantly produce seeds and plant fragments, supplementing food for detritivore populations.
The current study revealed that Cauricara eburnea, which is not known to drink fog [49], increased slightly through the 1990s, in an opposite trend to all the other species. Cauricara eburnea is more commonly encountered in lichen fields closer to the coast (Figure 9), where fog is more prevalent [103]. When fog was prevented from reaching the larvae of the eight tenebrionid species at Gobabeb, they either died (three species) or developed more slowly [52]. Perhaps C. eburnea benefits from fog due to enhanced larval development or the improved palatability of fog wetted food. The absorption of moisture by detritus during humid conditions [40] enhances its fungal community [21], a potential food source for tenebrionids.
Insects 2021, 12, x FOR PEER REVIEW versity enabled by complex time niches elucidate Barrows' [94] hypothesis that ships to hydrological patterns could explain the high diversity of tenebrionids h in the Coachella Valley dune field in California.

Population Responses to Fog
The increase in Namib fog from low, in the 1970s, to high, during the 1990s 2c), allowed the separation of the effects of fog and rainfall. Particularly during fog years of the early 1990s, when all indices related to rainfall were low and most populations were declining, associations of beetle populations with fog were im for the eight Namib species that declined more gradually than other species [49] rectly benefits tenebrionids [39,[95][96][97], but it also enables some perennial plants up fog water [98][99][100][101][102] to constantly produce seeds and plant fragments, supple food for detritivore populations.
The current study revealed that Cauricara eburnea, which is not known to d [49], increased slightly through the 1990s, in an opposite trend to all the other Cauricara eburnea is more commonly encountered in lichen fields closer to the coas 9), where fog is more prevalent [103]. When fog was prevented from reaching th of the eight tenebrionid species at Gobabeb, they either died (three species) or de more slowly [52]. Perhaps C. eburnea benefits from fog due to enhanced larval d ment or the improved palatability of fog wetted food. The absorption of moistur tritus during humid conditions [40] enhances its fungal community [21], a poten source for tenebrionids.

Recovering from Low Abundance
Many periodically abundant species were sometimes scarce for extended joining other perpetually rare species occurring at the study site. The recorded fluctuation in the number of focal species present in any given year (Figure 4) is p an illusion of the local extinction of some species. A temporary fivefold increase

Recovering from Low Abundance
Many periodically abundant species were sometimes scarce for extended periods, joining other perpetually rare species occurring at the study site. The recorded annual fluctuation in the number of focal species present in any given year (Figure 4) is probably an illusion of the local extinction of some species. A temporary fivefold increase in trapping effort during the abundance trough revealed that previously unrecorded species were still present at the site, though at very low densities. In contrast to mesic areas, where tenebrionid species dropping from common to rare is considered a sign of an increased risk of extinction [104], this study indicates that many Namib species cope with temporary rarity. One of the key topics of biodiversity is how rare species persist [105], whether in a disturbed tropical forest [106] or a hyperarid environment subject to extreme pulse-reserve fluctuations.
Diapause has not been demonstrated in Namib tenebrionids. Eggs are not dormant. Larvae can prolong their development by several months [52,89]. However, even the longest larval development, of 19 months, would usually not be sufficient to carry a population through from one effective rainfall to the next. By contrast, adults of all the eight species examined by Rössl [52] had a minimum natural lifespan of 27 months and up to 73 months (or longer, observations were terminated). These observations indicate that adults are, by far, the most enduring life stage, lasting several years, and individuals may experience more than one effective rainfall. Extreme longevity by adults is, thus, a key feature of Namib tenebrionids. Fog, dew, nocturnal subsurface vapour [38,107], and light rain in winter appear important for sustaining them long after effective rainfalls [39].
Immigration could be a mechanism of recovery. Local populations could be replenished from a neighbouring source population. Although tenebrionids are apterous, they have been observed to move several kilometres during their lifetime [95,[108][109][110]. Such species respond to triggering events by increasing in abundance in their main habitat and expanding their range. For example, the seven group F species are usually encountered in the riverbed of the Kuiseb River [59]. After a series of unusually high rainfalls and river flooding events between 2006 and 2018, these riparian species ventured more than 2 km across the grass covered gravel plain, where they were recorded.
Repopulation from distant locations may be slow. The maximum ranging distance of the most mobile species, Onymacris plana, is 10 km (R. Pietruszka personal communication), barely far enough to cover the path width of a thundercloud (Figure 1), and far less than the much greater distances (tens to hundreds of kilometres) between adjacent annual rainfall paths across the Namib [22,24]. In addition, there may be times when no rain falls for many years over an entire region of the Namib, and all populations of a species become scarce. Such populations can only recover by a few survivors reproducing.
The ability for rapid local recruitment by resident populations is, therefore, a key feature. The timing of rainfall strongly influences the timing and magnitude of responses. Summer rain allows summer active adults to multiply immediately. For instance, Z. moralesi reproduced, developed, and metamorphosed in 75 days or less [52]. It is, therefore, possible to recruit a fresh cohort of adults within the same annual breeding season and increase the irruption.
Namib tenebrionid populations have several characteristics consistent with the "storage effect" [111], which facilitates coexistence among species that rely on common resources [112]. Existing in a fluctuating environment, Namib beetles regularly pass through bottlenecks of low resource availability when reduced to a few individuals. These individuals are mature, capable of reproducing at any time, are long lived, and have overlapping generations. They are the population storage modules upon which regeneration is based when a pulse enables populations to increase again. When the survival of developing offspring in unpredictable environments is uncertain, bet-hedging reproduction is a successful strategy [113]. Iteroparous females of many Namib tenebrionids frequently produce small clutches of eggs [45,46,52,57,89,[114][115][116][117][118]. Females forage until they have enough resources to produce a clutch, lay it, and then forage again to produce the next clutch. Under optimal conditions, a female can produce one or more clutches daily, and some species do so throughout the year.
The latency of response in terms of tenebrionid population increase after rainfall depends on the time it takes for germinated ephemeral grass to turn into detritus, approximately one month, plus the shortest interval required for the next cohort of tenebrionids to develop. For Zophosini, this is 2-3 months (i.e., 3-4 months after rainfall), and for Adesmiini, 5-7 months (i.e., 6-8 months after rainfall) [52]. These periods roughly correspond with the lags for sustained increases in abundances (Table 1). However, not all species followed the "detritus" pattern, and those which did, did so at variable rates. Even within the numerically dominant group A, where annual abundance patterns were most strongly correlated (r = 0.47-0.80), patterns differed in detail (Figures 6 and 8), while members of other groups differed starkly, even those cued to common triggers. The strictly winter active C. velox sometimes only irrupted a year after winter rainfalls, indicative of lags in their recruitment capacity when triggered. Population responses to the triggers of some species operated within the constraints of differing phenology and larval longevity.
Differences in responses to pulses and rates of population decline result in time partitioning within the community. This partitioning could explain how so many Namib tenebrionid species coexist. Previous studies have recorded 41 tenebrionid species at the current gravel plain study site. With continuous trapping, the number could be as high as 54 (not all current records have been confirmed), with 82 tenebrionid species recorded in several habitats within a kilometre of Gobabeb [59]. Although the extraordinary high diversity and species radiation of Namib tenebrionids have been further illuminated since Koch's [28] landmark publications on that subject [66,[119][120][121][122][123], several hypotheses remain untested. The current study explains how different relationships to water and food availability enable so many species to persist sympatrically.

Population Variability
Wolda [70] summarised a widespread search for correlates and principles concerning the variability of insect populations, evaluating the relationship between stability and biome derivation. He considered the significance of mean AV values for 138 sets of temperate and tropical insects [70]. Only one of Wolda's AV values was higher than the highest value in the current study, three Namib species lie below Wolda's median, and only Epiphysa arenicola falls within Wolda's lower quartile. The mean AV value of all the focal species of Namib tenebrionids in the gravel plain (0.858) lies above Wolda's upper quartile of values (quartile 0-4: 0.018, 0.206, 0.412, 0.666, 5.250). It should, however, be noted that the minimum annual abundance of all but one of the current focal species was zero, which tends to render AV values high [70].
What is the significance of the wide range of AV values for tenebrionid species (0.182-4.979, Table 1)? An answer to this question requires a species by species analysis of the correlates of similarities and differences in the AV values. The species with the highest AV, Eustolopus octoseriatus, is known to feed on fresh grass after effective rain [26], in other years remaining quiescent, buried in the sand for several years until the next rain. AV values > 1 of some of the other species were due to the periodic local range expansions, from the riverbed onto the gravel plain, by seven species during the decade of high rainfalls following 2006. The lowest AV value (0.182) was for E. arenicola, one of the few nocturnal focal species that only responded to the successive exceptionally heavy rainfalls of 1976/1978 and 2006/2011, with the first increase in adults showing two years after the last of these event pairs, peaking three years later and gradually declining over the next decade ( Figure 6). Another low AV (0.288) was for Z. amabilis, a species recorded every year, the most responsive of all the species to any winter rainfall, even if only light. Cauricara velox, a highly seasonal winter active species with low AV, is a small, long legged species that is highly mobile, searching large areas of gravel plain for widely scattered detritus, of which it continued to find sufficient to moderate population change. These examples illustrate how the wide AV range reflects sympatric tenebrionids existing in different time niches.

Long Term Observations
This study emphasises the fundamental rationale of long term ecological research [124]. Forty five years of observations enabled the recording of some species that were scarce for long intervals and common for short periods, and allowed the identification of population characteristics and novel analyses of tenebrionid population dynamics in the Namib Desert. Identification of the triggers to population increases required replicated observation of sporadic rainfall events. Identifying species with similar population signatures required long datasets across extended periods with different hydrological patterns.
Critical for achieving the continuity required for obtaining such long term data is the continuous institutional operation of field stations, in this case, the Gobabeb Namib Research Institute, founded in 1963 to improve understanding of the Namib Desert compared to other arid and mesic systems globally [125]. Labour intensive live pitfall trapping, requiring over 150 person-days annually, year-in-year-out, continuously conducted at three sites and intermittently at three others [59], was possible only in the close vicinity of the field station with the participation of interns as part of their training in ecology.
Long term studies of invertebrates and their climatic and ecological drivers in arid environments are rare [81]. The current analyses enhance the value of continuing the long term observations of Namib tenebrionids. There is a wealth of further information in the existing published dataset [69]. Further analyses could include examining the biological mechanisms of extreme irruptions (e.g., E. octoseriatus) or the ecological underpinnings of responses to winter rainfall. The pervasiveness of rarity in the desert, whether a temporary bottleneck or a permanent characteristic of species, can best be investigated against the background of long term records. While there have been numerous studies of the common tenebrionid species in the Namib, especially Adesmiini, the current long term records encourage ecological and ecophysiological studies of other species, in order to improve understanding of the extraordinary tenebrionid diversity of the Namib. Continuous records of the kind assembled here provide an invaluable foundation for short term studies to build an interconnected picture of ecosystem functioning that other means cannot achieve.
Climate change is a core feature of LTER. Specifically, in this context, there are concerns worldwide about insect populations collapsing due to climate change [126,127]. While the current 45-year dataset lends itself to such analyses, this requires examining several other factors not considered in the current paper. The records of the Namibia Meteorological Service indicate that, in the 140 years before 2020, three of the four years when rainfall exceeded 100 mm in the hyperarid Central Namib occurred during the 45 years of this study. The unusual sequence of high rainfall years (>40 mm) after 2006 was accompanied by surges in the abundance of many species and a return to a previous condition, not only of tenebrionids and ephemeral grasses but also perennial plants [17,[82][83][84][85][86][87]. This long term resilience of Namib communities could reflect the high tenacity of desert organisms and/or general ecosystem health in a large national park with minimum pollution and none of the blanket application of pesticides commonly practised across rangelands and croplands [128]. Further analyses need to incorporate temperature and carbon sequestration or emission and microbial ecology to enable a more in depth understanding of Namib ecology relating to tenebrionid populations faced with climate change.

Conclusions
Detritivorous tenebrionids persist in the hyper-arid Namib because detritus produced by rainfall events prolongs the presence of their populations. Adults are long lived and maintain a bet-hedging reproductive strategy, and many use NRM to overcome water limitations during long intervals without effective rainfall events, allowing them to irrupt after the next rainfall pulse.
Many species respond to particular kinds of rainfall-e.g., summer rainfall with its flush of primary productivity, or winter rain with its lingering soil moisture-or require different intensities of such events to respond at all. Despite the wide range of triggers, initial response times, and population change rates, species show several discrete nodes, defining the common population signatures of abundance patterns. Population signatures show categorical differences among species in how they respond to rainfall of different magnitudes in different seasons. Nevertheless, nearly all population changes can be related to hydrological pulses.
These observations of the fundamental importance of hydrological triggering events concur with Noy-Meir's [129] autecological perspective. The population changes of individual species in the study area are driven by hydrological events but are species specific, multifaceted, and affected by several environmental or antecedent conditions besides rainfall. By responding selectively to alternative triggering events, sympatric species show temporal patterns and magnitudes of population fluctuation more diverse than predicted by Noy-Meir's [3] original model. The great age of the Namib [130] would allow sufficient time for these divergent patterns to evolve. Numerous field technicians and assistants operated the pitfall traps and associated thrice-weekly data collection, almost continuously, for 45 years. Other than Vilho Mtuleni, who assisted for ten years, they cannot all be named here. This laudable effort for so long by so many cannot be underrated. Roland Vogt shared updated GNRI rainfall data. Mary-Lou Penrith, Sebastian Endrödy-Younga, and Eugene Marais advised identifying voucher specimens, although the author is responsible for the species designations in the dataset. Klaus Birkhofer kindly performed the Mantel test and commented on a draft manuscript, as did Suzanne Milton, Tim O'Connor, Mary Seely and four referees. Sylvia Thompson of the Southern African Science Service Centre for Climate Change and Adaptive Land Management (SASSCAL) adapted and published the current dataset and related metadata. This paper is dedicated to Mary Seely, who laid the foundation of this project.

Conflicts of Interest:
The author declares no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.  Table A1. Annual rainfall at Gobabeb between 1963-2020, summer (October to March) and winter (April-September) rainfall, amounts, and intervals between effective rainfall events, calculated grass productivity generated by these events, and the amount of detritus calculated from productivity and decay rates.  Appendix C Figure A1. Average monthly rainfall (mm) at Gobabeb over 58 years.