We conducted our study in and around the city of Canberra, Australian Capital Territory (ACT), southeastern Australia (35° 17′ 35. 64″ S; 149° 07′ 27. 36″ E). Canberra is Australia's eighth largest city covering an area of 810 km 2 . The city supports a population of 375,000 people, which is projected to double by 2056 [37] . Canberra is a highly planned city described as the “Bush Capital” because of the extensive suburban tree cover and 34 nature reserves flanking the urban boundary [38] . The city is situated in the ecologically diverse Southern Tablelands region west of the Great Dividing Range. Lowland box-gum Eucalyptus woodlands and grasslands once dominated the region [39] . Box-gum grassy woodlands are characterised by two dominant species, yellow box (Eucalyptus melliodora) and Blakely's red gum (E. blakelyi) that occur in association with other eucalypt species, including apple box (E. bridgesiana), red box (E. polyanthemos), red stringybark (E. macrorhyncha), and scribbly gum (E. rossii). Extensive land clearance for stock grazing and urban development has led to a near 95% decline in intact box-gum grassy woodlands, which is now listed as a critically endangered ecological community [40] . What vegetation remains exists in semi-natural nature reserves or as highly modified isolated remnant patches and scattered paddock and urban trees [41] , [42] .

We confined our sampling effort to a single vegetation type: the predicted pre-European (pre-1750) extent of box-gum grassy woodland. Within this vegetation type, we stratified sampling according to two dominant land-use types and five geographic zones, creating a total of 10 strata. Our land-use types were: (1) nature reserves, which are designated semi-natural areas managed for conservation; and (2) urban greenspace, made up of publicly accessible parklands (60%), roadside margins (24%), remnant vegetation (9%), and sports grounds (7%). Urban greenspace accounted for 11% of the total urban environment in our study area. We divided our study landscape into five geographic zones to capture variability and avoid biasing sampling effort to areas with specific local or historical attributes (e.g. fire history). An equal number of fixed area plots (50×20 m; 0.1 ha) were randomly allocated by land-use type (n = 100) and geographic zone (n = 40). This resulted in a total of 200 plots or 20 ha of sampled land from 28 reserves and 100 urban greenspaces. Plots were >250 m apart to minimise spatial dependence and allocated to greenspace ≥0.2 ha.

We measured the diameter at breast height over bark (DBH; 1.3 m above ground) of every living and dead tree in each plot. We measured only the largest stem of multi-stemmed trees [43] . Trees with stems <1.3 m above the ground were measured at the base of the stem. The number of naturally regenerating and planted seedlings ≤10 cm (DBH) were counted in each plot and formed the first size class of our tree population. We identified all living trees to species level. Each tree was inspected for hollows from all angles on the ground using binoculars (10×25). One observer (DSL) completed this task to reduce multi-observer bias and maintain consistency in hollow identification [44] . Our objective was not to determine the absolute number of hollows but rather relative hollow occurrence per tree. We selected a minimum entrance size of 2 cm for hollows. This was because: (1) the full range of hollow-dependent vertebrate taxa, including marsupials, birds, and bats, would be accounted for; and (2) hollows smaller than 2 cm were difficult to reliably identify from the ground [45] .

2.5. Simulation model

The simulation model described in [12], tracks the mean DBH of trees, including hollow-bearing trees, in separate size cohorts over time. The model has pre-defined rates of tree mortality and recruitment applied at each time step. For this study, we ran separate simulations for native tree populations occurring in nature reserves and urban greenspace. Exotic trees were recorded only in the urban greenspace and accounted for 30% of all recorded trees. We excluded exotic trees from our analyses because only native trees were recorded with hollows in our study area. Simulation models for both land-use types were parameterised with the following baseline data: the current number of native trees in existing stands sorted by DBH cohort; the predicted age and growth rate of trees; the frequency of regeneration events; the number of seedlings at each regeneration event; and the rate of tree mortality.

There were five principle steps in our modelling process (summarised in Fig. 1 and described further in Summary S1):

(1) We calculated the mean number of trees in 10 cm DBH size cohorts (ranging from 0.1–10 cm to >100 cm) for each native tree species and dead trees, using data collected in each land-use type (Table S1).

(2) We used a generalised logistic regression model with a binomial distribution and logit link to establish a relationship between hollow occurrence (i.e. the presence of at least one hollow ≥2 cm; binary response) and tree size (i.e. DBH; explanatory variable). We also fitted tree species as an explanatory variable in our model. Based on correlations in hollow occurrence by DBH between individual species, we identified three distinct species groupings. Species group one included yellow box, apple box, brittle gum (E. mannifera), broad-leaved peppermint (E. dives), bundy (E. goniocalyx), mealy bundy (E. nortonii), brown barrel (E. fastigata), alpine ash (E. delegatensis), ribbon gum (E. viminalis), mountain gum (E. dalrympleana), candlebark (E. rubida) and ironbark (E. sideroxylon). Group two included Blakely's red gum, red box, red stringybark and scribbly gum. Group three was dead trees. We found that species groups differed significantly (Wald statistic = 101.5; P<0.001) from each other (Table 1). The relationship between tree size and hollow presence was highly significant in our model (Wald statistic = 388.1; P<0.001). The area under the receiver operating characteristic curve of our model was 0.92, indicating that the discriminating ability of our model was excellent [46]. For each species group, we derived separate model equations which took the form: Logit (Pr. Hollows) = −7.112+(0.086 x DBH) + (species group estimate).

(3) We established a relationship between DBH and tree age using the following equation: Age = 0.02×π×(DBH standardised /2)2, where DBH standardised is the yellow box equivalent diameter for each tree. Yellow box is the only tree species for which data exist to establish a relationship between age and DBH [47]. We scaled all DBH values for each tree species relative to that of a yellow box equivalent using the method described in [18], [26]. To do this, we first calculated each DBH value as a proportion of the maximum DBH recorded for each tree species and then multiplied this value by the largest DBH recorded for yellow box in our study area (151 cm). Therefore, we assumed that all species had proportionally equal growth rates that were similar to that of yellow box. Although this approach is not ideal because it is unlikely to yield precise age estimates for each species, it currently is the most practicable solution available in the absence of age-DBH relationship data for other eucalypt species [26], [48]. Therefore, our model had a degree of uncertainty related to tree growth rates, as these data likely differ for each species. However, a previous study [12] found that long-term predictions for mature trees is not sensitive to uncertainty in this variable and suggests that the focus should instead be on testing the effects of uncertainty for other parameters in the model.

(4) We simulated tree regeneration in both land-use types to ensure that uncertainties associated with regeneration were reflected in our models. Tree regeneration is an event-driven process that can be sporadic and influenced by natural phenomena and/or anthropogenic factors such as climate, competition, and planting effort [31], [49]. At each regeneration event, viable seedlings may or may not establish and survive over time. To simulate these uncertainties, the number of seedlings ha−1 for each run of our model was drawn randomly from a Poisson distribution with the mean equal to the mean number of trees recorded in the 0–10 cm DBH cohort for each species group. For species group one and two in urban greenspace, the mean number of trees in the 0–10 cm DBH cohort was 11 and 13 seedlings ha−1, respectively. For species group one and two in nature reserves, the mean number of trees in the 0–10 cm DBH cohort was 119 and 193 seedlings ha−1, respectively. The time-step for each run of the model was equivalent to the average age of trees in the 0–10 cm DBH cohort for both land-use types, which was approximately 8 years.

(5) Annual tree mortality was modelled in a density-dependent manner to reflect declines in the number of trees over successive DBH cohorts or as trees age. Therefore, we assumed that tree densities would naturally thin out over time due to factors such as competition among conspecifics [50]. To simulate this process, we calculated annual mortality for each DBH cohort using the equation: 1 - s (1/y), where s is the proportion of trees that survive from one cohort to the next, and y is the number of years it takes trees to progress from one cohort to the next by 10 cm DBH increments. However, in some urban greenspaces (e.g. roadside margins), density-dependent mortality may be less pronounced as tree survivability may instead be predominantly influenced by tree planting and protection efforts. Therefore, for urban greenspace, we also tested the mean annual mortality rate across all cohorts, which yielded similar model trajectories to density-dependent mortality. We decided to apply density-dependent mortality to both land-use types for consistency and because a majority of urban greenspace sampled constituted parklands and remnant vegetation where natural regeneration and density-dependent mortality may still occur. We set 500 years as the maximum age that living trees will remain standing in both land-use types. This is based on the only longevity estimate available for eucalypts in our study area [47]. It is reasonable to assume that for other eucalypt species this age would also be the upper limit of survivability. Therefore, model uncertainties pertaining to species longevity are likely to be over-estimated and based on a best-case longevity. We assumed that once trees died in urban greenspace, they no longer functioned as hollow-bearing trees into the next time step. This is based on local tree management policies that facilitate dead tree removal on public land [51]. However, for nature reserves, we conservatively estimated that dead trees could remain standing for at least 50 years after initial mortality (i.e. 550 years in total), based on observations of the standing life of dead trees in Eucalyptus forests [52], however, we acknowledge the paucity of available data to support this estimate.