Discussion

When making predictions for ecological systems it is seldom clear from the outset which models to use and at what scale and resolution the modelling should be performed (Evans et al. 2013). Based on the joint posterior parameters distribution from hierarchical Bayesian models fitted to an extensive colonisation-extinction dataset on deadwood-dependent fungi, combined with realistic forest projection data, we show that the future trends predicted were sensitive to all four questions addressed – to the type of modelling performed, the landscape-scale occupancy of the model species which affects their colonization-extinction rates, the spatial scale of model fitting and the resolution of the resource-unit data. For our model species, the resource-unit resolution had a strong impact on the predictions especially for the species that frequently uses the smaller deadwood that were excluded from the coarse resolution data. Type of model (occupancy vs. colonisation-extinction model) substantially affected the magnitude of the predicted change, while the effect of the spatial scale of model fitting was also considerable. We encourage the use of colonisation-extinction models over occupancy models (or more generally, Species Distribution Models, SDMs), modelling the process at the finest resource-unit resolution that is utilizable by the species, and conducting projections for the same spatial scale and resource resolution at which the model fitting is conducted.

COLONISATION-EXTINCTION MODELS PRODUCE MORE REALISTIC PREDICTIONS

The occupancy models, corresponding to the frequently applied SDMs (Franklin and Miller 2010), predicted what we believe is unrealistically positive population development. Our conclusion is based on knowledge about the study system and population development of the focal species during the recent decades. Compared to the colonisation-extinction models, the occupancy models predicted higher occurrence probabilities and less steep future declines in the production land leading to more positive increases across all the forest land combined. Future declines are thus underestimated with occupancy models, especially if habitat amount is decreasing and the distances to dispersal sources are consequently increasing. Many of these species have slow life history which is often associated with rarity (Pilgrim et al. 2004). The occupancy models reflect the species distribution patterns which reflect the past rather than the current amount and connectivity of the habitat. Even more, occupancy SDMs often use data collected over a long time period during which the environment may change. The colonisation-extinction models are more realistic because they reflect the rate of change from one time step to another. Their higher realism, that they more mechanistically model the process leading to the occupancy pattern, may also explain why they were less sensitive to the spatial scale modelled and the resource resolution. Limitations of their use may be the costs of making another survey of the system, and the time span necessary for changes to take place.
The colonization-extinction rates observed at the patch and plot scales in this study were surprisingly high. Several local colonisations and extinctions had taken place during just 9-11 years, which challenges the view of very long time lags, from decades to much over hundred years, before a new equilibrium between the metapopulation and its environment is reached (Sverdrup-Thygeson et al. 2014). The high turnover rate may be partly explained by the ecology of our focal species which are not confined to very large or slowly decomposing dead trees. However, our results also suggest that in many species of deadwood-dependent fungi, the delay in response to environmental change is shorter than previously thought. Despite this, metapopulation equilibrium cannot be assumed as the colonization-extinction models project lower future species occurrence than the occupancy models. This is especially so for P. ferrugineofuscus with a lower ratio of colonization/extinction. The species is thus tracking the changes in its environment with a delay, especially in the production forest with the highest rate of forest stand and deadwood turnover. The colonisation-extinction models account explicitly for the temporal change, while occupancy models assume that the current occurrence pattern is at metapopulation equilibrium with the environment.

CONSIDERATIONS OF APPROPRIATE SPATIAL SCALE OF MODEL FITTING

The predictions of the future population development depend strongly on the chosen spatial scale of the statistical model fitting. For the less frequent P. ferrugineofuscus the predicted population increase by the year 2110 ranged from 0% to 42%, depending on which of the three models were applied in the projections. We generally recommend conducting model fitting and simulation at a small spatial scale. This allows modelling and projecting the dynamics at the level at which the local population dynamics take place, including accounting for proximal variables within each patch and among patches. However, this recommendation of simulating detailed dynamics ignores the computational power required. Moreover, for making projections for a landscape or region, simulation of complete deadwood and population dynamics across the chosen spatial scale is required, ideally including dispersal between patches. However, for rare species with slow colonization-extinction dynamics and few occurrences on a small proportion of logs in each patch (here especially P. ferrugineofuscus ), simulating detailed, small-scale deadwood dynamics may be inefficient. For such species, model fitting and projection simulation at a larger scale (here plot or patch) may be more appropriate, especially if the general question of the study concerns a landscape or region. Thus, conducting modelling and projection simulations at a more aggregated spatial resolution is acceptable. On the other hand, when modelling at a larger spatial scale, more distal predictors (e.g. stand age) are selected – these affect the species more indirectly than the proximal predictors they replace (Merow et al. 2014). The use of the more distal predictors may bring a higher level of uncertainty into the analyses, as it assumes a strong correlation between the distal predictors and the resources they replace. Moreover, if there is bias in this assumed correlation, then this bias is transferred into biased projections.

APPROPRIATE RESOURCE RESOLUTION DEPENDS ON THE ECOLOGY OF THE STUDY SPECIES

Resource-unit resolution can have a considerable influence on the predictions of future population development. For P. viticola the most striking difference in the projections was between using the fine or coarse resolution deadwood data. Excluding the smaller deadwood units resulted in the conclusion that this species will decline in the production land, while when including them the decline was much reduced. For P. ferrugineofuscus the population trends based on the coarse and fine deadwood data were more similar. This is because of the preference of P. ferrugineofuscus for larger-diameter dead trees and consequently the models for this species having deadwood volume (influenced mostly by larger trees) as the significant covariate of resource availability. With different minimum sizes of deadwood inventoried, the deadwood quantities such as density and volume of deadwood – the measures of resource availability used as covariates in the models and projections – may also change (Hottola et al. 2009). However, it may also be wise to choose the resource-unit resolution of analysis during the initial exploratory analysis. For example, a species may occur on a substrate of subordinate quality (e.g. small diameter logs) in a high-quality area (old-growth forest with high species abundance) resulting from mass effect. If erroneously assuming that it may occur on such substrate also in low-quality areas (albeit at low probability) and if this substrate is very common in these lower-quality areas, then one is likely to overestimate the future occupancy of this species, especially in low-quality areas. This may be the case forP. ferrugineofuscus whose colonization probability increases with diameter (Jönsson et al. 2008), but which only occasionally occurs on the very common 5-10 cm logs. It may thus be justified to exclude the small resource units from the survey or analyses as their influence on population dynamics is minor (Loos et al. 2015). Another option, if data quantity allows, is to include the interaction between substrate size and forest age. See Appendix S1 for more discussion on resource resolution and species ecology.

RELIABLE PREDICTION OF FUTURE OCCUPANCY

Despite the differing occurrence probabilities and rate of change in future occupancies produced by the occupancy and colonisation-extinction models, the direction of the change was usually the same. This is partly explained by the fact that the covariates selected for the colonisation probabilities were, in most cases, the same as those selected for the occupancy probabilities. Arguably, precise predictions of biological responses to environmental change, especially if extrapolating beyond current conditions and into the future, require elaborate mechanistic process-based models, driven by the detailed life history of the species (Evans et al. 2013). However, for essentially all species, including deadwood-dependent fungi, the data required to parameterise such models are still lacking. Inaccurate estimation of the rate of change in occupancy will lead to severe bias in future projections, e.g. when addressing the effects of global change (Dietrich et al. 2012) that may increase habitat turnover rates, making population persistence more dependent on a high number and good connectivity of habitat patches (Johst et al. 2011). The potential sources of bias in our predictions that we identified are detailed in Appendix S1. Nevertheless, with models for colonisations and extinctions accounting for key variables driving these metapopulation dynamics, such as the availability of suitable resource units, habitat quality (e.g. forest age) and spatial connectivity, we may detect the true future patterns and trends if they are strong.