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.