Appendix S1: Further description of and justification for entries in Table 1 in the main text.
Prediction goals:
Abundance:
Strictly speaking, Poisson process models estimate relative, not absolute, abundance.
Some population-based “mechanistic” models (e.g., Crozier and Dwyer 2006, Buckley and
Kingsolver 2012) have only predicted intrinsic population growth rate (and thus distribution),
but by inclusion of density dependence these models could be modified to predict
abundance.
Required data inputs:
Known occurrences:
Because hybrid models use a species distribution model (SDM), occurrence data are needed to
fit the SDM.
Some abundance-based SDM approaches require data on abundance or a proxy of it (e.g.,
Maravelias et al. 2000, Rouget and Richardsson 2003), while Poisson process models require
only occurrences.
Abiotic drivers:
Phenology models use abiotic drivers as inputs, but of course additional physiological
information would be needed to establish the link between those drivers and phenology.
Biotic drivers:
If biotic drivers affect vital rates, information on those drivers would be needed. For example,
Buckley (2008) needed to use data on abundance of insect prey to incorporate a key biotic
driver. While SDMs could, in principle, include presence/absence or abundance of other
species as predictors, they typically use only climate data; demographic models have more
often quantified the impact of biotic interactions. For the full approach, abundances of
interacting species at all times and sites would need to be predicted.
Vital rates at low density
In parameterizing a demographic range model, vital rate estimates should be corrected for
density dependence to obtain their low-density values. Diez et al. 2014 did so; Merow et al.
2014 did not.
Effects of intraspecific density
Some hybrid SDMs (e.g., Keith et al. 2008, Dullinger et al. 2012) included a population ceiling,
but to date only Cabral et al. 2013 have included density-dependence directly in vital rates.
Some population-based “mechanistic” models have required information about intraspecific
density dependence. For example, Buckley (2008) predicted equilibrium abundance, and to
do so needed to scale lizard territory size to population density.
Dispersal
Hybrid models use SDMs in different ways. Some (e.g., Keith et al. 2008, Cabral et al. 2013)
used the SDM partially or entirely to track the changing locations of suitable habitat patches.
To predict distribution change, such models would require dispersal data. (In some
scenarios, Keith et al. also made the carrying capacity a function of the probability of
occurrence.) Instead, Dullinger et al. (2012) made both the carrying capacity and vital rates
functions of the probability of occurrence predicted by an SDM. Although this model could
have been used to predict distribution or local abundance in the absence of information
about dispersal, it did include dispersal by means of mechanistic sub-models to predict
dispersal distances that used properties of plants and seeds, of wind, and of the movements
of animal dispersers.
Dynamic range models estimate dispersal and demography simultaneously using spatially
distributed abundance data; no input data on dispersal per se are needed.
Complexities taken into account
Living dead populations
We question whether, by tying vital rates or carrying capacity to probability of occurrence,
hybrid SDM models are accounting for biases caused by living dead populations.
To date, tests of dynamic range models used simulated unstructured data; it is untested
whether the fitting method could discern vital rate combinations that would lead to some
life stages persisting for a time even after eventual extinction becomes inevitable.
Population-based "mechanistic" models, demographic range models, demographic equilibrium
abundance models, and the full approach would not be “fooled” into assigning the
conditions experienced by living-dead populations as being suitable, or assigning non-zero
equilibrium abundance under such conditions. In addition, the full approach would be able
to predict when and where living dead populations will occur.
Source/sink dynamics
We question whether, by tying vital rates or carrying capacity to probability of occurrence,
hybrid SDM models are accounting for biases caused by source/sink dynamics.
Effects of dispersal on local abundance
Dullinger et al. (2012) allowed seeds arriving from elsewhere to contribute to the local
population. While it is less clear that Keith et al. (2008) did the same, they likely did.
Population cycles
Cabral et al. (2013) used a model that would allow density feedback cycles; it is not clear that
this is true for other hybrid SDMs.