A total of 16 climate variables were incorporated to train species distribution models. 

These variables include:

Directly calculated annual variables:  

 MAT: mean annual temperature (°C)

 MWMT: mean warmest month temperature (°C)

 MCMT: mean coldest month temperature (°C)

 TD: temperature difference between MWMT and MCMT, or continentality (°C)

 MAP: mean annual precipitation (mm)

 AHM: annual heat-moisture index (MAT+10)/(MAP/1000))

 SHM: summer heat-moisture index ((MWMT)/(MSP/1000))   

Derived annual variables:  

 DD<0 (or DD_0): degree-days below 0°C, chilling degree-days

DD>5 (or DD5): degree-days above 5°C, growing degree-days

PAS: precipitation as snow (mm). For individual years, it covers the period between August in the previous year and July in the current year

 EMT: extreme minimum temperature over 30 years (°C)

 EXT : extreme maximum temperature over 30 years (°C)

 CMD: Hargreaves climatic moisture deficit (mm)

 RH: mean annual relative humidity (%)

 CMI: Hogg’s climate moisture index (mm)

The modelling for this project was split into two distinct models, the first (deep neural network 1) is a land cover model used to add additional variables to the species model, and reclassify anthropogenically modified land cover, this model was created by my colleague Nicholas Boyce. 

The second model was split into two related models, the first of which (deep neural network 2a) was a presence/absence model (probability of species being present), and the second (deep neural network 2b) predicts species frequencies using only inventory plots where the species was observed as present.

Land Cover Modelling with Deep Neural Networks:

As additional predictor variables, I used the output from the predictive land cover model provided by Boyce (2025, unpublished). Briefly, MODIS land cover classification data was used as a dependent class variable to train a deep neural network, except agriculture and urban classes were omitted from the training process. Predictor variables used included 14 climate and 12 topographic variables, and the model was then applied to the same variables for the same area, replacing agriculture and urban classes with the landcover class (other than agriculture and urban) that had the highest probability according to the neural network. The probability of a specific land cover type, e.g. the probability of deciduous forest coverer, was then used as additional predictor variables for individual tree species models. This model output land cover proabilities for 19 land cover classifications, which were used as 19 additional predictor variables, the removal of built-up and agricultural land allows the species models to act as habitat suitability maps, reflecting where a species' range may have been cut short due to anthropogenic activity.

Species Frequency Modelling with Deep Neural Networks: 

To predict species frequency across North America, we implemented a two-part zero-inflated modeling framework (DNN 2a and 2b), commonly referred to as a hurdle model (Zuur et al., 2009, Martin et al. 2005). This modelling approach addresses the prevalence of 0's in species frequency data. 

The first model (DNN 2a) is a binary classifier: This model tells us whether a species is likely to occur or not, it gives us the probability of occurence. 

The second model (DNN 2b) predicts species frequency, but is trained on only plots where the species has observed presence. 

The results were then combined through simple multiplication, which has given the best reflection of true species distributions.

Sampled climate data (from ClimateNA), topographic data (from DEMs), and land cover probabilities were paired with aggregated forest plot data (from U.S. and Canadian National Forest Inventories) to train the Deep Neural Networks. It then predicted species frequencies based on the trainging data onto interpolated ClimateNA data at a 5km resolution across North America.

Training data: Aggregated forest inventory sample plots with matched predictor variables.

Prediction: The model was run with the known species frequency data from the plots and then predicted onto the 5km spaced points covering North America; giving continent wide frequency predictions. 

Output: Predicted species frequencies were then rasterized and maps of species distributions and frequencies were created for the most prevalent North American species.

These maps indicate where species are most likely to occur under current conditions, helping validate forest inventories, inform seed selection, and better understand habitat suitability.