Introduction

Protected areas (PAs) are ecosystem-scale management tools aimed at mitigating the impacts of anthropogenic disturbance on the natural world and preserving culturally and ecologically important landscapes1,2. For PAs to achieve their goal of protecting biodiversity and ecosystem function, it is essential that they be placed in areas where they will have maximal benefit2. To this end, the International Union for Conservation of Nature (IUCN) recommends that PAs should be created "to achieve the long-term conservation of nature with associated ecosystem services and cultural values”3. While ‘long-term conservation’ is at the heart of the PA concept, this aim is increasingly being challenged by human-induced climate change4,5,6,7,8. The conservation challenges posed by climate change are so pronounced that some estimates predict that as few as 8% of PAs will remain effective by the end of the century9. There has thus been a growing volume of calls for the design of a forward-looking, climate-ready network of PAs8,10,11,12.

From the perspective of PA planning, climate change is expected to result in three broad shifts away from the current climate: a change in the mean, a change in the variance, and a change in symmetry13,14. Though changes in mean conditions can certainly have a pronounced impact on the effectiveness of PAs7,9, the second behaviour, a change in the variance (here termed “stochasticity”), brings a unique set of challenges that species must respond to15. As local conditions become more variable, the frequency of extreme weather events such as droughts, floods, or fires increases16,17,18 and phenologies become less predictable19. High levels of environmental stochasticity can reduce population growth rates20, drive phenological changes in life history events21,22, compromise food security23,24, reduce body sizes25,26, and even alter species’ behaviour27,28. It is therefore unsurprising that environmental variability has been associated with increased extinction risk, at both the population29,30, and species levels31,32,33,34,35. Indeed, negative responses to extreme weather events are so widespread that they have been recorded in 57% of all known species36. Considering these factors, the identification of relatively stable, low-variance regions should be an important consideration in the design of a network of PAs that is resilient to stochastic changes. Yet, while mentions of less-predictable weather and extreme events are becoming more frequent in public discourse and conservation research alike36,37, environmental variability is still rarely incorporated into PA research38,39.

We address this knowledge gap by estimating environmental stochasticity across Canada and assessing its relationship with species richness, and Canada’s network of PAs. The impacts of climate-change and the consequential increase in environmental stochasticity will be particularly important for Canada. As the second largest country in the world, Canada contains ca. 25% of the world’s intact wilderness40 and has currently protected ca. 13.8% of its terrestrial area through a ca. 1,360,000 km2 network of 13,042 PAs41. Canada’s large network of PAs is thus of particularly high global relevance40. Yet, as a northern country, Canada’s ecosystems are at a disproportionately greater risk to the effects of future climate change, with some regions forecasted to warm by more than twice the global average42,43,44. Indeed, a recent synthesis found that climate change is already negatively impacting as many as a third of Canada’s COSEWIC-listed species45. While Canada has signed onto the Kunming-Montreal Global Biodiversity Framework (i.e., the 30 by 30 initiative, see ref. 46), and is therefore expected to more than double the total amount of area protected by 2030, climate change poses a challenge to the efficacy of Canada’s PAs43. The effective use of existing PAs and the designation of new PAs will thus require a better understanding of how susceptible Canada’s wildlife and PAs are to environmental stochasticity and what areas might be well-suited for future protection.

In this study, our four main objectives are to: (i) estimate the spatially-explicit environmental variability across terrestrial Canada; (ii) use these estimates to assess environmental stochasticity within Canada’s network of PAs; (iii) assess the relationship between environmental stochasticity and both species richness and extreme temperature events in Canada; and (iv) identify areas that are productive, stable, and well-suited for future protection. We use more than four decades of remotely sensed Normalized Difference Vegetation Index (NDVI;47) data and Generalised Additive Models (GAMs;48) to model and map spatially-explicit, long-term trends in both the mean and variance in environmental productivity across Canada. Importantly, environmental stochasticity represents the unpredictable, stochastic variation that remains after accounting for both inter-annual and seasonal trends in mean conditions. Without first de-trending the mean, an estimate of the variance in NDVI values would primarily capture seasonal trends (see e.g., refs. 49,50). Thus, we leveraged the flexibility and interpretability of GAMs to quantify both the seasonal cycles in NDVI as well as the complex, large-scale trends across space and time. The model residuals then provided a measure of how observed NDVI values deviated from the mean, with the variance of the residuals thus capturing how stable or unstable ecosystems are over time. NDVI is a remotely-sensed indicator of photosynthetically active biomass with values that range between −1 and 147, where values close to 1 indicate lush vegetation, values around 0 indicate land with little or dry vegetation (rock, sand, snow, or ice), and values between 0 and −1 typically correspond to water. NDVI is a well-supported indicator of ecosystem productivity51,52 that has been found to correlate positively with both plant and animal species richness53,54,55. In the context of climate change, in regions where vegetative greenness is high and stable, enhanced evapotranspiration and shading have been shown to have a buffering effect on temperature and lower the risk of extreme temperature events56,57. NDVI has also been demonstrated to be strongly correlated with temperature and precipitation51,54,58,59, and extreme weather can leave a lasting signature on a region’s NDVI60,61. Spatially-explicit estimates of the variance in NDVI are thus a useful measure of local ecosystem stability and the impact of prevailing weather conditions on ecological systems and biodiversity. The resulting spatial layers help serve as screening tools for identifying priority areas for protection. To this end, we identify candidate areas by adopting 30% thresholds of stability, productivity, species richness, and extreme temperature events to reflect Canada’s commitment to the Kunming-Montreal Global Biodiversity Framework and protecting 30% of its terrestrial area by 2030. Although this study is focused on environmental variability and PAs in Canada, both the overarching framework and the modelling approach can be readily applied to other regions and used by the organisations tasked with stewarding nature throughout the world.

Results

Spatiotemporal trends in mean NDVI

When modelling seasonal and long-term patterns in greenness across Canada, the GAM explained 84.7% of the deviance in NDVI and estimated substantial spatial and temporal variation (Fig. 1). Mean annual NDVI fluctuated across years, with a sharp and rapid decrease near the switch from AVHRR to VIIRS sensors in 2014 (Fig. 1B), but the change was small relative to the change in mean NDVI within years (Fig. 1C). Seasonally, the model-estimated mean NDVI was lowest in winter, increased in spring and peaked mid-summer before decreasing in fall (Fig. 1C). Mean NDVI also varied substantially across the fifteen ecozones (Fig. 1D). The Atlantic Maritime, Mixedwood Plain, and Boreal Shield ecozones had some of the highest mean NDVI values, whereas the more northern ecozones (e.g., Arctic Cordillera, Northern Arctic, and Southern Arctic) had the lowest mean NDVI values.

Fig. 1: Modelled trends in NDVI across terrestrial Canada.
figure 1

A Depicts the spatially explicit mean NDVI between February 1981 and June 2025, as estimated from the Generalized Additive Model. B Depicts the model-estimated mean annual NDVI across Canada both within and outside of protected areas (PAs) for the 44-year period between 1981 and 2025. The vertical line indicates the switch from AVHRR to VIIRS sensors at the beginning of 2014. C Shows the model estimated mean NDVI across Canada for each day of year, both within and outside of protected areas. The 95% confidence intervals in (B, C) are so thin as to be hidden under the lines. The boxplots in (D) show the fitted mean NDVI across terrestrial Canada between February 1981 and June 2025 within and outside of protected areas in each of Canada’s 15 ecozones. All values were estimated at a 0.1∘ spatial resolution and then projected using the Canada Albers projection (ESRI:102001).

Full size image

In terms of environmental productivity in Canada’s PAs, the long-term trends suggest that, historically, NDVI was significantly higher in PAs than outside of them on average. Since ca. 2015, however, there has been a shift such that mean NDVI has become lower inside of PAs as compared to outside of them. However, the absolute difference was very small (<0.003), and this trend was not consistent across ecozones (Fig. 1D). Many regions had comparable levels of productivity within and outside of PAs, but others, such as the Boreal, Montane, and Taiga Cordilleras as well as the Hudson Plain, had substantially lower average NDVI inside of PAs. Average seasonal trends also appeared to be relatively consistent within and outside of PAs (Fig. 1C).

Spatiotemporal trends in the variance in NDVI

As with the mean, the variance in NDVI exhibited marked spatial and temporal variation (Fig. 2). Notably, there was a strong positive correlation between the mean and variance in NDVI (ρ = 0.728, P < 2.2 × 10−16; Fig. S3). The median ecozone-specific variance in NDVI ranged from near 0 to ca. 0.02, where a variance of 0.02 corresponds to a standard deviation of  ≈ 0.14 away from the mean NDVI expected under normal phenological patterns (Fig. 2D). Or, seen another way, at any point in time the greenness in ecozones such as the Arctic closely matched seasonal phenology, whereas in others, such as Canada’s montane or maritime ecozones, marked deviations from expected phenology were common. We also found that areas with higher mean NDVI (Fig. 1A) displayed greater variance (Fig. 2A), such as the Montane Cordillera, Boreal Plains, Boreal Shield, and Atlantic and Pacific Maritime ecozones. In addition to exhibiting strong spatial patterns, we found that the variance in annual NDVI across Canada has been steadily increasing since 1981, and that VIIRS data showed greater variance than AVHRR data (Fig. 2B). The seasonal cycle in the variance was similar to the seasonal trend in NDVI but offset by a season. NDVI variance was lowest in early spring, high in summer, and peaked in fall before decreasing again in winter (Fig. 2C). Across ecozones, there were no clear differences in the variance within versus outside of protected areas (Fig. 2D).

Fig. 2: Variance in NDVI across terrestrial Canada.
figure 2

A depicts the long-term variance in NDVI across terrestrial Canada. Values were constrained to the 99.8th percentile (0.04) for ease of visibility. Show the average variance in NDVI across Canada within and outside of protected areas over the years (B) and over day of year (C). Error bars indicate ±1 standard error, while the vertical line in (B) indicates the switch from AVHRR to VIIRS sensors at the beginning of 2014. Note that 2025 only had data until May 7th (127th day of year). The trends were estimated using Generalized Additive Models on the point estimates in the figures and should only be used for ease of visualization. The two points with estimated variance > 0.2 in panel B are for 2004. The boxplots in D show the variance in NDVI within and outside of protected areas in each of Canada’s 15 ecozones. All values were estimated at a 0.1∘ spatial resolution before projecting using the Canada Albers projection (ESRI:102001). For intuition, a variance of 0.02 corresponds to a standard deviation of ≈0.14 from expected phenology.

Full size image

Environmental stochasticity and species richness

While average conditions alone explained 77.2% of the deviance in species richness, a likelihood ratio test indicated that accounting for the variance in NDVI significantly improved the model’s fit to the data (ΛGLRT = 33.7, P < 2.2 × 10−16). As expected, there was a positive relationship between species richness and mean NDVI (Fig. 3A), however, there was also a strong, negative relationship between species richness and the variance in NDVI (Fig. 3B). There was also an interactive effect, such that species richness was estimated to be highest in regions with both a high mean productivity and low variance around that mean (Fig. 3C). In other words, high levels of environmental stochasticity were negatively related with species richness, with a particularly strong impact in highly productive ecosystems (see the upper right corner of the surface plot in Fig. 3C). Sensitivity analyses on the influence of measurement scale and the choice of richness data on these findings are presented in Appendix S1.

Fig. 3: Environmental productivity and stochasticity both affect species richness in Canada.
figure 3

The first two panels depict the model-estimated relative change in species richness with mean NDVI A and variance in NDVI B across terrestrial Canada, such that values >1 are “X” times above average and <1 are “1/X” times below average. The surface plot in C shows the interactive effect of mean NDVI and variance in NDVI on species richness. The grey areas in C represent regions of the parameter space that was insufficient data to generate reliable predictions. For visual clarity, values above 300 in C are set to 300. The shaded area in A, B depicts the 95% confidence intervals.

Full size image

Environmental stochasticity and extreme temperature events

We identified a total of 1,747,106 (13.0%) of the 1981–2024 monthly average temperatures across Canada as extreme, relative to the distribution of values between 1901 and 1980. The number of extreme months at any location ranged between 24 (4.5%) and 164 (31.1%) extreme months, out of 528 total months. Extreme temperatures occurred more often in the Arctic, Taiga, and northern Boreal Shield (Fig. S4A). There was a fairly pronounced, non-linear, bivariate relationship between the frequency of extreme temperature events and the mean and variance in NDVI (Fig. S4B). We observed a peak in extreme-temperature events when long-term mean NDVI was near 0.05, and NDVI variance was near 0.01. A secondary peak in extreme events was also present for mean NDVI near 0.15 and variance near 0.05, but there was little data to support the trend.

The GAM estimated strong and significant (P < 2.2 × 10−16; Fig. 4) nonlinear relationship between the number of extreme-temperature months and both mean NDVI and variance in NDVI. Again, the estimated number of extreme-temperature months peaked at NDVI values near 0.05 and variance in NDVI near 0.01. The number of months more than doubled as NDVI increased from −0.1 to 0.1 before decreasing to similar levels at NDVI ≈ 0.4. The frequency was approximately constant for mean NDVI between 0.4 and 0.6. Similarly, the number of extreme months increased rapidly for variance in NDVI < 0.01 but remained relatively similar for variance in NDVI > 0.01.

Fig. 4: Environmental productivity and stochasticity both covaried with the number of extreme-temperature months in Canada from 1981 to 2024.
figure 4

The first two panels depict the model-estimated relationships between the number of events and mean NDVI (A), and event frequency and variance in NDVI (B) across terrestrial Canada. The surface plot in (C) shows the estimated bivariate relationship of mean NDVI and variance in NDVI with the number of extreme temperature events. The grey areas in (C) represent regions of the parameter space that was insufficient data to generate reliable predictions. Note that the estimated relationships are not estimates of causal effect of NDVI on event frequency. The shaded area in (A, B) depicts the 95% confidence intervals.

Full size image

Productivity, stability, and future protected area planning

In light of Canada’s commitment to protect 30% of its terrestrial area by 2030, our three analyses of the best percentiles of NDVI mean, variance, and coefficient of variation yielded insight into areas worthy of consideration for future protection. Overall, this analysis indicated a strong discrepancy between current PAs and the most productive and stable habitats (Fig. 5).

Fig. 5: Mean and variance in NDVI can be used together to identify areas of interest for protection.
figure 5

The six maps indicate the protected areas in Canada as of 2024 A and the 30th percentiles containing the highest mean NVDI (B), the lowest variance in NDVI (C), the lowest coefficient of variation in NDVI (D), the highest species richness based on the IUCN's richness data (E), and the lowest number of months with extreme temperatures (F). Note the strong concordance between D–F. For ease of readability, values in the colour bars of C, D are capped at the 99.8th and 65.7th percentiles, respectively.

Full size image

The top 30th percentile of mean NDVI (i.e., Canada’s most productive habitats) had a minimum of 0.3066 and a mean of 0.3840 (95% CI: 0.3836–0.3843). It ran largely throughout the Montane Cordillera, Boreal Shield, Boreal Plains, Mixedwood Plains, and Atlantic Maritime ecozones (Fig. 5B). However, only 9.51% of the area (281,702 km2) was contained within PAs, leaving an additional 2,681,690 km2 of high-productivity habitat available for future protection. In contrast, 15.3% (1,058,478 km2) of the bottom 70th percentile was contained within PAs.

The bottom 30th percentile of the variance in NDVI (i.e., Canada’s most stable habitats) had a maximum of 0.008296 and a mean of 0.005419 (95% CI: 0.005405–0.005434), and was found mostly in Canada’s Arctic and Prairie ecozones, with some small areas scattered across the rest of the country (Fig. 5C). Again, only 12.8% (377,989 km2) was contained within PAs, leaving an additional 2,963,392 km2 of low-variance habitats available for future protection. In the top 70th percentile, 13.9% (962,191 km2) was contained within PAs.

Our third approach relied on the coefficient of variation to identify Canada’s most stable regions relative to the local, long-term mean. Since the coefficient of variation tended to infinity as NDVI approached zero, we set all negative coefficients of variation (i.e., for NDVI < 0) to infinity for this analysis. The bottom 30th percentile had a maximum of 0.3731 and a mean of 0.3113 (95% CI: 0.3110–0.3115), and it mainly included the Boreal Shield, Boreal Plains, Mixedwood Plains, and Atlantic Maritime ecozones. Once more, only 8.56% (253,811 km2) of the area was contained within PAs, leaving an additional 2,709,580 km2 available for future protection (Fig. 5D). In the top 70th percentile, 15.7% (1,086,369 km2) was contained in PAs.

The areas with the highest mean NDVI and lowest coefficient of variation tended to have the highest species diversity and lowest frequency of months with extreme temperatures (Fig. 5E, F). The upper 30th percentile of the IUCN’s species richness ran primarily along Canada’s southern border. Of this, 12.4% (367,333 km2) was contained within PAs, leaving an additional 2,596,059 km2 available for future protection. In contrast, in the lower 70th percentile, 14.1% was currently contained within PAs. The bottom 30th percentile of months with extreme temperatures was mainly throughout southern and Western Canada, but also included a substantial portion of the Western Arctic. Of the bottom 30th percentile, 11.7% was protected, while 14.4% of the remainder of Canada was within PAs.

Discussion

Identifying productive yet stable habitats that are buffered against high levels of environmental stochasticity should be an essential component of the establishment of a climate-ready network of PAs11. Our results support this need by mapping out the spatially-explicit variability in NDVI, modelling its relationship with both species richness and extreme-temperature events, and identifying regions that are currently underrepresented within Canada’s network of PAs. Our findings indicate that large tracts of Canada’s most productive and relatively stable habitats are currently underrepresented within the country’s network of PAs. For example, our analysis identified 2,709,580 km2 of currently unprotected land in the lower 30th percentile of the coefficient of variation in NDVI. This finding was not overly surprising, given the historical tendency to establish PAs in locations that were remote, at high elevation, and with low species richness or capacity for economic exploitation62. Nonetheless, our results indicate that Canada’s PAs may be particularly susceptible to the increase in stochastic weather events and climate patterns that have been observed across the world in recent decades31,63 and are also supported by our analyses (Fig. 4 and Fig. S4). Establishing new PAs within the areas we identified as being amongst Canada’s most productive and stable could improve Canada’s capacity to conserve species and ecosystems in the face of rapid, human-induced climate change14,63.

Our study reinforces that vegetative productivity, as measured through NDVI, is a key driver of species richness across Canadian ecosystems51,64,65. Consistent with ecological theory, areas with higher mean NDVI generally support greater richness, as enhanced primary productivity and resource availability sustain more diverse communities66. Yet, there is far more complexity to ecosystems than average conditions. From a theoretical perspective, stochastic environmental variation, in particular, has long been recognised to shape and constrain species’ life histories67,68,69,70. Our results highlight empirically that ecosystem stability, here measured through the variance in NDVI, is also an important factor in driving ecosystem-scale processes. While some heterogeneity can provide niche opportunities that promote biodiversity71, we found that high temporal stochasticity was associated with reduced richness. Notably, neither mean conditions nor stochasticity operated in isolation. We found an interactive effect such that species richness was highest in regions with high mean NDVI and low variance. Together, these findings suggest that both the magnitude and the stability of vegetation productivity should be considered when assessing biodiversity patterns in Canada. A note of caution is warranted here, however; the relationships uncovered in this study are only as robust as the data supporting them. Our richness modelling was based off of the IUCN’s richness data, which calculate richness from species-level expert range maps72. At large geographic scales, these data tend to be directionally consistent with more nuanced methods that incorporate habitat preferences73. At more local scales, however, the IUCN-based range maps can systematically over-estimate species richness, particularly where local habitat suitability is poor74. For instance, a recent analysis found that, on average, area of habitat range maps covered only 66 ± 28% of the area within the IUCN range maps for mammals and 64 ± 27% for birds75. While the overarching patterns identified in this study can be considered directionally accurate (see Appendix S1), the exact shape can differ with the underlying data. This can result in a biased understanding of the role of ecosystem productivity and stochasticity in shaping local patterns of species richness, and future work into both the nuances, and mechanisms underlying the richness trends identified in this study is clearly warranted.

Alongside the species richness trends, the relationship between extreme-temperature months and mean and variance in NDVI we identified suggests that areas of low mean NDVI and low variance in NDVI, primarily the northern and arctic regions of the country, are particularly susceptible to extremes in temperature. As extremes in temperature increase compared to baseline historical conditions, particularly in regions with low productivity and low variation in productivity, these results further highlight the importance of considering both mean and variance together. As Canada moves forward with its goal of increasing protected area coverage46 in the face of climate-driven changes in vegetation dynamics, the framework established in this study offers a flexible and informative way to assist in identifying a balance between environmental productivity and stability across spatial and temporal scales. While this work provides insight into the role of environmental stochasticity in shaping species richness, it also raises an important question: should we protect more stable regions as they support greater biodiversity, or those with more extreme events because they are already under greater stress? Answering this question is beyond the scope of this work, but it is an important aspect of conservation planning that requires local considerations and striking a balance between near-term versus long-term threats.

In terms of a path forward for establishing a climate-ready network of PAs, Canada is well-positioned to establish PAs in the remote northern landscapes where many of the country’s largest PAs already exist. While expanding the northern PA network remains important in the face of climate change and Arctic amplification (i.e., rapid Arctic warming relative to lower latitudes76,77,78), our results highlight that southern latitudes contain some of the most important areas for conserving Canada’s biodiversity. However, protecting southern regions presents more of a challenge to decision makers, as this is where the majority of the anthropogenic pressures from urban and industrial activity occur. Although PA establishment is generally supported by the public79, it has long conflicted with resource-extractive, agricultural, and other industries80. Additionally, Canada’s growing population, and corresponding increase in urban development present challenges to the establishment PAs in the priority areas identified in our analyses, especially near major urban centres81. Consequently, smaller, more fragmented PAs are more common in the south (Fig. 6). PA establishment has also become increasingly politicized, with attention fluctuating as priorities shift with changing governments82. Given these competing interests, our results are intended to help local, regional, and national governmental organisations prioritise PA creation in contested regions. In particular, the regions that combine a low NDVI coefficient of variation, high species richness, and a low frequency of extreme temperature events could provide ideal targets for future protection. An important caveat is recognising the colonial history associated with the establishment of PAs83. Although our analyses help identify locations that warrant consideration for protection, their inclusion into Canada’s network of PAs will require local stake-holder approval, as well as collaboration with local Indigenous communities, governments, and land stewards. Thus, while this work represents an important starting point for integrating environmental stochasticity into conservation planning, it should not be the sole guide in decision making. Instead, we recommend our findings be used to identify areas where more local efforts should be directed. In addition, it is important to emphasize that we do not intend to suggest that areas outside of the stable and productive habitat here identified are not worthy of protection. PAs are established for a range of conservation needs, and broad-scale factors such as those utilized here should be considered alongside local, and/or species-specific priorities. For instance, the ca. 200,000 ha Klinse-za/Twin Sisters PA in Northern British Columbia was established in 2024 to recover culturally important caribou populations through a partnership between the West Moberly and Saulteau First Nations, and the federal and provincial governments. While the Klinse-za/Twin Sisters PA is not contained within any of the priority areas identified in this study (Fig. S5), it is a valuable addition to Canada’s network of PAs and represents an important step towards protecting a threatened species and supporting reconciliation with Indigenous Peoples. Thus, while priorities may differ, our framework offers a set of tools that can be used to integrate environmental variability into decision making.

Fig. 6: Maps of long-term environmental productivity along with Canada’s protected areas and ecoregions.
figure 6

Maps of the Canadian protected areas (A) and ecoregions (B). Both are shown over a raster of the long-term mean NDVI between February 1981 and June 2025, after data cleaning but before any modelling. The data are shown at the original 0.05-degree resolution but reprojected using the Canada Albers projection (ESRI:102001).

Full size image

Beyond the points mentioned above, we note three main limitations and caveats to our study. First, our focus was on NDVI, a satellite-derived proxy of habitat greenness, which does not capture the acute and direct effects that extreme weather events can have on species. Extreme weather events can alter animal behaviour84, and result in poor body condition, reduced fitness, or even death24,85,86,87. In this context, we highlight the non-linear relationships between extreme temperature events and our measures of NDVI mean and variance (Figs. 4 and S4). While our focus here was on characterising these relationships across Canadian ecosystems, our models were not designed to infer causal mechanisms linking ecosystem stability to extreme weather events. Future work disentangling the mechanisms underlying these relationships and identifying the ecological factors that link extreme-temperature zones and high-productivity/stable areas is clearly warranted, and further research should explore these relationships in greater detail. Second, our spatially-explicit estimates of the variance in NDVI represent an important first step in understanding how environmental stochasticity will impact the effectiveness and stability of Canada’s PAs, but they were temporally static. In other words, use of these maps for future planning assumes that past environmental stochasticity is predictive of future stochasticity under climate change. The steady increase in environmental stochasticity we detected, along with increasingly frequent extreme weather events14,63, suggests that changes in the spatial pattern of variance over time should not be ignored. However, simultaneously estimating and predicting changes in mean and variance can be particularly complex. Quantifying stochasticity requires careful decisions about the spatiotemporal scale at which changes are considered as trends in mean conditions or stochastic events28,88,89. Location-scale models simplify this process by estimating both mean and variance under a single likelihood profile90, but their computational complexity can result in prohibitive fitting times, especially for datasets across large spatial scales. Nonetheless, the modelling framework applied here is flexible and can be adapted to a range of spatial scales, making it widely applicable across regions or goals. Projecting changes in the variance may thus prove more computationally and statistically feasible at smaller spatial scales. Finally, our third core limitation was that our analyses treated all PAs as identical. However, Canada has a range of different categories of PAs, including federally managed parks and reserves, provincial parks, bird sanctuaries, and Indigenous Protected and Conserved Areas41. Furthermore, PAs range dramatically in size from the 800-m2 Christie Islet Migratory Bird Sanctuary in British Columbia to the 63,000 km2 Queen Maud Gulf Migratory Bird Sanctuary in Nunavut41. Factors such as governance structure, size, age, and habitat heterogeneity are well known to influence the effectiveness of PAs4,91,92,93, so further research should assess how the different characteristics of PAs impact their effectiveness at buffering environmental stochasticity.

As noted in the introduction, climate change is expected to cause shifts away from the local historical mean, variance, and symmetry13,14. While our focus here was on the combined influence of the mean and variance, the importance of changes in asymmetry, or ‘skewness’ of the distribution should not be discounted. In the context of future climate change, a change in symmetry would result a greater shift towards one side of the distribution than the other (e.g., more wet days than dry days, or more hot days than cold days), with a potentially heavier tail. Given the clear impact of environmental stochasticity we documented here, studying species and ecosystem-scale responses to skewness represents an important avenue for future research. However, an important caveat here is that accurately quantifying spatially-explicit skewness will require accurate, spatially-explicit estimates of both the mean and variance, as any bias in the estimation of the first two statistical moments, which determine the mean and variance, will propagate into the estimates of the third moment, on which the estimate of skewness depends.

The conservation challenges posed by climate change are pronounced7,9,35 and should not be tackled via PAs alone4. However, safeguarding wildlife and ecosystems into the future will require proactive, forward-thinking conservation strategies94, and recent global initiatives aimed at increasing PA coverage offer a unique opportunity to address the need for a forward-looking climate-ready network of PAs8,10,11,12. Canada’s pledge to protect 30% of its terrestrial and marine habitat by 2030 as part of the Kunming-Montreal Global Biodiversity Framework (i.e., the 30 by 30 initiative) highlights the country’s intention to protect biodiversity, but extensive work is still necessary to achieve the targets. With only 13.8% of its terrestrial area currently contained within PAs, Canada will need to protect an additional 1.7 million km2 over the next four years. Our analyses support this goal by identifying large tracts of currently unprotected land worthy of consideration for future PAs. Findings such as those presented here will help inform Canada’s decision makers so that they may improve protected areas’ effectiveness and resiliency to a changing climate and increasingly stochastic environmental conditions. As we respond to and prepare for a world that is impacted by climate change and more frequent stochastic and extreme events, quantifying changes in both mean conditions and the variance around them is essential for ensuring that the planet’s ecosystems and the species within them can persist for decades to come.

Methods

Data acquisition and processing

Our study area consisted of the entirety of Canada’s ca. 9,984,670 km2 terrestrial area (Fig. 6). All analyses were conducted in R (v. 4.4.0;95) using open-source data. The scripts are openly available via GitHub at https://github.com/QuantitativeEcologyLab/stochasticity_parks. Data on Canada’s PAs as of the end of 2024 (Fig. 6A) were obtained from the Canadian Protected and Conserved Areas Database41. Marine PAs were removed prior to analysis, resulting in a set of 13,042 PAs that were included in our analyses. Data on Canada’s 15 terrestrial ecozones (Fig. 6B) were obtained from the Canada National Ecological Framework database96. Species richness data were obtained from the International Union for Conservation of Nature (IUCN) Red List of threatened species72. A digital elevation model was downloaded using the R package elevatr97 at an original resolution of 0.03∘ (z = 4). All rasters were cropped and masked to Canada’s terrestrial land borders, and major lakes and rivers were masked using a public shapefile of water bodies provided by Esri and Garmin International, Inc.98. However, since many water bodies were smaller than a pixel and water biases NDVI towards −1, we rasterized the shapefile at a 0.05∘ scale to estimate the proportion of each pixel within a water body. We excluded from analyses all cells with 40% or more area covered by water. Additional details are provided in the section on statistical modeling below.

To estimate and map changes in phenology and environmental stochasticity across Canada, we obtained NDVI data collected via the Advanced Very High Resolution Radiometer (AVHRR;47) and Visible Infrared Imaging Radiometer Suite (VIIRS;99) sensors47. These data have been collected at a daily resolution since 1981, at a 0.05∘ spatial resolution, and are openly available47,99. We downloaded daily global NDVI data between 1981-06-24 and 2025-06-07 from the NOAA website using the R package rvest (v. 1.0.4;100). Using the R package terra (v. 1.8-54;101), 16,024 rasters were cropped and masked to terrestrial Canada, and cloudy pixels were removed using each raster’s quality assurance layer. The rasters were then converted to a data frame after aggregating to a 0.1∘ spatial resolution to reduce computational demands. Finally, each row was annotated with its year, day of year, elevation, proportion of the pixel covered by water, and a binary variable indicating whether the pixel was mostly in a PA or not. This resulted in a dataset of 587 million unique NDVI observations.

Statistical modelling

Spatiotemporal trends in the mean and variance in NDVI

Environmental stochasticity, σ2, represents the unpredictable, stochastic variation that remains after accounting for predictable, long-term, and seasonal trends in mean conditions, μ. Our aim was to estimate, for any location \(\overrightarrow{u}\) across Canada, the variance in NDVI – denoted as \({\sigma }^{2}(\overrightarrow{u})\) to indicate that variance in NDVI was a function of the vector of spatial coordinates \(\overrightarrow{u}\). Estimating \({\sigma }^{2}(\overrightarrow{u})\) thus required a model that could accurately describe seasonal and inter-annual trends in the average NDVI over both time, t, and space, which we denote as \(\mu (t,\overrightarrow{u})\). To this end, we fit a Generalized Additive Model (GAM), using the bam() function from the mgcv package (v. 1.9-4;102), with the smoothness parameters estimated via fast Restricted Maximum Likelihood (fREML;103). Since the observed NDVI values ranged from -0.1 to 1, they were scaled to the interval [0, 1] via the linear transformation

$$Y=(({{{\rm{NDVI}}}}+0.1))/1.1\,,$$
(1)

in order to use a beta distribution with a logit link function.

The model predictors included smooth terms for space (i.e., latitude and longitude), year, day of year, elevation (m), and the proportion of water in a raster cell. To account for spatial differences in long-term and seasonal trends, the model included tensor product interactions between space and year as well as space and day of year. A tensor product interaction term between year and day of year was also included to account for changes in seasonal trends over the years. Finally, to estimate the difference in long-term and seasonal NDVI between protected and unprotected areas, we included a “by” smooth of year and day of year with a dummy variable representing whether the pixel was mostly inside (1) or outside (0) a protected area as of 2024 (section 7.2.5 of48). The final model for the mean thus had the form:

$$Y \sim \; \; {{{\rm{Beta}}}}(\mu ,\phi )\\ \eta \; = \; {{{\rm{logit}}}}(\mu )\\ \eta \; = \; {\beta }_{0}+{f\!\!}_{1}(lat,long)+{f\!}_{2}(year)+{f\!\!}_{3}(doy)+{f\!\!}_{4}(elevation)+\\ {f\!\!}_{5}(water)+{f\!\!}_{6T}(year,doy)+{f\!\!}_{7T}(lat,long,year)+\\ {f\!\!}_{8T}(lat,long,doy)+{f\!\!}_{9D}(year,PA)+{f\!\!}_{10D}(doy,PA),$$
(2)

where Y indicates the observed value of scaled NDVI, which follows a Beta distribution with mean μ and scale parameter ϕ, and the linear predictor (η) is a sum of the model intercept (β0) and smooth functions fj() of spatial coordinates \(\overrightarrow{u}\)(lat and long), integer year (year), day of year (doy), elevation above sea level (elevation; m), the proportion of the pixel covered by water (water), and the PA dummy variable as defined above. Tensor product interaction terms are indicated with fjT(), while functions fjD() indicate the terms estimating differences between protected and non-protected areas. Additional details on the smooth terms are provided in Table S1.

We then estimated the temporally constant \({\sigma }^{2}(\overrightarrow{u})\) using the residuals in NDVI, defined as the difference between the observed NDVI values and the (back-transformed) estimated mean NDVI:

$${\epsilon }_{i}={{{\rm{NDVI}}}}_{i}-\widehat{\mu }({t}_{i},{\overrightarrow{u}}_{i})={{{\rm{NDVI}}}}_{i}-(\widehat{{\mathbb{E}}}({Y}_{i})\times 1.1-0.1)$$
(3)

for the ith row of the dataset. To minimise the impact of any spatial bias in the estimated mean (Fig. S1), we estimated \({\sigma }^{2}(\overrightarrow{u})\) as the the variance of the residuals using the var() function from R. Therefore, for each location \(\overrightarrow{u}\) across all times t, indicated as the set \({\mathbb{U}}\) of size \({n}_{{\mathbb{U}}}\), the estimated variance was:

$${\widehat{\sigma }}^{2}(\overrightarrow{u})=\frac{1}{{n}_{{\mathbb{U}}}-1}{\sum }_{{\epsilon }_{i}\in {\mathbb{U}}}{\left({\epsilon }_{i}-\frac{1}{{n}_{{\mathbb{U}}}}{\sum }_{{\epsilon }_{i}\in {\mathbb{U}}}{\epsilon }_{i}\right)}^{2}$$
(4)

The final products of this modelling effort were two temporally static but spatially explicit maps of the estimated long-term mean and variance in NDVI across Canada between 1981 and 2025.

Environmental stochasticity and species richness

Using the estimates described above, we explored the effects of the mean and variance in NDVI on species richness in Canada. After annotating the IUCN’s species richness dataset with the estimated mean and variance in NDVI (n = 279,618), we fit another GAM using mgcv’s bam() function and smoothness parameters estimated via fast Restricted Maximum Likelihood (fREML). Because the IUCN’s richness data (here indicated as R) represent the mean richness across an area (i.e., real numbers  > 0), we assumed R followed a gamma distribution with a log link function. The predictors included smooth terms for mean NDVI, the variance in NDVI, and a tensor product interaction term between the mean and variance in NDVI. The model thus had the form:

$$Y \sim \; \; {{{\rm{Gamma}}}}({\mu }_{R},{\phi }_{R})\\ \eta \; = \;\log ({\mu }_{R})\\ \eta \; = \; {\beta }_{0}+{f}_{1}(\widehat{\mu }(\overrightarrow{u}))+{f}_{2}(\widehat{{\sigma }^{2}}(\overrightarrow{u}))+{f}_{3T}(\widehat{\mu }(\overrightarrow{u}),\widehat{{\sigma }^{2}}(\overrightarrow{u})),$$
(5)

where, again, f1() and f2() indicate smooth functions and f3T() indicates a smooth tensor product interaction term. We removed 257 points (0.09%) with var(NDVI)  > 0.04, since their high leverage resulted in substantial model instability. Additional details on the smooth terms are provided in Table S2. To quantify the impact of environmental stochasticity on species richness, we also fit a simpler model that excluded the smooth effect of the variance in NDVI and the tensor product interaction term, and we compared the models via a generalised likelihood ratio test.

Because the IUCN species richness data are derived from probable as opposed to observed occurrences, they can deviate from more robust methods such as range maps derived from Area of Habitat (AoH) rasters, or species distribution models (SDMs;73,74). In turn, this can impact any macro-ecological trends studied via these data. Although more robust richness data are preferable, they were not available for Canada beyond mammals and birds (see e.g., refs. 72,75). Thus, while the IUCN species richness data can exhibit spatial biases, they represent the most taxonomically complete species richness data available for the country. We address this concern in the Supplementary Methods, where we evaluate the sensitivity of our species richness trends to both the spatial scale at which the analyses were carried out, as well as the choice of underlying richness data. To assess the impact of scale, we systematically coarsened the species richness and environmental co-variate rasters from the original ~5 km grid, to a  ~ 75 km grid and re-ran the richness analyses described above. To explore the impact of the underlying richness data themselves, we obtained a spatial layer of the IUCN’s standard mammalian species richness data, as well as the IUCN’s AoH mammalian richness data. The AoH raster uses habitat and elevation data to refine the raw species ranges. We then re-evaluated the effects of the mean and variance in NDVI on mammalian species richness for each of these rasters. Overall, the modelled relationships between species richness and the mean and variance in NDVI were highly conserved across the different spatial scales we assessed, and directionally consistent across the two richness datasets, however, the shape of the partial effects did exhibit some notable differences in both the strength of the relations, and inflection points. As a result, there were regions with fairly pronounced differences between the two models, particularly in the Pacific Maritime, Arctic Cordillera, and Prairie ecozones, as well as in coastal and montane ecosystems. Furthermore, we could not assess the impact of scale on the species range estimates underlying the richness data (sensu74). Thus, while the overarching patterns can be considered robust to the influence of scale, and discrepancies between different species richness datasets, exact values should be interpreted with caution.

Environmental stochasticity and extreme temperature events

To further quantify the relationship between ecosystem stability and both \(\mu (\overrightarrow{u})\) and \({\sigma }^{2}(\overrightarrow{u})\), we performed an additional analysis on the relationship between the number of months with extreme mean temperatures and the mean and variance in NDVI. While there are numerous ways of quantifying extreme temperature events, our approach was based on a framework set out in the IPCC’s Sixth assessment report14, which defines extreme temperature events as times where the temperature was above or below a percentile for the same calendar period over a base period. To this end, we obtained spatially-explicit, monthly temperature means from 1901 to 2024 using the climatenaR package (v. 1.0) and ClimateNA v7.60104 and split the data into two groups. Using data from 1901 to 1980 (inclusive), we constructed reference distributions of monthly mean temperature for each of the 12 months at each location, \(\overrightarrow{u}\). We then used data from the years with both NDVI and historical temperature data (i.e., 1981 to 2024, inclusive) to count the number of months with extreme mean temperatures, relative to the distribution from the 1901–1980 reference period. We considered temperatures to be extreme if they were below the 2.5th or above the 97.5th percentiles of the reference data for the corresponding month. While our reference period includes some amount of climate change, we opted for contrasting against a baseline as it is in line with one of the primary ways that extreme weather events are characterised across fields14.

To quantify the relationship between the number of extreme months, the long-term mean NDVI and variance in NDVI, we again fit a GAM using mgcv’s bam() function and smoothness parameters estimated via fast Restricted Maximum Likelihood (fREML). Because the number of months (here indicated as M) was count data, we assumed M followed a Negative Binomial distribution with a log link function. The predictors included smooth terms for mean NDVI, the variance in NDVI, and a tensor product interaction term between the mean and variance in NDVI. The model thus had the form:

$$Y \sim \; {{{\rm{NB}}}}({\mu }_{M},{\phi }_{M})\\ \eta \; = \; \log ({\mu }_{M})\\ \eta \; = \; {\beta }_{0}+{f}_{1}(\widehat{\mu }(\overrightarrow{u}))+{f}_{2}(\widehat{{\sigma }^{2}}(\overrightarrow{u}))+{f}_{3T}(\widehat{\mu }(\overrightarrow{u}),\widehat{{\sigma }^{2}}(\overrightarrow{u})),$$
(6)

where, again, f1() and f2() indicate smooth functions and f3T() indicates a smooth tensor product interaction term. As above, we removed 53 points (0.14%) with var(NDVI) > 0.04, since their high leverage resulted in substantial model instability. Additional details on the smooth terms are provided in Table S3.

Identification of Priority Areas

In 2022, during the 15th annual Conference of the Parties of the Convention on Biological Diversity (COP15), Canada and 195 other signatory countries pledged to protect 30% of the world’s terrestrial and marine habitat by 2030 (i.e., Kunming-Montreal Global Biodiversity Framework, also known as the 30 by 30 initiative). With only 13.8% of its terrestrial area contained within PAs as of 2024, Canada will need to protect an additional ca. 1.7 million km2 over the next 5 years to meet this commitment. To help inform this process, we used our results to identify priority areas according to five different criteria: (i) the upper 30th percentile of mean NDVI (i.e., Canada’s most productive habitats); (ii) the lower 30th percentile of the variance NDVI (i.e., Canada’s most stable habitats); (iii) the lower 30th percentile of the coefficient of variation in NDVI (i.e., Canada’s most stable habitats, relative to their productivity); (iv) the upper 30th percentile of species richness; and (v) the lower 30th percentile of extreme temperature events. The relevant percentiles for each of these approaches were calculated using the quantile() function in R. We then identified the areas within each of these percentiles that were contained within protected areas. To avoid the discontinuity in coefficient of variation as \(\mu (\overrightarrow{u})\) approached zero, we converted all negative coefficients of variation to infinity before calculating the percentiles.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.