Philippa Kaur

How rapidly can the major functional components of a soil ecosystem appear in volcanic ash?
The overall conclusion from comparing the functional composition of the developing ash-soil with natural forest soils from the same climates, is that the major biological aspects of the system have developed surprisingly quickly. Already by the 24-month and 36-month stage, the ash-soil had a similar diversity of bacterial functional genes to a forest soil (Fig. 8).
This contrasts with the findings of Fujimura et al.3, who found that ash deposited by the Miyakejima volcano still showed a very distinct and low diversity community compared to that expected of normal forest soils. This difference could be attributable to differences in the initial chemical composition of the ash: the pH value of the Miyakejima ash studied by Fujimura et al.3 was much lower than the ash we sampled, due to the persistence of acids from the initial eruption, or acidic rainfall from later outgassing. Our Sakurajima ash samples had only a slightly acidic pH (5.2) at the time of harvesting, which was similar to the average value (5.14) of 251 ash samples from Sakarajima collected from 1955 to 200125, and they remained in the 5–6 pH range at both 24 months and 36 months. Even the ash soil mesocosm samples that were situated on the lower slopes of the Sakurajima volcano, and the nearby natural forest soils at Sakurajima, remained in the pH 5–6 range and had a similar gene composition to other sites, suggesting that the area around the Sakurajima volcano is not subject to frequent highly acidic rain events. The difference between the Sakurajima ash and the Miyakejima ash hints at the importance of details of the chemical environment of the ash for determining its development into a functioning soil ecosystem.
Another factor which may explain the difference between the paths of biota development of the ash from the two volcanoes is the relative availability of propagules. Our ash soils were surrounded by developed ecosystems which could provide a rain of propagules of microorganisms and bryophytes in windblown dust or in rain splash. By contrast the Miyakejima ash field was an area of extensive ecosystem destruction. If bryophytes and lichens had not been able to establish due to unavailability of propagules, an important source of photosynthetically-fixed energy would have been unavailable to the Miyakejima system. This would have impeded the development of a decomposer food chain, of mineral weathering by organic acids and chelates, and of buffering of soil pH and water content and nutrient storage on organic matter and clay surfaces.
Was there a lower taxonomic diversity than is normally found in a developed soil?
At the broadest level, from the metagenomes, the taxonomic composition of the biota of the developing ash-soil resembled that of the developed forest soils—with archaea, fungi, protists and metazoans occurring at similar relative abundances in the ash-soils and forest soils. In this sense, the ash-soil had developed remarkably quickly in terms of the basic taxonomic framework of a functioning soil ecosystem. Bryophytes and lichens were able to establish10,26 with their propagules small enough to enter through the gauze covering, and presumably played an important role in providing carbon and extra niches to the developing ecosystem—even though they are unlikely to be as supportive of a diverse soil biota as the extensive root systems of vascular plants.
There was however—continuing a pattern seen in the 24-month results reported by Kerfahi et al.10—a lower OTU and Shannon diversity of bacteria based on the 16S rRNA amplicon sequencing. The continuing lower OTU-level 16S taxonomic diversity of the ash soils might have had multiple causes.
Firstly, limitations on dispersal and colonization of the ash soil systems might have kept OTU diversity lower. It is assumed that the biota present were mostly derived from the surrounding forest ecosystems—as windblown or rain splashed material. Dispersal limitation of soil biota is likely to play some role in all volcanic ash fields, although the existence of nearby areas of surviving ecosystem is also common20,27. Most volcanic explosions or ash fields result in no more than a few square kilometres of landscape being completely devastated, and isolated pockets of vegetation that survive are common27,28—in this respect the proximity of our mesocosms to natural vegetation may be fairly realistic. In natural ash deposits, upwards colonization by soil biota from buried ‘legacy soils’ is also possible20. In our experiment, upwards colonization from soil below the pots was not possible, and the plastic gauze covering may have prevented access by insects, birds or seeds that could have brought incidental soil biota. It is thus difficult to know for sure whether the overall role of dispersal limitation in our mesocosm systems is stronger or weaker than would generally be the case in natural ash fields. Since natural ash fields themselves are also very heterogenous in terms of area, depth and degree of devastation of natural vegetation, it is especially hard to generalise.
Secondly, the relatively extreme chemical and physical conditions of the volcanic ash itself are also likely play a major role in limiting the bacterial taxonomic diversity of the ash-soil biota in the mesocosms. Although the pH of the ash in our mesocosm systems was not extreme, it may be expected to be droughty due to low organic matter content, and low in available nutrients and organic matter that could sustain soil food chains. Even by 36 months, the organic carbon of the ash-soil was still orders of magnitude lower than in the surrounding forest soils (Supplementary Fig. S1)10,26. Thus, fewer niche types may be viable in the environment of the developing ash.
Nevertheless, although lower level taxonomic diversity of bacteria is clearly lower than in the established forest soils, the metagenome results from the ash soil mesocosms show that most higher level taxonomic groups of bacteria, archaea and eukaryotes are already present by the 24-month and 36-month stage, emphasizing that in some respects the establishment of soil biota has been rapid. While DNA of dead microorganisms blown as dust could have provided the impression of populations being present, it seems unlikely that dead material would be able to disperse in the same relative proportions as in a forest soil, to give a metagenome that resembled a developed soil in all its major groups, in roughly the same relative abundances (Please refer to Fig. 1 in Kerfahi et al.10).
Was there a lower diversity of categories of functional genes of soil biota than are normally found in a developed soil, indicating less functional complexity in the early ash-soil system?
Surprisingly, the richness and diversity of functional gene categories at Level 4 of the SEED Subsystem was not significantly different between the ash mesocosms and the forest soils. Around 97% of the metagenome reads in the ash mesocosms and the forest soil were bacterial, so the much lower OTU diversity of bacteria in the mesocosms would be expected to give a lower functional diversity of genes. The contrast between patterns of taxonomic and functional diversity in the ash mesocosms emphasises the redundancy of gene functions in soil organisms—such that losing a high proportion of taxonomic diversity apparently has no effect on functional diversity. If the level of functional gene diversity is high, this implies that in a general sense the ecosystem can potentially perform a wide variety of functions. Greater functional diversity is also considered to result in greater resilience of the ecosystem29.
We had also hypothesized that the distinct chemical environment of the developing ash would result in increased relative abundance of a number of specific gene categories:
Is there an increased relative abundance of genes (or of prokaryotic genera) associated with autotrophy (e.g. Rubisco gene, coxL gene) in the ash-soils?
We searched for potential taxa and genes which might indicate autotrophic carbon fixation through chemosynthetic oxidation processes. We found a higher relative abundance of Ktedonobacteraceae (Chloroflexi) in the ash soils compared to forest soils, which is a pattern that was also found in previous ash studies21,30. Ktedonobacteraceae is a novel taxonomic group that has only been recently added to the phylogenetic tree of Chloroflexi30,31. Their genome has been reported to be large and they are known to have a wide potential for different metabolic mechanisms32. Ktedonobacteraceae are mostly found in extreme environments, including volcanic ash and hydrothermal vents30.
We had hypothesized that the coxL (carbon monoxide dehydrogenase large chain) gene—which is implicated in autotrophy—would be more abundant in the ash soil samples. Likewise, the rbcL (ribulose bisphosphate carboxylase large chain) gene is involved in carbon fixation and we hypothesized its greater abundance in the ash-soil mesocosms. However, in fact both rbcL and coxL had higher relative abundances in the forest soils.
Although coxL has been mostly linked with chemotrophic organisms living in an extreme environment, due to its potential role for assisting heterotrophic growth in the environments lacking organic matter21,33, it is also one of the more abundant genes in natural forest soils34. Noting that natural forest is one of the largest global sinks of atmospheric CO34,35, the high relative abundance of coxL gene might be due to high abundance of CO in natural forests. Also, the coxL gene might have the potential to participate in other metabolic pathways. The presence of coxL genes in many different types of organisms (e.g. plant symbionts, animal pathogens, etc.) suggests other roles of CO-oxidation by the coxL gene33.
The higher abundance of rbcL in the forest soils in our study might be related to photosynthetic C fixation by cyanobacteria in both the forest soil and ash soils. rbcL gene also have been found in many natural forest sites. By contrast, Fujimura et al.3 found rbcL to be more abundant in developing volcanic ash soils, which might be attributable to differences in the chemical composition of ash or due to details of the mesoocosm system used in our study.
Is there increased relative abundance of genes that are associated with acquisition of nutrients from abiotic sources rather than decomposition of organic matter (e.g. nitrogen fixation genes)?
Contrary to expectations we found no differences in the relative abundance of nitrogen fixation gene (nifH) between the ash soils and forest soils. It is possible that this reflects nitrogen being relatively more limiting in the forest soils, where there is an abundance of organic carbon. It is also possible that in the forest soils, the abundance of labile carbon in the rhizosphere of N-limited plants encourages N fixing bacteria through root secretions36.
Is there increased relative abundance of stress response genes and dormancy related genes?
As hypothesized, we found that dormancy related genes were more abundant in the ash mesocosms than in the forest soils. This would seem to be adaptive in terms of survival of a well-drained ash-soil, low in organic matter, which is apt to dry out. This would depend, however, on the detailed microclimate. Field measurements suggested that in sunny conditions the microclimate in the static air in the trays in which our pots were held was generally around 0.5–1 °C higher than in the open air a meter away, although this difference disappeared in cloudy conditions and at night10. It is possible that our mesocosms (exposed in open sunlight, but covered by a gauze) would have either retained or lost moisture more easily than the soils, and that this might have affected the frequency of drying. We had also anticipated that stress response genes would be more common in the ash mesocosms. However, in this case the stress response category was less common than in the forest soil, surprisingly suggesting that at a cellular level stresses are in fact less common in the ash-soil.
Is there decreased relative abundance of cell–cell interaction related genes?
As anticipated, genes related to cell–cell interactions such as regulation and cell signalling genes and virulence, disease, and defense genes (Fig. 7a,b) were relatively less abundant in the ash mesocosms. This seems to emphasize that complex interactions are less common in the developing ash system than in a fully developed soil with its more abundant and diverse carbon sources. However, bacterial genes found as part of CRISPRs were relatively less abundant in the forests, implying lower intensity of defense mechanisms of bacteria against viruses in the forests compared to ash soils. The relatively low OTU diversity of the ash soils may perhaps allow greater spread and mortality of viruses through populations, necessitating greater investment in defences.
Since Odum37, it has been noted that developing ecosystems tend to be based on tighter and more effective interactions as succession continues. For example, Morriën et al.38 found that during secondary succession of old field ecosystems, co-occurrences of taxa become more predictable and carbon cycling in the decomposer chain more efficient. Empirically our findings seem to agree with the same paradigm, as we found cell–cell interaction genes found to be more abundant in the developed forest soils. It would be very interesting to directly measure decomposer carbon cycling efficiency in ash-soil mesocosm systems as they develop.
Although we focused on 16S rRNA amplicon sequence data for comparing OTU level diversity between samples as taxonomic assignment based on MG-RAST pipeline is very limited39,40, we had briefly compared the family level bacterial community composition assigned based on metagenome sequence data and based on 16S rRNA amplicon sequence data. It is still debatable if whole genome sequencing, which is free from primer bias, is superior in this respect to 16S rRNA amplicon sequencing40. Our data supports the idea that at the bacterial family level, metagenome sequencing covered a larger variety of taxonomic groups than 16S rRNA sequencing. More

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The long-term population dynamics (i.e., extinction or persistence in an equilibrium value) of the system (2) is mainly dependent on the constant allocation of energy between life-history functions. In the case of population persistence, there is a unique long-term allocation strategy towards reproductive functions that maximizes the population abundance and minimizes individual consumption. In addition, this strategy is dependent on the parameters associated with both fertility ((kappa ) and ({mathscr {B}}_0)) and survival ((xi _{c}) and (e_{1/2})) costs.
Preliminary results
To investigate long-term dynamic patterns, we will relate the energy states of reproduction and maintenance, resource density and population abundance at the end of reproductive seasons, namely in the time sequence ({ntau ^+}_{nge 0}). In the system (4) the relationships between the state variables are the same for each (tau ) unit of time. Then, there is a transformation that relates to the vector ( (R,E_ {r}, E_ {m},P) ((n + 1)tau ^+) ) with ( (R,E_ {r}, E_ {m}, P) (n tau ^+) ) such that ( (n + 1) tau ^+ – ntau ^+ = tau ). This relationship is determined by the following discretization (or stroboscopic map) of the impulsive differential system (4):

$$begin{aligned} left{ begin{array}{lll} E_{r}((n+1)tau ^+)&=(1-kappa gamma )[E_{r}(ntau ^+)+alpha Phi (n,P(ntau ^+))],\ &{}&{}\ E_{m}((n+1)tau ^+)&=dfrac{{mathscr {B}}_0[E_{m}(ntau ^+)+(1-alpha )xi _{c}Phi (n,P(ntau ^+))]}{{mathscr {B}}_0+gamma [E_{r}(ntau ^+)+alpha Phi (n,P(ntau ^+))]},\ P((n+1)tau ^+)&=left{ 1-mu +dfrac{gamma [E_{r}(ntau ^+)+alpha Phi (n,P(ntau ^+))]E_{m}((n+1)tau ^+)}{e_{1/2}+E_{m}((n+1)tau ^+)}right} P(ntau ^+)e^{-lambda tau } end{array} right. end{aligned}$$
(6)

and (R(ntau ^+)=K), where the function (Phi ) defined by (5) is evaluated at (t=(n+1)tau ) and extended to (p=0):

$$begin{aligned} Phi (n,p)=left{ begin{array}{ll} dfrac{R_{max}(e^{lambda tau }-1)}{lambda }, &quad text {if}, p=0, \ &{}\ dfrac{K-R((n+1)tau )e^{lambda tau }}{p}+dfrac{lambda }{p}displaystyle int _{ntau }^{(n+1)tau }{R(s)e^{lambda (s-ntau )}ds}, & quad text {if}, pne 0, end{array} right. end{aligned}$$
(7)

for any (nge 0). Indeed, in non-reproductive seasons the consumer–resource dynamics are described by the continuous component of the system (4), which can be solved. Directly we have (P(t)=P(ntau ^+)e^{-lambda (t-ntau )}) for any (tin (ntau ,(n+1)tau ]). In addition, the per capita consumption rate (1) can be expressed in terms of ( R'(t)). Therefore, reproductive and maintenance energy rates are determined by

$$begin{aligned} E_r'(t)=-alpha frac{R'(t)e^{lambda (t-ntau )}}{P(ntau ^+)}quad text {and}quad E_m'(t)=-(1-alpha )xi _{c}frac{R'(t)e^{lambda (t-ntau )}}{P(ntau ^+)},quad tin (ntau ,(n+1)tau ]. end{aligned}$$

Integrating these functions in the interval ( (n tau , t] ), we obtain

$$begin{aligned} E_r(t)&= {} E_{r}(ntau ^+)+alpha Phi (t,R(t),P(ntau ^+)) end{aligned}$$
(8)

$$begin{aligned} E_m(t)&= {} E_m(ntau ^+)+(1-alpha )xi _{c}Phi (t,R(t),P(ntau ^+)). end{aligned}$$
(9)

Evaluating Eqs. (8)–(9) at ( t = (n + 1)tau ) (end of the non-reproductive season), we have

$$begin{aligned} E_r((n+1)tau )&= {} E_{r}(ntau ^+)+alpha Phi (n,P(ntau ^+)), end{aligned}$$
(10)

$$begin{aligned} E_m(n+1)tau )&= {} E_m(ntau ^+)+(1-alpha )xi _{c}Phi (n,P(ntau ^+)), end{aligned}$$
(11)

with (Phi (n,P(ntau ^+))= Phi ((n+1)tau ,R((n+1)tau ),P(ntau ^+))) and (P((n+1)tau )=P(ntau ^+)e^{-lambda tau }) for any (nge 0). In addition, evaluating the discrete component of system (4) at (t=(n+1)tau ), we obtain

$$begin{aligned} E_{r}((n+1)tau ^+)&= {} (1-kappa gamma )E_{r}((n+1)tau ), end{aligned}$$
(12)

$$begin{aligned} E_m((n+1)tau ^+)&= {} frac{{mathscr {B}}_0E_m((n+1)tau )}{{mathscr {B}}_0+gamma E_r((n+1)tau )}, end{aligned}$$
(13)

$$begin{aligned} P((n+1)tau ^+)= & {} left[ 1-mu +gamma E_{r}((n+1)tau )frac{E_{m}((n+1)tau ^+)}{e_{1/2}+E_{m}((n+1)tau ^+)}right] P((n+1)tau ). end{aligned}$$
(14)

Finally, substituting the Eqs. (10)–(11) into the Esq. (12)–(14) we obtain the discretization given by Eq. (6).
In order to obtain the equilibrium points of system (6), we can solve the following equations:

$$begin{aligned} e_{r}&= {} (1-kappa gamma )[e_{r}+alpha Phi (rho )],\ e_{m}&= {} dfrac{{mathscr {B}}_{0}[e_{m}+(1-alpha )xi _{c}Phi (rho )]}{{mathscr {B}}_0+gamma [e_{r}+alpha Phi (rho )]},\ rho&= {} left{ 1-mu +gamma [e_{r}+alpha Phi (rho )]dfrac{e_{m}}{e_{1/2}+e_{m}}right} rho e^{-lambda tau }, end{aligned}$$

where (e_{r}:=lim _{nrightarrow +infty }{E_{r}(ntau ^+)}), (e_{m}:=lim _{nrightarrow +infty }{E_{m}(ntau ^+)}), (rho :=lim _{nrightarrow +infty }{P(ntau ^+)}) and then, (Phi (rho ):=lim _{nrightarrow +infty }{Phi (n,P(ntau ^+))}). From the first equation, we have (e_{r}=(1-kappa gamma )alpha Phi (P)/kappa gamma ) and then (e_{m}=kappa {mathscr {B}}_0 (1-alpha )xi _{c}/alpha ) for (Pin {0,rho }) such that (Phi (0)=R_{max}(e^{lambda tau }-1)/lambda ) and

$$begin{aligned} Phi (rho )={mathscr {A}},quad text {where}quad {mathscr {A}}=dfrac{e^{lambda tau }-1+mu }{{mathscr {B}}_0}cdot left{ dfrac{e_{1/2}xi _{c}^{-1}}{1-alpha } +dfrac{kappa {mathscr {B}}_0}{alpha }right} . end{aligned}$$
(15)

Therefore, assuming (lambda =0), we have (Gamma (rho )=K-{mathscr {A}}rho ) (from equations (7) and (15)) where (Gamma :=lim _{nrightarrow +infty }{R((n+1)tau )}), (rho ) is the solution of

$$begin{aligned} r_0ln left( dfrac{K-{mathscr {A}}rho }{K}right) -{mathscr {A}}=-R_{max}tau , end{aligned}$$

if, and only if,

$$begin{aligned} rho =dfrac{K}{{mathscr {A}}}left[ 1-exp left( dfrac{{mathscr {A}}-R_{max}tau }{r_0}right) right] . end{aligned}$$
(16)

Long-term population dynamics
From the discretization (6), there are two dynamic behaviors for the long-term population abundance: extinction (see Fig. 2a) and persistence (see Fig. 2b).
Figure 2

Long-term behavior of solutions of the model (4). Peak values correspond to the solution of the discrete model (6) in its population component. (a) Extinction behavior, considering (alpha in {0.1,,0.8}) as energy allocation strategy toward reproductive and (b) persistence behavior considering (alpha in {0.35,, 0.55}). We consider the following parameter set (eta =(2,0.5,2,0.25,500,2,1,0.5,0.5,0.86,alpha ,0.1)) where the constant of fertility costs is described by (kappa =(1+gamma )^{-1}).

Full size image

The differentiation of these behaviors strongly depends on the individual consumption of resources defined throughout each non-reproductive season by

$$begin{aligned} C_{I}(t) = frac{[K-R(t)]e^{lambda (t-ntau )}}{P(ntau ^+)},, tin (ntau ,(n+1)tau ]. end{aligned}$$

At the end of each non-reproductive season, namely at the time ( t = (n + 1) tau ), the individual consumption is given by

$$begin{aligned} C_I((n+1)tau ) = frac{[K-R((n+1)tau )]e^{lambda tau }}{P(ntau ^+)}, end{aligned}$$
(17)

where (R((n+1)tau )) is the non-consumed resource density by the population, the amount that is obtained from the implicit solution of the resource density equation in the continuous component of the system (4). Thus, projecting the individual consumption of the resource into the long term, and taking (Gamma (rho )=(K-{mathscr {A}}rho +lambda {mathscr {I}})e^{-lambda tau }), the expression (17) assumes the form

$$begin{aligned} C_{I}^{infty }(rho )=left{ begin{array}{ll} {mathscr {A}}+dfrac{K(e^{lambda tau }-1)-lambda {mathscr {I}}}{rho },&{}quad text {if}, rho ne 0,\ &{}\ dfrac{R_{max}(e^{lambda tau }-1)}{lambda },&{}quad text {if}, rho =0, end{array}right. end{aligned}$$
(18)

where ({mathscr {I}}:=lim _{nrightarrow +infty }{int _{ntau }^{(n+1)tau }{R(s)e^{lambda (s-ntau )}ds}}). On the one hand, the individual consumption ( C_{I}^{infty } ) is composed of a basis amount corresponding to the term ({mathscr {A}} ) and an amount resulting from the equal division of a resource not consumed by individuals dying during the non-reproductive season, ( K(e^{lambda tau } -1) – lambda {mathscr {I}}). Furthermore, when the population experiences a reduced mortality during the non-reproductive season (i.e., ( lambda approx 0) ), the individual consumption is ( C_{I}^{infty } (rho ) approx {mathscr {A}} ). On the other hand, whether the population abundance is low, the per capita resource is high, implying an individual consumption close to (R_ {max} (e^{lambda tau } -1) / lambda ) (equivalent to taking the limit of ( C_{I}((n+1)tau )) as ( P(ntau ^+)rightarrow 0 )). Certainly, this quantity does not represent the effective individual consumption, but rather establishes an upper limit for this and therefore represents a value of non-persistence. Thus, behaviors related to the equilibrium solutions of the discrete system (6) can be differentiated by the threshold value

$$begin{aligned} {mathscr {U}}=dfrac{C_{I}^{infty }(0)}{C_{I}^{infty }(rho )}. end{aligned}$$

In particular, when the mortality of the population is low, the long-term abundance is described by Eq. (16) and the threshold value assumes the following form ({mathscr {U}}=R_{max}tau /{mathscr {A}}). Thus, we conclude that the persistence of the population is established when ({mathscr {U}} >1) and extinction when ({mathscr {U}}le 1).
Finally, we can see that the stabilization of population size in the long term is in response to a dense-dependent behaviour where the per capita growth rate in the long term is (r_{infty }:={alpha {mathscr {A}}/kappa }{mathscr {S}}(e_m)) equivalent to mortality fraction (mu ), where (e_{m}=kappa {mathscr {B}}_{0}(1-alpha )xi _{c}/alpha ) is the equilibrium value of energy maintenance after the reproductive season. In addition, the derivative of r with respect to P is

$$begin{aligned} dfrac{dr}{dP} = gamma dfrac{dPhi }{d P}left{ alpha {mathscr {S}}(E_{m})+(E_{r}+alpha Phi )dfrac{d{mathscr {S}}}{dE_{m}}cdot dfrac{dE_{m}}{dPhi }right} , end{aligned}$$

where (dPhi /d P1) then the long-term population behavior is persistence.

Proof
We divide the proof into two cases: (kappa gamma =1) and (0 More

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To produce our global Forest Landscape Integrity Index (FLII), we combined four sets of spatially explicit datasets representing: (i) forest extent23; (ii) observed pressure from high impact, localized human activities for which spatial datasets exist, specifically: infrastructure, agriculture, and recent deforestation27; (iii) inferred pressure associated with edge effects27, and other diffuse processes, (e.g., activities such as hunting and selective logging)27 modeled using proximity to observed pressures; and iv) anthropogenic changes in forest connectivity due to forest loss27 (see Supplementary Table 1 for data sources). These datasets were combined to produce an index score for each forest pixel (300 m), with the highest scores reflecting the highest forest integrity (Fig. 1), and applied to forest extent for the start of 2019. We use globally consistent parameters for all elements (i.e., parameters do not vary geographically). All calculations were conducted in Google Earth Engine (GEE)60.
Forest extent
We derived a global forest extent map for 2019 by subtracting from the Global Tree Cover product for 200023 annual Tree Cover Loss 2001–2018, except for losses categorized by Curtis and colleagues24 as those likely to be temporary in nature (i.e., those due to fire, shifting cultivation and rotational forestry). We applied a canopy threshold of 20% based on related studies e.g.31,61, and resampled to 300 m resolution and used this resolution as the basis for the rest of the analysis (see Supplementary Note 1 for further methods).
Observed human pressures
We quantify observed human pressures (P) within a pixel as the weighted sum of impact of infrastructure (I; representing the combined effect of 41 types of infrastructure weighted by their estimated general relative impact on forests (Supplementary Table 3), agriculture (A) weighted by crop intensity (indicated by irrigation levels), and recent deforestation over the past 18 years (H; excluding deforestation from fire, see Discussion). Specifically, for pixel i:

$${mathrm{P}}_{mathrm{i}} = {mathrm{exp}}left( { – {upbeta}_1{mathrm{I}}_{mathrm{i}}} right) + {mathrm{exp}}left( { – {upbeta}_2{mathrm{A}}_{mathrm{i}}} right) + {mathrm{exp}}left( { – {upbeta}_3{mathrm{H}}_{mathrm{i}}} right)$$
(1)

whereby the values of β were selected so that the median of the non-zero values for each component was 0.75. This use of exponents is a way of scaling variables with non-commensurate units so that they can be combined numerically, while also ensuring that the measure of observed pressure is sensitive to change (increase or decrease) in the magnitude of any of the three components, even at large values of I, A, or H. This is an adaptation of the Human Footprint methodology62. See Supplementary Note 3 for further details.
Inferred human pressures
Inferred pressures are the diffuse effects of a set of processes for which directly observed datasets do not exist, that include microclimate and species interactions relating to the creation of forest edges63 and a variety of intermittent or transient anthropogenic pressures such as selective logging, fuelwood collection, hunting; spread of fires and invasive species, pollution, and livestock grazing64,65,66. We modeled the collective, cumulative impacts of these inferred effects through their spatial association with observed human pressure in nearby pixels, including a decline in effect intensity according to distance, and partitioning into stronger short-range and weaker long-range effects. The inferred pressure (P′) on pixel i from source pixel j is:

$$Pprime _{i,j} = P_jleft( {w_{i,j} + v_{i,j}} right)$$
(2)

where wi,j is the weighting given to the modification arising from short-range pressure, as a function of distance from the source pixel, and vi,j is the weighting given to the modification arising from long-range pressures.
Short-range effects include most of the processes listed above, which together potentially affect most biophysical features of a forest, and predominate over shorter distances. In our model, they decline exponentially, approach zero at 3 km, and are truncated to zero at 5 km (see Supplementary Note 4).

$$begin{array}{l}{mathrm{w}}_{i,j} = alpha ,{mathrm{exp}}( – lambda {mathrm{d}}_{i,j}),,,,,,[{mathrm{for}},{mathrm{d}}_{{mathrm{i,j}}} le {mathrm{5km}}]\ {mathrm{w}}_{i,j} = {mathrm{0}},,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[{mathrm{for}},{mathrm{d}}_{i,j} > {mathrm{5km}}]end{array}$$
(3)

where α is a constant set to ensure that the sum of the weights across all pixels in the range is 1.85 (see below), λ is a decay constant set to a value of 1 (see67 and other references in Supplementary Note 4) and di,j is the Euclidean distance between the centers of pixels i and j expressed in units of km.
Long-range effects include over-exploitation of high socio-economic value animals and plants, changes to migration and ranging patterns, and scattered fire and pollution events. We modeled long-range effects at a uniform level at all distances below 6 km and they then decline linearly with distance, conservatively reaching zero at a radius of 12 km65,68 (and other references in Supplementary Note 4):

$$begin{array}{l}{mathrm{v}}_{i,j} = gamma ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[for,d_{i,j} le 6km]\ {mathrm{v}}_{i,j} = gamma left( {12 – d_{i,j}} right)/6,,,,[{mathrm{for}},6{mathrm{km}}, < ,{mathrm{d}}_{i,j} le 12{mathrm{km}}]\ {mathrm{v}}_{i,j} = 0,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,[for,{mathrm{d}}_{i,j} > 12{mathrm{km}}]end{array}$$
(4)

where γ is a constant set to ensure that the sum of the weights across all pixels in the range is 0.15 and di,j is the Euclidean distance between the centers of pixels i and j, expressed in kilometers.
The form of the weighting functions for short- and long-range effects and the sum of the weights (α + γ) were specified based on a hypothetical reference scenario where a straight forest edge is adjacent to a large area with uniform human pressure, and ensuring that in this case total inferred pressure immediately inside the forest edge is equal to the pressure immediately outside, before declining with distance. γ is set to 0.15 to ensure that the long-range effects conservatively contribute no more than 5% to the final index in the same scenario, based on expert opinion and supported e.g., Berzaghi et al.69 regarding the approximate level of impact on values that would be affected by severe defaunation and other long-range effects.
The aggregate effect from inferred pressures (Q) on pixel i from all n pixels within range (j = 1 to j = n) is then the sum of these individual, normalized, distance-weighted pressures, i.e.,

$$Q_i = mathop {sum}_{j=1}^{n} {P{prime}_{i,j}}$$
(5)

Loss of forest connectivity
Average connectivity of forest around a pixel was quantified using a method adapted from Beyer et al.70. The connectivity Ci around pixel i surrounded by n other pixels within the maximum radius (numbered j = 1, 2…n) is given by:

$${mathrm{C}}_i = mathop {sum}_{j=1}^{n} {left( {{mathrm{F}}_j{mathrm{G}}_{i,j}} right)}$$
(6)

where Fj is the forest extent is a binary variable indicating if forested (1) or not (0) and Gi,j is the weight assigned to the distance between pixels i and j. Gi,j uses a normalized Gaussian curve, with σ = 20 km and distribution truncated to zero at 4σ for computational convenience (see Supplementary Note 2). The large value of σ captures landscape connectivity patterns operating at a broader scale than processes captured by other data layers. Ci ranges from 0 to 1 (Ci∈[0,1]).
Current Configuration (CCi) of forest extent in pixel i was calculated using the final forest extent map and compared to the Potential Configuration (PC) of forest extent without extensive human modification, so that areas with naturally low connectivity, e.g., coasts and natural vegetation mosaics, are not penalized. PC was calculated from a modified version of the map of Laestadius et al38. and resampled to 300 m resolution (see Supplementary Note 2 for details). Using these two measures, we calculated Lost Forest Configuration (LFC) for every pixel as:

$${mathrm{LFC}}_i = 1 – left( {{mathrm{CC}}_i/{mathrm{PC}}_i} right)$$
(7)

Values of CCi/PCi  > 1 are assigned a value of 1 to ensure that LFC is not sensitive to apparent increases in forest connectivity due to inaccuracy in estimated potential forest extent – low values represent least loss, high values greatest loss (LFCi∈[0,1]).
Calculating the Forest Landscape Integrity Index
The three constituent metrics, LFC, P, and Q, all represent increasingly modified conditions the larger their values become. To calculate a forest integrity index in which larger values represent less degraded conditions we, therefore, subtract the sum of those components from a fixed large value (here, 3). Three was selected as our assessment indicates that values of LFC + P + Q of 3 or more correspond to the most severely degraded areas. The metric is also rescaled to a convenient scale (0-10) by multiplying by an arbitrary constant (10/3). The FLII for forest pixel i is thus calculated as:

$${mathrm{FLII}}_i = left[ {10/3} right] (3 – {mathrm{min}}(3,,[P_i + Q_i + {mathrm{LFC}}_i]))$$
(8)

where FLIIi ranges from 0 to 10, forest areas with no modification detectable using our methods scoring 10 and those with the most scoring 0.
Illustrative forest integrity classes
Whilst a key strength of the index is its continuous nature, the results can also be categorized for a range of purposes. In this paper three illustrative classes were defined, mapped, and summarized to give an overview of broad patterns of integrity in the world’s forests. The three categories were defined as follows.
High Forest Integrity (scores ≥ 9.6) Interiors and natural edges of more or less unmodified naturally regenerated (i.e., non-planted) forest ecosystems, comprised entirely or almost entirely of native species, occurring over large areas either as continuous blocks or natural mosaics with non-forest vegetation; typically little human use other than low-intensity recreation or spiritual uses and/or low-intensity extraction of plant and animal products and/or very sparse presence of infrastructure; key ecosystem functions such as carbon storage, biodiversity, and watershed protection and resilience expected to be very close to natural levels (excluding any effects from climate change) although some declines possible in the most sensitive elements (e.g., some high value hunted species).
Medium Forest Integrity (scores  > 6.0 but More

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