A framework for the restoration of seed dispersal and pollination

Species reintroduction is a management strategy to restore ecosystem functioning through the reestablishment of ecological interactions and related ecological processes, like pollination and seed dispersal. Selecting the best species to achieve this goal remains challenging. We present a trait‐based framework to estimate the effects of species reintroductions on seed dispersal and pollination. Our framework assesses the potential contribution of a consumer species (e.g. seed disperser) by considering both the originality of its interactions and the availability of resources it consumes. Originality refers to the degree of uniqueness versus redundancy of a species' interactions compared with the interactions of the current consumer community. Resource availability, defined by the distribution of trait values in the resource community that enable interactions (like fruit size), determines the potential magnitude of a species' effect. The framework also allows assigning different weights to unique interactions, thereby facilitating decisions on whether to prioritize species that potentially add unique interactions if selected for reintroduction. Using our framework, we compared the potential effects of two reintroduced frugivores (agoutis and howler monkeys) on seed dispersal in an Atlantic Forest site. While both species have similar potential effects when not accounting for interaction originality, howlers interact with more common fruit's trait values, whereas agoutis have more unique interactions and with a broader variety of trait values. We also provide ways of generalizing our approach to include other factors, e.g. species abundances, to assess the consequences of other scenarios affecting community composition, such as species extinctions and invasions.


Introduction
The contemporary biodiversity crisis deeply affects the functioning of ecosystems and the provision of ecosystem services (Malhi et al. 2016).Species are connected through trophic interactions.Local extinctions can trigger cascading effects in the community, where the loss of a species at one trophic level can influence species at other levels, often affecting ecosystem functioning (Estes et al. 1978;Dirzo et al. 2014).For example, the extinction of apex predators can increase the abundance of herbivores, consequently decreasing plant abundance and diversity (Estes et al. 2011).Herbivore extinctions, in turn, can affect plant diversity (Terborgh et al. 2008) and evolution (Galetti et al. 2013).
Some interaction losses can be reversed through species reintroduction (Seddon et al. 2014).Although they were initially proposed as a management strategy for species conservation (Seddon et al. 2007), reintroductions are now used as a tool to restore ecosystem functioning through the reestablishment of Author contributions: ARL, PRG, FASF, ATCD conceived the idea; ARL, PRG, ATCD developed the model; ARL selected, organized, and analyzed the data; ARL, FASF, ATCD led the writing of the manuscript; ARL, PRG, FASF, ATCD contributed to the drafts and gave their final approval for publication.
interactions that support processes such as pollination, seed dispersal, and predation (Oliveira-Santos & Fernandez 2010;Svenning et al. 2016).It is well established that reintroduction of apex consumers can produce strong restorative changes in ecosystem functions (Estes et al. 2011).Yellowstone is a classic example, where the reintroduction of wolves (Canis lupus) decreased the abundance of elk (Cervus elaphus), allowing recovery of the biomass of its food plants (Ripple & Beschta 2012).However, when it comes to seed dispersal and pollination, selecting species to restore functioning is a harder task, as at lower trophic levels (i.e.among herbivores), there are often many potential species to choose, and their roles are rarely well known.
When considering seed dispersal and pollination, a species' role can be partially determined by functional traits (Dehling et al. 2016).Differences in trait values suggest divergence in resource use, which, combined with abundance (V azquez et al. 2007), determine a species' contribution to these ecological processes.For instance, frugivores with larger gape sizes preferentially consume larger fruits, while smaller frugivores can only consume smaller fruits (Bender et al. 2018).The functional niche of a community can be described by the combination of trait values of the species of this community (Carmona et al. 2016).Shifts in species composition, such as reintroductions, can change a community's functional niche, and analyzing such changes can help to understand how reintroductions will affect ecosystem functioning.In a community that has been depleted of all its large seed dispersers, the reintroduction of a large frugivore would complement its community's functional niche by reestablishing missing interactions, whereas reintroducing smaller frugivores could ensure the persistence of interactions during population fluctuations and species extinctions, therefore increasing stability (Schleuning et al. 2015).Thus, functional traits can be used to infer how reintroductions can benefit a given process (Montoya et al. 2012).
The contribution of a species to the functional niche of its community is known as originality (Kondratyeva et al. 2019).The more different a species is, the less its functional niche overlaps with the rest of its community, and therefore the more original it is (Dehling et al. 2016).Thus, species originality can be used to estimate the effect of reintroductions on ecological processes, as it will define whether reintroducing a given species will add missing interactions or ensure the persistence of the present interactions.However, taxonomic groups as distinct as birds, primates, bats, and rodents can participate in the same ecological process.This makes it difficult to select traits that are relevant and comparable across taxa and, therefore, to include all taxa locally engaged in a single analysis.To overcome this issue, Dehling and Stouffer (2018) proposed the concept of the process-related niche (PR niche hereafter), which uses resource traits to build the functional niche of the consumer community.For instance, small bees can enter and pollinate flowers with long corolla tubes, similar to large butterflies with long proboscis.Quantifying the traits of the flowers with which each pollinator interacts, instead of their own traits, allows comparison between their roles.In this context, high originality values indicate that a consumer species interacts with resource traits that are less consumed by other species in its community (Dehling & Stouffer 2018).In this sense, an original species will add to the diversity of functions, increasing niche complementarity, while a species with lower originality will contribute to the redundancy of the process, ensuring that interactions will still occur in case of species extinction (Schleuning et al. 2015).
Interactions are not only determined by the matching of traits but also by resource availability (V azquez et al. 2007), which, from a trait perspective, can be incorporated in the representation of the functional niche of the resource community.In this sense, resource availability can be represented by the distribution of trait values of the resource community that are relevant for allowing interactions to occur, such as fruit size or corolla length.Among consumer species with the same originality value, the one that interacts with more frequent trait values of the resource community is expected to have larger effects (V azquez et al. 2007).Thus, we argue that the selection of potential species for reintroduction, aiming at a given ecological process, should consider both species' originality and the availability of trait values with which a given species interacts.
In this study, we build an analytical framework to predict the effects of candidate species for reintroduction on ecological processes.To the best of our knowledge, our framework is the first analytical tool developed to select species for reintroduction with the goal of reestablishing trophic interactions and ecosystem functioning.We illustrate our framework with a focus on the reintroduction of consumer species, which is the main target of reintroduction in the literature (Seddon & Armstrong 2016).First, using the concept of PR niche, we provide an estimate of the originality of candidate species by comparing the resource trait values with which the candidate interacts with the resource trait values which the current consumer community interacts.Then, we propose an index that integrates the originality of interactions and the availability of resources to express the potential effect of candidate species on the ecological process of interest.We also introduce an estimate of the amplitude of the functional niche, a measure indicating how broad the range of trait values with which a species interacts in relation to the available trait values in the resource community.Finally, we exemplify the framework with a case study, comparing the potential effect of reintroduced agoutis (Dasyprocta leporina) and howler monkeys (Alouatta guariba) in Tijuca National Park, a defaunated Atlantic Forest fragment in Rio de Janeiro, Brazil.In Supporting Information, we show how to expand the framework to incorporate different types of community data (e.g.species abundances, Supplement S1) and compare the effects of species or taxa present in a community (Supplements S2 and S3) allowing to explore the consequences of extinctions and invasions on the studied ecological process.Additionally, we provide both theoretical and empirical examples illustrating the framework's application for comparing the effects of species or taxa present in a community (Supplement S4; Table 1).

Methods
Our model uses trait probability density (TPD) to build the niche of resource and consumer communities (Carmona et al. 2016).The niche is built in a functional space where the probabilities of finding an individual with a given trait value in the community are distributed on axes representing traits.The niche of a community is built from the combination of the niches of all its species.The niche of a species can be estimated in different ways.Here, we used the most commonly available data type and directly estimated functional niches of communities using the average trait values of species.However, Carmona et al. (2016) reported other methods to build niches of species, which can also be used in our framework.
In our framework, TPD is used to build functional spaces representing the functional niche of the resource community and the PR niche of the consumer community.For the resource community, the functional niche represents the distribution of trait values in the community, whereas the PR niche of the consumer community gives the probability of consumer species interacting with different trait values of the resource community.In this way, resource traits are used to build the niche of both resource and consumer communities.Although TPD can consider species' relative abundances when estimating the niche of a community, we left abundance out of our model, as this information is often not available and it can be difficult to predict the abundance that the reintroduced species will achieve in the future.Nevertheless, we generalize the approach to incorporate abundance into the model (Supplement S1).
We calculated the TPD with kernel density estimates using the ks package in R (Chac on & Duong 2018).The TPDs of species and communities were estimated and analyzed using R 3.6.2(R Development Core Team 2019).The R script with the functions we used is available at (https://github.com/annarlandim/Species-potential-effect-according-to- Landimet-al.-2022).

A Framework for Estimating the Effects of Candidate Species for Reintroduction on Ecological Processes
Studies that analyze species effects on ecological processes usually consider the niche of a single trophic level (e.g.resource or consumer) within the interaction (Dehling et al. 2020).We argue that for a deeper understanding of ecological processes resulting from trophic interactions, both consumer and resource communities should be considered.The functional niche of the resource community represents the availability of potential interactions, whereas its overlap with the PR niche of the consumer community represents the realization of these interactions (Fig. 1).If the PR niche of a candidate species for reintroduction has a large overlap with the PR niche of the present consumer community, we can expect this species to increase process stability by increasing the chances that the interaction persists in case of population fluctuations and extinctions (Fig. 1A), that is, increasing the redundancy of ecological interactions.In contrast, if overlap is low, it will bring new potential interactions (Fig. 1B).However, such new interactions will only occur if Is included in the model to ease its interpretation, as the weight given to originality increases with increasing theta.
the functional niche of the resource community overlaps with the PR niche of the reintroduced species, which is not always the case (Fig. 1C).Furthermore, if the reintroduced species interacts with frequent trait values of the resource community's functional niche, its role will be larger than if it interacts with rare trait values (Fig. 1D).We represent by Y i the potential effect that species i, a candidate species for reintroduction into the consumer community, has on the ecological process Y under investigation.The potential effect depends on the functional originality of the species and the availability of resources, the latter represented by the functional niche of the resource community.To estimate the potential effect of species i on a certain ecological process if reintroduced, we first need to build the PR niche of the consumer community in which the species will be reintroduced.The PR niche of the consumer community, denoted by C, is composed of the weighted average of the PR niches of its current set of species: where S j is the PR niche of a species currently occurring in the community and N is the current species richness of the community.The PR niche of the consumer community (C) and of each In (A), the candidate species would not add new interactions, but would interact with common trait values in the resource community.In (B), the candidate species would add new interactions and consequently has higher originality than in (A).In (C) and (D) we show that the effect of candidate species does not depend only on its originality but also on the probability of encountering resource species with trait values with which it interacts.In (C), as the candidate species does not interact with trait values present in the resource community, it would not be possible to be reintroduced.In (D), two candidate species have the same originality, but species 1 interacts with more frequent trait values in the resource community.
of its species (S j ) are trait probability densities, which means that they are positive and their integral equals 1.Note that C and S j are functions of the resource's traits.If we consider seed dispersal, for example, for a species j from the consumer community, S j (x) represents the probability that species j consumes fruits with an average trait value x.
To compare potential effects, candidate species for reintroduction should be added separately in the analysis of the consumer community's PR niche.This step is necessary to estimate their originality.The total PR niche of the consumer community (T), with the inclusion of the PR niche of the candidate species (S i ), can be computed as a weighted average: The originality of the candidate species, denoted by O i , is the full contribution that species i will add to the consumer community if reintroduced.This is the result of the balance between the species' uniqueness and redundancy.Uniqueness expresses the set of trait values that are not shared with other species in the community, whereas redundancy is the set of shared trait values (Kondratyeva et al. 2019).The originality of species i is estimated by dividing its PR niche by its community's PR niche: In this sense, O i (x) represents the proportion of the PR niche of the consumer community that will be occupied by species i if reintroduced.Note that it is a positive function bounded by 1.The closer to 1, the more unique species i is regarding interactions with the resource's trait value x, that is, species with greater originality interact with resource trait values with which other consumers rarely or never interact.For seed dispersal, for example, in a community where most frugivores disperse small seeds, a frugivore that disperses large seeds will display high originality.
We also need to estimate the functional niche of the resource community, which represents the availability of resources in our framework.As in Equation 1, the functional niche of the resource community (R) is composed of the aggregation of the functional niches of all its species (P k ): The main difference from Equation 1 is that the functional niche of the resource community is built with the resource traits and, therefore, is not a PR niche.R and P k are also functions of resource's traits.For resource species k, P k (x) provides the probability of finding a fruit with trait value x produced by species k.
Finally, we describe the potential effect of the reintroduction of species i on the ecological process of interest (Y i ).To do so, we introduce the scaling parameter θ ≥ 1.The higher the value of θ, the higher the weight that the researcher assigns to originality when estimating the potential effect.By varying θ, one can explore how stable the level of the potential effect of a given species is amid changes in the weight of originality values.A sharp increase in Y i as θ increases means that species i is highly original and that its originality reaches its maximum in a set of rare trait values in the resource community.In contrast, the potential effect of species i remains stable with the increase of θ when the species is not unique or when its originality reaches its maximum close to the region of trait values where the resource community reaches its maximum.We define the potential effect Y i of a candidate species as follows: In this equation, O i (x), introduced in Equation 3, is the probability that when an individual with trait value x is consumed, the consumer is from candidate species i.This probability captures the originality of species i's interactions.R(x) denotes the resource community's functional niche, as detailed in Equation 4. It represents the probability of finding an individual with trait value x in the resource community.R(x) provides the magnitude of species i's potential effect.The presence of this function in the equation indicates how the potential effect of species i is modulated by the distribution of resources in the community.Specifically, the more frequent the trait values species i interacts with, the greater the magnitude of its effect.Finally, the potential effect of species i, Y i (θ), defined by the two previous terms, quantifies the proportion of the PR niche of the consumer community that could be occupied by species i, considering the originality of its interactions and weighted by the availability of resources.It varies between 0 and 1 and is an increasing function of θ.When θ increases to infinity, the potential effect converges to the maximum value of its originality, that is, to O i (x 0 ), where x 0 is the trait value at which species i is more unique.
The role of candidate species i after its reintroduction can be understood by examining its potential effect Y i variation in θ.The higher the overall value of the function, the greater the species potential effect on the process.When θ is equal (or close) to 1, Y i (1), provides the average value of species i's originality, O i , weighted by the resource community's functional niche R. A high value of the potential effect indicates that species i participates in many interactions in which the resource community's functional niche R is large.In this case, the potential effect is more sensitive to modifications of the resource community.The picture changes for large values of θ.By increasing θ, a higher weight is given to interactions in which the participation of species i is large or unique.Therefore, if the presence of the species is necessary or crucial for the interaction to occur, the value of the species effect Y i (θ) will be large.The potential effect of a species is less sensitive to the resource community's functional niche (R) for large values of θ.
process and can help interpret its potential effect (Y i ).Here, we introduce the species i niche amplitude A as follows: In this equation, 1 S i x ð Þ> 0 f g is the indicator function of the PR niche of the candidate consumer species i and 1 R x ð Þ > 0 f g denotes the resource community's functional niche, R. For species i, the indicator function is equal to 1 when an interaction with trait value x is possible and equal to 0 when there is no interaction.For the resource community, the indicator function is equal to 1 when the trait value x is present in the community and equal to 0 when it is not.Therefore, A i stands for the range of trait values with which species i interacts divided by the extent of the set of trait values available in the resource community.We divide by the range of traits values of the resource community such that the niche amplitude A i is a number between 0 and 1.
By definition, generalist species have a large niche amplitude and specialists have a small niche amplitude.If a generalist species has a small potential effect for θ = 1, it either has low originality or does not interact with frequent trait values in the resource community.If it has high originality at some trait values, these trait values are not frequent in the resource community.To investigate whether there are points of high originality, one must calculate the potential effect for high values of θ.A similar analysis can be achieved for a specialist species with a large potential effect for θ = 1.In this case, the species has high originality for traits that are common in the resource community.Therefore, to better interpret the role of a species in an ecological process, both its potential effect Y i and its niche amplitude A i must be considered.

Case Study
We illustrate our framework using the seed dispersal network of Tijuca National Park (3,953 ha), within Rio de Janeiro city, Brazil.For centuries, most of this area was exploited for coffee farming and coal production.In the mid-19th century, it began to be reforested to restore the city's water supply (Padua 2002).Due to the Park's history and its isolation by an urban matrix, it has an impoverished fauna where many important original vertebrates are missing.
Tijuca's seed dispersal network has been intensely modified since its deforestation.Most large seed dispersers, such as muriqui (Brachyteles arachnoides) and lowland tapir (Tapirus terrestris), were extirpated.The absence of these species has had an impact on large seeded plants that depend on larger animals to be dispersed.In 2010, a refaunation project (i.e.sequential reintroduction of recently extinct species with the main goal of restoring ecological processes; Oliveira-Santos & Fernandez 2010) started in Tijuca.Since then, agoutis (Dasyprocta leporina) and howler monkeys (Alouatta guariba) have been reintroduced (Fernandez et al. 2017).However, to date, no studies have compared their contribution to seed dispersal considering the present frugivore community and resource availability.In this case study, we compared the potential effects on seed dispersal of the two reintroduced species.In the future, this framework will assist in the selection of new species and the sequence of reintroductions.
To use the framework, it was first necessary to build Tijuca's seed dispersal network (Mittelman et al. 2022).We collected data on frugivores and zoochoric plants occurrence in Tijuca Figure 2. Reintroduced species' potential effects on the seed dispersal of Tijuca.The larger the value of θ, the larger the weight given to originality when estimating the potential effect (Y i , as represented in the y-axis).For low values of θ (i.e.approximately <10), the rate of increase in agoutis' potential effect is notably steeper than that of howlers, as shown by the slope in the curves, indicating that agoutis are more original.However, as they have similar effects for θ = 1, howler monkeys interact with more common trait values in the resource community.
(ICMBio 2008) and used the Atlantic Frugivory dataset (Bello et al. 2017) for information on species interactions.Second, the traits data were collected in Google Scholar by searching for "species scientific name" AND (fruit OR seed) AND (length OR diameter).With the seed dispersal network and data on its fruits and seeds trait values, we constructed the frugivore community's PR functional niche (Eq. 1) and plant community's functional niche (Eq.4) using R's ks package (Chac on & Duong 2018).We did not include seed length because a Principal component analysis showed a strong correlation between variables (Pearson correlation = 0.9, Supplement S5).
In order to compare the potential effect of agoutis and howlers reintroduced in Tijuca, we added their PR niche to the frugivore community separately (Eq.2) to estimate their originality (Eq.3).Then, we estimated their potential effect's variation in θ (Eq.5) until the stabilization of the function and their niche amplitudes (Eq.6).

Results
We found that agoutis have a higher potential effect (reflected on the y-axis) for all values of θ (a control parameter that increases the weight given to originality when estimating a species' potential effect; Fig. 2).Moreover, the potential effect of agoutis increases more sharply than that of howlers, as evidenced by the slope of the curves in Figure 2. Thus, agoutis are more original.Agoutis also presented a greater niche amplitude (A agouti = 0.99 and A howler = 0.44), indicating that they are more generalist than howlers.However, as they have similar potential effects for θ = 1, we can infer that the functional niche of howlers is larger than that of agoutis for frequent values of traits in the resource community.Therefore, while howlers interact more often with frequent fruit trait values in the plant community, agoutis add rare interactions to Tijuca's seed dispersal network and interact with a wider set of resource trait values.

Discussion
Refaunation projects with the goal of mitigating the effects of species extinction have been increasingly common lately (Seddon & Armstrong 2016).However, to date, we still lack tools for predicting species effects on ecological processes in refaunated areas.Using our analytical framework, practitioners should be able to choose species for reintroduction aiming at functional targets.For instance, increasing niche complementarity (Tilman et al. 1996) can be achieved by reintroducing species that interact with resources that are not used by the local consumer community.Practitioners could also use our model if they are interested in increasing redundancy by reintroducing species that feed on resources already used by the local consumer community.Increasing the number of species with similar roles in the ecosystem can result in a higher response diversity (sensu Elmqvist et al. 2003), as different species tend to respond differently to environmental changes (Walker et al. 1999), and consequently, enhance stability.In our case study, we demonstrated that the reintroduction of agoutis added rare interactions in the network, potentially increasing niche complementarity.On the other hand, our model indicates that howler monkeys interact with more frequent trait values of the resource community, and its reintroduction should foster functioning (here seed dispersal) and stability.Similar analyses could be performed to select future reintroductions to plan the restoration of ecosystems with functional goals (Laughlin 2014).Genes et al. (2017) proposed a conceptual framework to assess the success of reintroductions by accounting for the reestablishment of species interactions.The success of the reintroduction would thus be reached when reintroduced species reestablish a predefined proportion or the totality of the interactions it was expected to realize.This approach is entirely based on the quantity of interactions represented by the number of species with which a reintroduced animal is expected to interact.Our framework advances on this approach by adding a functional aspect to this assessment.For instance, it is possible to identify species for reintroduction that will interact with the most frequent trait values of the plant functional niche.Additionally, our framework can also complement multiple-sites SWOT (strengths, weaknesses, opportunities, threats) analysis for reintroductions (White et al. 2015) and indicate areas that would benefit the most with certain species, by simulating the effect of reintroductions in distinct sites with different consumers and resource communities.
Developing tools to predict species effects on ecological processes is fundamental to understanding the consequences of changes in community composition on ecosystem functioning (Lavorel & Garnier 2002;Chac on-Labella et al. 2022).We have extended our framework so that it can be applied to other processes that result in shifts in community composition.These alternatives can be used to evaluate the effects of future extinctions and the consequences of past ones.As species differ in their effect on ecosystem processes (Chac on-Labella et al. 2022), the consequences of extinctions on ecological processes will depend on the complementarity of species' roles (Fründ et al. 2013).This means that the extinction of more original species is expected to have stronger effects on ecosystem functioning, while redundancy is important for stabilizing communities (Peralta et al. 2014) and prevents secondary extinctions in food webs (Sanders et al. 2018).Our framework can also be used to analyze the impact of exotic invasive species on ecological processes.As suggested by (Finerty et al. 2016), to predict the effect of exotic species on ecosystem functioning, we need to know if this species can shift its community's trait space.By accessing the originality of exotic species, we could infer their potential effect on ecosystem processes and even assess whether such impacts are likely to have negative or positive consequences.For instance, if an exotic species interacts with rare trait values in the resource community, possibly filling the role of an absent native species, or if it is very original and does not compete for resources with native species.
With this framework, our main goal was to estimate the potential effect of a consumer species on a particular ecological process.One might argue that our model is oversimplified because the role of species in trophic interactions is often dependent on species abundance (V azquez et al. 2007).While our framework does not explicitly account for abundance, its Framework for restoration of ecological processes emphasis on the functional niches of consumer and resource communities offers insights into specific functional "gaps" that can be filled with targeted reintroductions.Estimating species abundances prior to their reintroduction can be challenging.Moreover, even more simplified models using the convex hull representation of the functional niche are commonly used (Cornwell et al. 2006) and effectively characterize species roles in ecological processes (Dehling et al. 2020).Other determinants of trophic interactions were left out of our model, such as species phenology, which explains to a great extent the properties of plant-animal mutualistic trophic interactions (Encinas-Viso et al. 2012); and the quality of interactions, which are important determinants of ecosystem functioning (Schleuning et al. 2015;Landim et al. 2022).When evaluating potential species to be reintroduced in a certain area, other aspects related to the quality of interaction should be considered.
In a changing world, improving restoration management and understanding the effects of changes in community composition are fundamental.Our framework is a useful tool for predicting how species reintroductions will affect ecological processes resulting from trophic interactions, as it informs the role of species in relation to their interactions.We believe that the models presented here will provide decision-makers with a tool that will improve their capacity to restore ecological interactions and reestablish ecological functions and processes.This holistic approach is essential for more effective ecosystem restoration.

Figure 1 .
Figure 1.Conceptual model showing different examples of combinations between the niche of resource and consumer communities and the candidate species for reintroduction.The resource community R (green) represents the available niche space for potential interactions.The PR niche of the consumer community C(red)  represents the portion of the resource's functional niche that can be consumed (realized interactions).The PR niche of candidate species are shown in yellow and blue.All representations are trait probability densities and therefore have integral = 1.In (A), the candidate species would not add new interactions, but would interact with common trait values in the resource community.In (B), the candidate species would add new interactions and consequently has higher originality than in (A).In (C) and (D) we show that the effect of candidate species does not depend only on its originality but also on the probability of encountering resource species with trait values with which it interacts.In (C), as the candidate species does not interact with trait values present in the resource community, it would not be possible to be reintroduced.In (D), two candidate species have the same originality, but species 1 interacts with more frequent trait values in the resource community.

Table 1 .
Notation, name, and description of the variables used in the framework.Amplitude of the candidate species' process-related nicheThe range of trait values from the resource community with which the candidate species will interact with if reintroduced.C Process-related niche of the consumer community The probability of a species from the consumer community interacting with trait values of the resource community.
i Candidate species' potential effect on the targeted ecological processGives the potential effect of a candidate species in terms of interactions' originality and resource availability.That is, informs if the candidate species will add rare or common interactions and if these interactions will be with frequent trait values of the resource community or not.θ Parameter theta Does not have an ecological meaning.