Two roles for ecological surrogacy: Indicator surrogates and management surrogates

Ecological surrogacy – here defined as using a process or element (e.g., species, ecosystem, or abiotic factor) to represent another aspect of an ecological system – is a widely used concept, but many applications of the surrogate concept have been controversial. We argue that some of this controversy reflects differences among users with different goals, a distinction that can be crystalized by recognizing two basic types of surrogate. First, many ecologists and natural resource managers measure “indicator surrogates” to provide information about ecological systems. Second, and often overlooked, are “management surrogates” (e.g., umbrella species) that are primarily used to facilitate achieving management goals, especially broad goals such as “maintain biodiversity” or “increase ecosystem resilience.” We propose that distinguishing these two overarching roles for surrogacy may facilitate better communication about project goals. This is critical when evaluating the usefulness of different surrogates, especially where a potential surrogate might be useful in one role but not another. Our classification for ecological surrogacy applies to species, ecosystems, ecological processes, abiotic factors, and genetics, and thus can provide coherence across a broad range of uses.     

Terrestrial invertebrate surveys and rapid biodiversity assessment in New Zealand: lessons from Australia

Although invertebrates play a key role in the environment, their conservation and use in environmental monitoring is often considered “too difficult” and consequently ignored. One of the main problems in dealing with invertebrates is that even limited sampling can yield large numbers of specimens and an enormous diversity of species. Other problems include the taxonomic impediment (i.e. high proportions of invertebrate taxa are undescribed and there are few specialists available to identify specimens), the lack of knowledge on species distribution, diversity and ecological roles, and the fact that invertebrates are undervalued by the general public. A number of rapid biodiversity assessment (RBA) approaches have been suggested to overcome these problems. RBA approaches generally fall into four categories: (1) restricted sampling in place of intensive sampling (sampling surrogacy); (2) the use of higher taxonomic levels than species (species surrogacy); (3) the use of recognisable taxonomic units (RTUs) identified by non-specialists (taxonomic surrogacy); and (4) the use of surrogate taxa in place of all taxa (taxon-focusing). Australia has a long history of using invertebrates in terrestrial ecological studies, and in developing and using RBA approaches. Therefore, New Zealand could benefit from the experienced gained in Australia. Potentially one of the most useful RBA approaches to take in New Zealand involves focusing resources and attention on a limited range of taxa. However, this requires substantial communication, discussion, and agreement over which taxa should be selected for conservation priorities and environmental monitoring in terrestrial ecosystems.     

A test for assessment of saproxylic beetle biodiversity using subsets of “monitoring species”

In European forests, large scale biodiversity monitoring networks need to be implemented – networks which include components such as taxonomical groups that are at risk and that depend directly on forest stand structure. In this context, monitoring the species-rich group of saproxylic beetles is challenging. In the absence of sufficient resources to comprehensively survey a particular group, surrogates of species richness can be meaningful tools in biodiversity evaluations. In search of restricted subsets of species to use as surrogates of saproxylic beetle richness, we led a case study in Western Europe.Beetle data were compiled from 67 biodiversity surveys and ecological studies carried out from 1999 to 2010 with standardised trapping methods in France and Belgium. This large-scale dataset contains 642 forest plots, 1521 traps and 856 species. Twenty-two simplified species subsets were identified as potential surrogates, as well as the number of genera, a higher taxonomic level, taking into account, for each surrogate, the effort required for species identification, the practical monitoring experience necessary, the species conservation potential or the frequency of species occurrence. The performance of each surrogate was analyzed based on the following parameters: overall surrogacy (correlation between subset richness and total species richness), surrogacy vs. identification cost balance, surrogacy variation over a wide range of ecological conditions (forest type, altitude, latitude and bio-geographical area) and consistency with spatial scale. Ecological representativeness and ability to monitor rare species were supplementary criteria used to assess surrogate performance.The subsets consisting of the identifiable (or only easy-to-identify species) could easily be applied in practice and appear to be the best performing subsets, from a global point of view.The number of genera showed good prediction at the trap level and its surrogacy did not vary across wide environmental gradients. However, the subset of easy-to-identify species and the genus number were highly sensitive to spatial scale, which limits their use in large-scale studies. The number of rare species or the species richness of single beetle families (even the best single-family subset, the Cerambycidae) was very weak surrogates for total species richness. Conversely, the German list of monitoring species had high surrogacy, low identification costs and was not strongly influenced by the main geographical parameters, even with our French and Belgian data.In European-wide monitoring networks, such internationally validated subsets could be very useful with regard to the timing and cost-efficiency of field inventories.     

Birds as surrogates for biodiversity: An analysis of a data set from southern Québec

Surrogacy analysis consists of determining a set of biotic or environmental parameters which can be rapidly assessed in the field and reliably used to prioritize places for biodiversity conservation. Whether adequate surrogate sets exist remains an open and relatively unexplored question though its solution is central to the aims of conservation biology. This paper analyses the surrogacy problem by prioritizing places using surrogate lists and comparing these results with those obtained by using more comprehensive species lists. More specifically, it explores (i) the possibility of using bird distributions, which are often easily available, as surrogates for species at risk (endangered and threatened species), which are presumed to be an important component of biodiversity; and (ii) the methodological question of how spatial scale influences surrogate success. The data set analysed, from southern Québec, is one of the most complete biotic data sets available at the regional scale. Contrary to some previous analyses, the results obtained suggest that the surrogacy problem is potentially solvable.     

The surrogacy potential of white-tailed sea eagle nesting habitat on islands of the Baltic Sea

In order to tackle the current biodiversity crisis, a plethora of tempting shortcuts, such as the surrogate species approach, have recently been used to pinpoint important areas for protection. At the same time, species-specific conservation programmes are implemented in order to ameliorate the status of target threatened species. In the cases where species-specific programmes are evaluated and found to provide no apparent benefit to the target species, it is important to evaluate whether such conservation efforts may benefit other taxa sharing the same landscape with the target species. Here we assess the surrogacy potential of white-tailed sea eagle (WTSE) nesting habitat as indicator of biodiversity richness (using vascular plants and fungi as surrogated taxa) on islands of the Archipelago Sea in South-western Finland. We compared species richness on islands with and without a WTSE nest. We found weak evidence that islands with a WTSE nest support higher richness of vascular plants than islands without a nest. Conversely, we found no evidence that WTSE nests could be valid surrogates for fungi species inhabiting old-growth forests. Within the spatio-temporal and ecological limits of the present study, we suggest that the nesting habitat of WTSE may hold some surrogate potential for taxa, such as vascular plants, that may indicate high habitat diversity. This finding however remains to be confirmed. At the same time, it appears evident that the WTSE nesting habitat has poor surrogate potential with regards to old-growth forests. Overall, our findings line up with a growing body of other studies calling for caution and careful evaluation of the surrogacy efficiency of single species.     

Different surrogacy approaches for stream macroinvertebrates in discriminating human disturbances in Central China

Due to the difficulty of identifying many taxa of freshwater invertebrates to species, many researchers have assessed the utility of surrogates for species-level identifications (e.g. higher taxa) in bioassessment programs. Here, we examined the efficiency of two different approaches to species surrogacy, one using coarser taxonomic resolution and a second approach based on random aggregation (“Best practicable aggregation of species”, BestAgg), in portraying patterns of stream macroinvertebrates in Central China. The main objectives were: (1) to compare the discriminatory power of biodiversity indices and assemblage structure for different levels of human disturbances based on different taxonomic resolution and on BestAgg; (2) to identify the congruence of assemblage-environment and biodiversity-indices-environment relationships for datasets at the species level versus those at surrogate levels. We found that genus-level and BestAgg datasets accurately reproduced the pattern of species-level communities, whereas family- and order-level datasets did not. Specifically, both genus-level and BestAgg approaches performed almost as well as species-level data in distinguishing sites subjected to different disturbance levels. Most of the environmental variables that were important for species-level assemblages, also emerged as significant when analyzing genera and BestAgg surrogates, as shown by both analyses of indices and assemblage composition according to distance-based ordination models. Our results suggest that genus-level taxonomy, which resulted in the least loss of ecological information relative to species-level identification, is sufficient in studies of community ecology and bioassessment of stream macroinvertebrates in Central China. In addition, the BestAgg approach, which required identification of fewer taxa than genus-level analysis, has a similar ability to depict multivariate patterns of macroinvertebrate assemblages and differentiate different disturbance levels. Applying our results could enhance speed and cost-effectiveness of freshwater biomonitoring and bioassessment programs; however, independent determination of best taxonomic level and BestAgg will be required whenever a new geographic area or habitat type is assessed.     

Proportion of treatment effect mediated by surrogate endpoints

One of the central aims in randomized clinical trials is to find well‐validated surrogate endpoints to reduce the sample size and/or duration of trials. Clinical researchers and practitioners have proposed various surrogacy measures for assessing candidate surrogate endpoints. However, most existing surrogacy measures have the following shortcomings: (i) they often fall outside the range [0,1], (ii) they are imprecisely estimated, and (iii) they ignore the interaction associations between a treatment and candidate surrogate endpoints in the evaluation of the surrogacy level. To overcome these difficulties, we propose a new surrogacy measure, the proportion of treatment effect mediated by candidate surrogate endpoints (PMS), based on the decomposition of the treatment effect into direct, indirect, and interaction associations mediated by candidate surrogate endpoints. In addition, we validate the advantages of PMS through Monte Carlo simulations and the application to empirical data from ORIENT (the Olmesartan Reducing Incidence of Endstage Renal Disease in Diabetic Nephropathy Trial).     

On the Myths of Indicator Species: Issues and Further Consideration in the Use of Static Concepts for Ecological Applications

The use of static indicator species, in which species are expected to have a similar sensitivity or tolerance to either natural or human-induced stressors, does not account for possible shifts in tolerance along natural environmental gradients and between biogeographic regions. Their indicative value may therefore be considered at least questionable. In this paper we demonstrate how species responses (i.e. abundance) to changes in sediment grain size and organic matter (OM) alter along a salinity gradient and conclude with a plea for prudency when interpreting static indicator-based quality indices. Six model species (three polychaetes, one amphipod and two bivalves) from the North Sea, Baltic Sea and the Mediterranean Sea region were selected. Our study demonstrated that there were no generic relationships between environment and biota and half of the studied species showed different responses in different seas. Consequently, the following points have to be carefully considered when applying static indicator-based quality indices: (1) species tolerances and preferences may change along environmental gradients and between different biogeographic regions, (2) as environment modifies species autecology, there is a need to adjust indicator species lists along major environmental gradients and (3) there is a risk of including sibling or cryptic species in calculating the index value of a species.     

Higher taxa as surrogates of species richness of spiders in insect‐resistant transgenic rice

Abstract Biodiversity assessments can often be time‐ and resource‐consuming. Several alternative approaches have been proposed to reduce sampling efforts, including indicator taxa and surrogates. In this study, we examine the reliability of higher taxon surrogates to predict species richness in two experimental rice fields of Fujian Province, southeastern China during 2005 and 2009. Spider samples in transgenic and nontransgenic plots were collected using a suction sampler. Both the genus and family surrogates had significant and positive linear relationships with species richness in the transgenic and nontransgenic rice fields. The rice varieties did not significantly influence the linear relationships. Our findings suggest that higher‐taxon surrogacy could be a useful alternative to complete species inventory for risk assessments of transgenic rice.     

Enhancing autonomy in paid surrogacy

The gestational surrogate – and her economic and educational vulnerability in particular – is the focus of many of the most persistent worries about paid surrogacy. Those who employ her, and those who broker and organize her services, usually have an advantage over her in resources and information. That asymmetry exposes her to the possibility of exploitation and abuse. Accordingly, some argue for banning paid surrogacy. Others defend legal permission on grounds of surrogate autonomy, but often retain concerns about the surrogate. In response to the dilemma of a ban versus bald permission, we propose a 'soft law' approach: states should require several hours of education of surrogates – education aimed at informing and enhancing surrogate autonomy.     

Recommendations for Assessing the Effectiveness of Surrogate Species Approaches

Surrogate species approaches, including flagship, focal, keystone, indicator, and umbrella, are considered an effective means of conservation planning. For conservation biologists to apply surrogates with confidence, they must have some idea of the effectiveness of surrogates for the circumstances in which they will be applied. We reviewed tests of the effectiveness of surrogate species planning to see if research supports the development of generalized rules for (1) determining when and where surrogate species are an effective conservation tool and (2) how surrogate species should be selected such that the resulting conservation plan will effectively protect biodiversity or achieve other conservation goals. The context and methods of published studies were so diverse that we could not draw general conclusions about the spatial or temporal scales, or ecosystems or taxonomic groups for which surrogate species approaches will succeed. The science of surrogate species can progress by (1) establishing methods to compare diverse measures of effectiveness; (2) taking advantage of data-rich regions to examine the potential effectiveness of surrogate approaches; (3) incorporating spatial scale as an explanatory variable; (4) evaluating surrogate species approaches at broader temporal scales; (5) seeking patterns that will lead to hypothesis driven research; and (6) monitoring surrogate species and their target species.     

Reconstructing feminist perspectives of women’s bodies using a globalized view: The changing surrogacy market in Japan

This paper aims to evoke an alternative viewpoint on surrogacy, moving beyond popular Western feminist beliefs on the practice, by introducing the history and current context of East Asian surrogacy. To elaborate a different cultural perspective on surrogacy, this paper first introduces the East Asian history of contract pregnancy systems, prior to the emergence of the American invention of ‘modern’ surrogacy practice. Then, it examines Japanese mass media portrayals of cross-border surrogacy in which white women have become ‘convenient’ entities. The results of the analysis show how Japanese culture has adopted a rhetoric about the use of white women as convenient surrogate mothers in the global commercial surrogacy market. An essential aspect of surrogacy is the premise that a woman’s reproductive function should be accessible to others. Past discussions among feminists have neglected this important point. Moreover, they share the assumption that white surrogacy clients are exploiters, who take advantage of women of colour as surrogate mothers. The current situation in Asia flips this perspective—with white women regarded as easier targets for exploitation by wealthy people of colour. For Asian clients, Westerners can be easily regarded as ‘others’ whom they can use for their reproductive needs. In today's globalized era, the surrogacy industry is no longer for affluent Westerners only. Considering this change, it is crucial to discuss surrogacy issues by reconstructing feminist perspectives with a globalized view, to help protect women’s bodies, regardless of nationality, ethnicity, skin colour, or religion.     

Effectiveness of biological surrogates for predicting patterns of marine biodiversity: a global meta-analysis

The use of biological surrogates as proxies for biodiversity patterns is gaining popularity, particularly in marine systems where field surveys can be expensive and species richness high. Yet, uncertainty regarding their applicability remains because of inconsistency of definitions, a lack of standard methods for estimating effectiveness, and variable spatial scales considered. We present a Bayesian meta-analysis of the effectiveness of biological surrogates in marine ecosystems. Surrogate effectiveness was defined both as the proportion of surrogacy tests where predictions based on surrogates were better than random (i.e., low probability of making a Type I error; P) and as the predictability of targets using surrogates (R(2)). A total of 264 published surrogacy tests combined with prior probabilities elicited from eight international experts demonstrated that the habitat, spatial scale, type of surrogate and statistical method used all influenced surrogate effectiveness, at least according to either P or R(2). The type of surrogate used (higher-taxa, cross-taxa or subset taxa) was the best predictor of P, with the higher-taxa surrogates outperforming all others. The marine habitat was the best predictor of R(2), with particularly low predictability in tropical reefs. Surrogate effectiveness was greatest for higher-taxa surrogates at a <10-km spatial scale, in low-complexity marine habitats such as soft bottoms, and using multivariate-based methods. Comparisons with terrestrial studies in terms of the methods used to study surrogates revealed that marine applications still ignore some problems with several widely used statistical approaches to surrogacy. Our study provides a benchmark for the reliable use of biological surrogates in marine ecosystems, and highlights directions for future development of biological surrogates in predicting biodiversity.     

Dynamic species co‐occurrence networks require dynamic biodiversity surrogates

In conservation it is inevitable that surrogates be selected to represent the occurrence of hard‐to‐find species and find priority locations for management. However, species co‐occurrence can vary over time. Here we demonstrate how temporal dynamics in species co‐occurrence influence the ability of managers to choose the best surrogate species. We develop an efficient optimisation formulation that selects the optimal set of complementary surrogate species from any co‐occurrence network. We apply it to two Australian datasets on successional bird responses to disturbances of revegetation and fire. We discover that a surprisingly small number of species are required to represent the majority of species co‐occurrences at any one time. Because co‐occurrence patterns are temporally dynamic, the optimal set of surrogates, and the number of surrogates required to achieve a desired surrogacy power, depend on sampling effort and the successional state of a system. Overlap in optimal sets of surrogates for representing 70% of co‐occurring species ranges from zero to 57% depending on when the surrogacy decision is made. Surrogate sets representing early successional communities over‐estimate the power of surrogacy decisions at later times. Our results show that in dynamic systems, optimal surrogates might be selected in different ways: 1) use short‐term monitoring to choose a larger number of static less‐informative surrogates; 2) use long‐term monitoring to choose a smaller number of static high‐power surrogates that may poorly represent early successional co‐occurrence; 3) develop adaptive surrogate selection frameworks with high short‐term and long‐term surrogacy power that update surrogate sets and capture temporal dynamics in species co‐occurrence. Our results suggest vigilance is needed when selecting surrogates for other co‐occurring species in dynamic landscapes, as selected surrogates from one time may have reduced effectiveness at a different time. Ultimately, decisions that fail to acknowledge dynamic species co‐occurrence will lead to uninformative or redundant surrogates.     

Searching for biodiversity indicators in running waters: do bryophytes, macroinvertebrates, and fish show congruent diversity patterns?

The degree to which different taxonomic groups show congruence in diversity patterns has attracted increased attention, yet such studies on stream biota are lacking. We examined environmental correlates of and congruence in the species richness patterns of bryophytes, macroinvertebrates, and fish in 101 boreal streams in Finland. Congruence in species richness among the taxonomic groups was generally low, mainly because of their differing responses to major environmental gradients. Bryophytes and macroinvertebrates showed the strongest degree of congruence, but even this relationship had a relatively weak predictive power. Bryophyte diversity showed the strongest relationship with water colour, followed by habitat stability, and stream size. Macroinvertebrate diversity increased with stream size, and further variation was accounted for by water colour and acidity. Fish species richness showed a weak and complex relationship with geographical location, stream size, and in-stream habitat characteristics. The regression models explained 23, 45, and 26% of the variation in species richness of bryophytes, macroinvertebrates, and fish, respectively. Our results suggest that indicator taxa may be of limited value in stream biodiversity inventories. Habitat-based approaches are suggested as an alternative surrogate measure in the conservation evaluation of lotic biodiversity.     

Biodiversity surrogacy: indicator taxa as predictors of total species richness in Brazilian Atlantic forest and Caatinga

The use of indicator taxa as biodiversity surrogates has received widespread attention in conservation planning, but remains a highly contentious issue. Here we assess biodiversity surrogacy in the two most important biomes of tropical northeastern Brazil, Atlantic forest and Caatinga. We examine the extent to which species richness is correlated among taxonomic groups, and assess relationships between the richness of individual groups, and combinations of groups and total species richness. We introduce a new approach to dealing with autocorrelation between focal taxon richness and total species richness, using standardized data such that each taxon is given equal weight. Our Atlantic forest data covered seven taxa (bryophytes, pteridophytes, trees, ants, euglosine bees, birds, and mammals; total of 768 species) sampled from 12 sites; in Caatinga it was four taxa (trees, spiders, beetles and ants; total of 184 species) from 25 sites. Our results showed that: (1) in nearly all cases the species richnesses of individual taxa were significantly correlated with each other; (2) the species richnesses of most individual taxa were significantly correlated with total species richness in both biomes; (3) only two taxa were required for excellent (R ² > 80%) surrogacy of total species richness in both biomes; and (4) the same two taxa (trees and ants) can provide reasonable (R ² > 60%) surrogacy for total richness in these contrasting biomes. Our findings therefore suggest that the ‘shopping basket of taxa’ required for effective biodiversity surrogacy may not only need to be very small (two taxa), but may also be very limited in composition.     

The potential contribution of vegetation ecology to biodiversity research

The contribution of vegetation ecology to the study of biodiversity depends on better communication between the different research paradigms in ecology. Recent developments in vegetation theory and associated statistical modelling techniques are reviewed for their relevance to biodiversity. Species composition and collective properties such as species richness vary as a continuum in a multi-dimensional environmental space; a concept which needs to be incorporated into biodiversity studies. Different kinds of environmental gradients can be recognised and species responses to them vary. Species response curves of eucalypts to an environmental gradient of mean annual temperature have been shown to exhibit a particular pattern of skewed response curves. Generalised linear modelling (GLM) and generalised additive modelling (GAM) techniques are important tools for biodiversity studies. They have successfully distinguished the contribution of environmental (climatic) and spatial (history and species dispersal ability) variables in determining forest tree composition in New Zealand. Species richness studies are examined at global, regional and local scales. At all scales, direct and resource environmental gradients need to be incorporated into the analysis rather than indirect gradients e.g. latitude which have no direct physiological influence on biota. Evidence indicates that species richness at the regional scale is sensitive to environment, confounding current studies on local/regional species richness relationships. Plant community experiments require designs based on environmental gradients rather than dependent biological properties such as productivity or species richness to avoid confounding the biotic components. Neglect of climatic and other environmental gradients and the concentration on the collective properties of species assemblages has limited recent biodiversity studies. Conservation evaluation could benefit from greater use of the continuum concepts and statistical modelling techniques of vegetation ecology. The future development of ecology will depend on testing the different assumptions of competing research paradigms and a more inclusive synthesis of ecological theory.     

FAIR TRADE INTERNATIONAL SURROGACY

Since the development of assisted reproductive technologies, infertile individuals have crossed borders to obtain treatments unavailable or unaffordable in their own country. Recent media coverage has focused on the outsourcing of surrogacy to developing countries, where the cost for surrogacy is significantly less than the equivalent cost in a more developed country. This paper discusses the ethical arguments against international surrogacy. The major opposition viewpoints can be broadly divided into arguments about welfare, commodification and exploitation.
It is argued that the only valid objection to international surrogacy is that surrogate mothers may be exploited by being given too little compensation. However, the possibility of exploitation is a weak argument for prohibition, as employment alternatives for potential surrogate mothers may be more exploitative or more harmful than surrogacy. It is concluded that international surrogacy must be regulated, and the proposed regulatory mechanism is termed Fair Trade Surrogacy. The guidelines of Fair Trade Surrogacy focus on minimizing potential harms to all parties and ensuring fair compensation for surrogate mothers.     

Robust approach to combining multiple markers to improve surrogacy

Identifying effective and valid surrogate markers to make inference about a treatment effect on long-term outcomes is an important step in improving the efficiency of clinical trials. Replacing a long-term outcome with short-term and/or cheaper surrogate markers can potentially shorten study duration and reduce trial costs. There is sizable statistical literature on methods to quantify the effectiveness of a single surrogate marker. Both parametric and nonparametric approaches have been well developed for different outcome types. However, when there are multiple markers available, methods for combining markers to construct a composite marker with improved surrogacy remain limited. In this paper, building on top of the optimal transformation framework of Wang et al. (2020), we propose a novel calibrated model fusion approach to optimally combine multiple markers to improve surrogacy. Specifically, we obtain two initial estimates of optimal composite scores of the markers based on two sets of models with one set approximating the underlying data distribution and the other directly approximating the optimal transformation function. We then estimate an optimal calibrated combination of the two estimated scores which ensures both validity of the final combined score and optimality with respect to the proportion of treatment effect explained by the final combined score. This approach is unique in that it identifies an optimal combination of the multiple surrogates without strictly relying on parametric assumptions while borrowing modeling strategies to avoid fully nonparametric estimation which is subject to the curse of dimensionality. Our identified optimal transformation can also be used to directly quantify the surrogacy of this identified combined score. Theoretical properties of the proposed estimators are derived, and the finite sample performance of the proposed method is evaluated through simulation studies. We further illustrate the proposed method using data from the Diabetes Prevention Program study.     

Validation of surrogate markers in multiple randomized clinical trials with repeated measurements: canonical correlation approach

Part of the recent literature on the evaluation of biomarkers as surrogate endpoints starts from a multitrial context, which leads to a definition of validity in terms of the quality of both trial-level and individual-level association between the surrogate and true endpoints (Buyse et al., 2000, Biostatistics1, 49-67). These authors concentrated on cross-sectional continuous responses. However, in many randomized clinical studies, repeated measurements are encountered on either or both endpoints. A challenge in this setting is the formulation of a simple and meaningful concept of "surrogacy."Alonso et al. (2003, Biometrical Journal45, 931-945) proposed the variance reduction factor (VRF) to evaluate surrogacy at the individual level. They also showed how and when this concept should be extended to study surrogacy at the trial level. Here, we approach the problem from the natural canonical correlation perspective. We define a class of canonical correlation functions that can be used to study surrogacy at the trial and individual level. We show that the VRF and the R2 measure defined by Buyse et al. (2000) follow as special cases. Simulations are conducted to evaluate the performance of different members of this family. The methodology is illustrated on data from a meta-analysis of five clinical trials comparing antipsychotic agents for the treatment of chronic schizophrenia.