# Global, robust and comparable digital carbon assets

Sadiq Jaffer12, Michael Dales12, Patrick Ferris12, Thomas Swinfield13 Derek
Sorensen2, Robin Message4, Srinivasan Keshav12, Anil Madhavapeddy12
1Cambridge Centre for Carbon Credits, University of Cambridge
2Department of Computer Science and Technology, University of Cambridge
3Department of Zoology, University of Cambridge
4Lambda Cambridge Ltd

###### Abstract

Carbon credits purchased in the voluntary carbon market allow unavoidable
emissions, such as from international flights for essential travel, to be
offset by an equivalent climate benefit, such as avoiding emissions from
tropical deforestation. However, many concerns regarding the credibility of
these offsetting claims have been raised. Moreover, the credit market is
manual, therefore inefficient and unscalable, and non-fungible, therefore
illiquid. To address these issues, we propose an efficient digital methodology
that combines remote sensing data, modern econometric techniques, and on-chain
certification and trading to create a new digital carbon asset (the PACT
stablecoin) against which carbon offsetting claims can be transparently
verified. PACT stablecoins are produced as outputs from a reproducible
computational pipeline for estimating the climate benefits of carbon offset
projects that not only quantifies the CO2 emissions involved, but also allows
for similar credits to be pooled based on their co-benefits such as
biodiversity and jurisdictional attributes, increasing liquidity through
fungibility within pools. We implement and evaluate the PACT carbon stablecoin
on the Tezos blockchain, which is designed to facilitate low-cost transactions
while minimizing environmental impact. Our implementation includes a contract
for a registry for tracking issuance, ownership, and retirement of credits,
and a custodian contract to bridge on-chain and off-chain transactions. Our
work brings scale and trust to the voluntary carbon market by providing a
transparent, scalable, and efficient framework for high integrity carbon
credit transactions.

###### Index Terms:

Sustainability, Blockchains, Climate change

##  I Introduction

To meet the 2015 Paris Agreement’s goal of limiting temperature increases to
below two degrees of pre-industrial levels, countries and organisations must
rapidly decarbonise and transition towards net zero carbon emissions. Since
there will always be some unavoidable residual emissions, every net zero
pathway incorporates carbon credits that represent avoided, reduced or removed
emissions. Emitters use these credits to offset their climate harming
emissions. The demand for voluntary carbon market (VCM) credits is already
high and projected to grow from $2bn in 2023 to $250bn by 2050 [1].

Carbon credits aim to balance unavoidable climate harm (e.g. from
international air travel [2]) with an equivalent climate benefit from
sequestered [3] or avoided [4] carbon emissions. For this asset class to be
credible, however, the claimed climate benefits need to add up to be at least
as effective as the climate harms being offset. Unfortunately, the current VCM
has numerous credibility gaps due to the overestimation of climate benefit
[5]. Moreover, it has high transaction and intermediary costs [6], and is
subject to significant price fluctuations [7], which make the long term
investments in credit-generating projects hard to sustain, particularly for
nature-based projects [4] which can require decades to realise their climate
benefit [8].

Our research goal is to use the emerging technology of digital ledgers and
permissionless blockchains to solve this problem. Specifically, recently,
fiat-backed tokens, known as “fiat stablecoins”, have become widely
deployed[9]. The largest, Tether, has a market capitalisation of nearly $100bn
as of January 2024[10]. Fiat stablecoins offer cross-border transactions at
minimal cost with low volatility. These stablecoins have three useful digital
properties:

  * •

Self-adjusting valuation: the value of a fiat currency is determined only by
the supply and demand against other currencies and commodities

  * •

Fungibility: individual coins can be transparently interchanged for each other

  * •

Liquidity: sufficient quantities of stablecoins are usually available for
transactions to clear quickly and at low cost

These properties are useful for carbon credits, as well. Self-adjusting
valuation allows the value of a project to be determined by the market, taking
into account the current knowledge state of project implementation, rather
than set by the project owner by fiat, thus increasing trust in this
valuation. Fungibility allows credits to be traded across projects, rather
than having a project-linked credit that cannot be compared with credits from
other projects. Liquidity allows the owner of a carbon credit to feel secure
that their investment can be recouped by sale in the market with a low
transaction fee.

For these reasons, this paper discusses the design and implementation of the
PACT stablecoin and its use to provide scale and trust in the VCM.
Specifically, we define a structure for creating PACT stablecoins – digital
tokenised carbon assets that are open to scientific examination, auditable on
a public ledger, and comparable against each other. This provides a basis for
scaling the VCM to allow participants to offset their necessary emissions
efficiently, which will result in more finance being injected to increase the
supply of nature-based protection interventions, which is urgently needed to
stem the devastation of natural environments due to anthropogenic actions
[11].

The contributions of our work are as follows:

  * •

We present the design of the PACT carbon stablecoin

  * •

We discuss the implementation of our stablecoins as on-chain tokens using a
reproducible computational pipeline using public trusted data and smart
contract-based registries

  * •

We demonstrate how the PACT carbon stablecoin addresses the scale and trust
issues in the voluntary carbon market

The remainder of the paper is laid out as follows. Section II provides the
necessary background to our work. In section III we present the design of the
PACT stablecoin which addresses the properties discussed earlier in this
section. Sections IV and V detail and evaluate our implementation of the PACT
stablecoin respectively. We then discuss how our work relates to existing
initiatives and future opportunities in section VI.

##  II Background

###  II-A Problems in the Voluntary Carbon Markets

The Taskforce on Scaling Voluntary Carbon Markets, the precursor to the
Integrity Council for Voluntary Carbon Markets (ICVCM), along with McKinsey
estimated the market for voluntary carbon credits could reach $50bn by 2030
[1]. Despite this there are widespread concerns that credits from REDD+
(Reduced Emissions from Deforestation and forest Degradation) projects, which
make up more than 40% of the voluntary carbon market [12], overestimate their
climate benefit [5, 13] due to pessimistic baselines. The remaining
$\approx$40% of credits sold in 2022 were Renewable Energy credits [14], the
additionality of which are unclear with the financial competitiveness of
renewables [15]. Verra, the largest certifier of carbon credits on the
voluntary market with over 70% market share [14], have several avoided
deforestation methodologies VM0007 [16], VM0015 [17] and VM0009 [18] – all of
which afforded project developers some freedom in creating their own
baselines. Verra have committed to phasing out these methodologies by 2025
[19].

Baselines chosen on a per-project basis result in wildly different
additionality and are thus not comparable. This makes REDD+ credits issued
under Verra methodologies difficult to value, makes them non-fungible and thus
limits available liquidity. This has led to concerns that the voluntary carbon
market is becoming a lemons market “where buyers have no way of distinguishing
quality, so some sellers flood the market with bad products, leading to a
breakdown of trust and ultimately market collapse.” [20].

###  II-B Carbon Credit Valuation

The problems with the existing markets lead us to applying econometric
techniques to the problem of valuing carbon credits, which we will explain
next. Each carbon credit stems from an intervention project that either
removes or avoids the emission of CO2. An example of an avoided emissions
intervention is to replace palm oil plantations which clearcut tropical
rainforest with mixed-forest cocoa plantations that have lower yield but
preserve the forest environment [4, 21]. The project has a base cost in the
form of the resources required to apply these incentives to shift the local
economy away from deforestation. The project is then analysed for the
additional tonnes of avoided CO2e (Carbon Dioxide Equivalent) from the
intervention for a resulting $/CO2e tonne. Calculating the additional tonnes
involves quantitatively and reliably determining the following values, each of
which requires specialised inspection of the nature of the intervention
involved.

Creating carbon stablecoins presents different challenges from conventional
fiat stablecoins, which we examine next.

####  II-B1 Additionality

The additionality of a project is the CO2e removed or avoided by the project’s
intervention [22]. This is determined against a business-as-usual case or a
baseline via a counterfactual analysis [23, 24]. For some project types, such
as Direct Air Capture [3], determining this baseline is relatively simple –
one is unlikely to pull CO2 from the atmosphere and sequester it without being
paid to do so. For others though, especially nature-based projects such as
avoided deforestation, the choice of baseline is more complicated. Overly
pessimistic baselines can lead to over-estimates of project CO2e benefits [25,
26], whilst underestimation make many projects financially unviable. To
further complicate valuation, projects from the same jurisdiction may use
differing methods for determining their baselines [27].

####  II-B2 Leakage

Project interventions may cause unintended climate damage outside of their
project area. Consider an avoided deforestation project that simply shifts
deforestation to the area surrounding the project – this has ultimately not
led to an avoidance of carbon being emitted into the (shared!) atmosphere
[28]. Leakage can be local, as in the previous example, or it can be global
where forgone production from the intervention leads to sustained demand
shifting supply of that commodity to elsewhere in the world [29]. Accounting
for local leakage can be assessed using data from the areas surrounding the
project. On the other hand, global leakage is a much harder problem as it
requires knowledge of the specific interventions carried out by the project to
account for e.g forgone production of a particular commodity.

####  II-B3 Permanence

Many classes of projects are impermanent; the net CO2e removed or avoided has
a risk of being later released back in to the atmosphere either during or
after the end of the project [30]. This is especially true of nature-based
projects where natural ecosystems are always vulnerable to net loss
disturbances such as fire, disease or floods. We therefore need compare
between projects where one offers permanent carbon sequestration but the other
offers a potentially larger but impermanent emissions avoidance. When a
portfolio of projects with different levels of impermanance are pooled, we
need a mechanism to make these comparable or else they represent different
levels of climate benefit.

###  II-C Carbon Credit Fungibility

Many intervention projects represent augmented or alternative livelihoods to
local people, and thus offer co-benefits beyond just their value in removing
or avoiding CO2e. These co-benefits range from increasing or avoiding the
reduction of biodiversity and natural habitats [31], to increasing the
prosperity of local inhabitants [32] and the promotion of equality and fair
redistribution of wealth in the region [33]. For most buyers of carbon
credits, projects offering these co-benefits can attract significant premiums
since they help to balance a portfolio of worldwide interventions against a
variety of environmental, social and corporate governance (ESG) factors.

Project | ALadj | eP | £project | £PACT | Biodiversity | Livelihood | Justice
---|---|---|---|---|---|---|---
Climeworks | 1 | 1 | 900 | 900 | C | B | A
CarbonCure | 1 | 1 | 145 | 145 | C | B | A
African rainforest conservation | 0.23 | 0.35 | 5.8 | 73 | A | A | A
Ecuadorian rainforest conservation | 0 | 0.20 | 15 | — | A | B | B
Mexican tree planting | 0.48 | 0.36 | 17.5 | 101 | B | A | A
University of Cambridge Woodland Creation | 1 | 0.77 | 112 | 145 | B | B | A
UK Fenland conservation | 1 | 0.75 | ? | ? | C | B | B
TABLE I: PACT evaluation of several project interventions (reproduced from
[24])

A carbon asset should ideally be interchangeable across different
interventions, since it ultimately represents some tonnes of CO2e that are
avoided or removed, as calculated from the additionality, leakage and
permanence values of the project (§II-B). However, the co-benefits of the
project illustrate that in reality projects differ through the interventions
used on the ground, their effectiveness and the jurisdiction(s) in which they
take place. This matters hugely in practice since any credit-generating
project is subject to a risk of reversal or over-crediting, and so a single
controversial project in a larger pool of carbon credits can inflict
reputational damage to a well-intentioned purchaser [34]. Since the carbon
markets are currently voluntary, this blowback leads to adverse selection
effects in the market, and the preferred action for well-intentioned
purchasers is therefore often inaction (i.e. non-participation in carbon
credits) that hinders wider adoption of offsetting.

It is therefore essential that carbon stablecoins are not only accurate
representations of the quantitative emissions benefits, but that they also
track the qualitative co-benefits and allow for buyers to define their own
thresholds for fungibility. One buyer may value biodiversity preservation much
more than another buyer, and therefore not treat otherwise-equivalent (from an
emissions perspective) assets equivalently.

###  II-D Carbon Credit Liquidity

It is not unusual for a carbon credit-generating project to last for decades,
especially those based around natural climate solutions. Project developers
thus often face delays of years between starting a project and realising the
climate benefit which allows carbon credits to be issued and sold [35]. If
trees are planted, or forests are not cut down, it can take 5-10 years from
the inception of the project to verify the initial benefit of avoided
emissions from net forest carbon stock. Therefore, the existing carbon market
is extremely supply constrained due to the unusual upfront financing needs
[36]. Another differentiator from fiat stablecoins, is that the available pool
of carbon stablecoins steadily decreases due to the fact that every carbon
stablecoin can only be spent once (dubbed as “retired”) to offset climate
damage, which ensures that there is a further constant pressure on supply.

Meanwhile, the demand for carbon credits is forecast to grow to $250bn by
2050[1]. Left to itself, this will cause the price to soar (leading to
organisations and individuals not being able to offset) or for junk supply of
credits (resulting in, at best, minimal climate benefit). The other (more
desirable) direction is that a carbon credits market dramatically increases
the supply of projects available by incentivising early financing for
promising projects, but without making future promises about emissions that
may not pan out in practise.

##  III Architecting our PACT carbon stablecoin

We have so far examined the differentiating properties – both quantitative and
qualitative – needed from a carbon stablecoin. We next examine how we overcome
these complexities and enable carbon credits to be valued effectively and
transacted at low cost whilst still acknowledging their respective co-
benefits. We dub our carbon stablecoin a PACT (for “Permanent Additional
Carbon Tonne”) as it systematically accounts for the permanence, additionality
and leakage (§II-B) for every project [37].

###  III-A PACT Valuation

Currently, carbon projects self-declare their own background baselines, and
then calculate their additionality against that baseline. This is problematic
since different projects would have declared different baselines, and thus
would not be comparable (and their valuations in fiat would be accordingly
skewed). This leads to a huge range of prices per tonne in the current market.
Our carbon stablecoin design instead uses global, comparable baselines by
deploying modern econometric techniques [24] that can be measured digitally
for a class of project intervention (e.g. satellites for avoided deforestation
or restoration forestry projects). This then implies that any set of carbon
credits can be quantitatively compared regardless of their intervention type.

The PACT comparability property allows for robust relative valuation between
projects; if a single permanent additional carbon tonne (PACT) of Direct Air
Capture is $1000 then a REDD+ avoided deforestation credit [38] offering the
same at $150 indicates one is over- or under-priced. An example set of
projects can be found in Table I. The $AL$ and $eP$ represent additionality,
leakage and permanence results, and $\pounds_{project}$ is the base price per
tonne of the project. $\pounds_{PACT}$ represents the adjusted and comparable
price across projects. The remaining columns show the ratings for the project
– textual analysis is attached to the PACT metadata. We go into more detail
about these calculations later (§V).

We also use digital measurement reporting and verification (dMRV) where
possible (e.g. satellites for forests) to give us a global basis on which to
calculate the valuation. A reproducible calculation infrastructure then acts
as a transparent oracle, enabling data feeds into a blockchain- or ledger-
based tokenisation platform. Without all of these pieces, carbon credit values
are prone to significant volatility and risk of being junk credits due to
methodological or measurement errors. Together, however, these valuation
techniques allow carbon projects to be significantly more reliably valued in
terms of price per tonne.

###  III-B PACT Fungibility

Quantifying projects against comparable baselines transitively enables their
eventual price (which combines the base cost of the intervention) to also be
comparable. However projects – especially those that are nature-based – come
with significant co-benefits such as improvements to biodiversity and local
livelihoods which need to be qualitatively analysed and scored more broadly
than the precision required of CO2e calculations. These co-benefits must be
tracked with each PACT issued by the project, so that the buyer can filter
pooled PACTs on the basis of their threshold for these co-benefits, reflecting
their own risk appetite and strategic ESG drivers.

PACT carbon stablecoins are therefore augmented with additional metadata that:

  * •

categorises them based on qualitative ratings, much like bonds. These ratings
are simple A/B/C rating and come with associated textual descriptions. Common
categories include biodiversity preservation ratings, local livelihood impact,
and justice frameworks that check topics such as free-and-informed-consent for
indigenous inhabitants.

  * •

defines the political jurisdiction in which a project takes place. Many buyers
wish to spread out their portfolio of carbon credits across geographies to
minimise risk of reversal (e.g. due to wildfires) [39].

  * •

describes the source of funding for the carbon project, to facilitate
“greenwashing” checks for buyers that do not wish to be associated with
certain sources of funds (e.g. from fossil-fuel processing).

A pooled token can credibly reflect a PACT (permanent additional carbon tonne)
across different projects, and buyers can also select their contents based on
criteria that matter to them (such as a minimum biodiversity benefit). Thus
with PACTs pooled by their co-benefits and jurisdiction, we can achieve
fungibility within pools.

###  III-C PACT Liquidity

With PACTs pooled according to co-benefits and jurisdiction, risk can be
spread across the pool much more robustly. Once the overall market risks
drops, it becomes more viable to justify the financing of new supply of carbon
credits via new interventions, which would result in significant numbers of
tokens backed by each pool being available. This fungibility can then enable
liquidity on decentralised financial infrastructure such as automated market
makers (AMMs).

Increased liquidity on digital trading infrastructure opens up new uses, such
as allowing real-time carbon offsetting and on-demand offsetting with
immediate retirement. This is currently not possible on conventional carbon
markets, since the purchase of credits is a time-consuming process that
involves bilateral negotiations with brokers and careful per-project checking
to minimise the risk of reputational damage.

##  IV Implementing the PACT carbon stablecoin

Figure 1: System architecture showing the evaluation oracle feeding carbon
credits (climate benefit) into a smart contract system. Clients can depend on
oracles to calculate emissions harm, and indexers can track global progress.

To address the valuation, fungibility and liquidity of carbon credits, we
construct a solution comprised of several components:

  * •

Reproducible computational pipelines that mechanise the evaluation of projects
enabling transparent checking of calculations by third parties

  * •

Pooling mechanisms that group underlying projects by their co-benefits
permitting fungible tokens that increase liquidity and enable automated
trading

  * •

Emissions-efficient carbon credit issuance and retirement tracking via a smart
contract-based registry that permits for both on- and off-chain trading

We now describe how we implement the PACT stablecoin architecture (§III) as
on-chain tokens in our experimental prototype (see Figure 1). Before
considering the individual components of the proposed system, we first
introduce the econometric techniques and frameworks we have built to make this
possible.

###  IV-A Algorithmic quantification of project climate benefit

The short form to calculate a PACT value is $(A-L)\times eP$, where the
project additionality $A$ is adjusted by leakage $L$ and multiplied by the
equivalent permanence $eP$. That formula is a general ex-post framework for
quantifying the climate benefit of a given project within a specified
timeframe, described in detail in the literature [24, 37, 40]. To summarise,
the method involves a two-step calculation process.

####  IV-A1 Calculation of Additionality and Leakage

A project is defined as a set of polygon boundaries within a given
jurisdiction. The first step involves determining the additionality and
leakage of the project area, i.e., the additional climate benefit generated as
a direct result of the project and unintended climate damage observed as a
consequence of the project. This is achieved by comparing the observed
outcomes with a statistical counterfactual, which represents the business as
usual case.

####  IV-A2 Adjustment to equivalent Permanence

The next step adjusts the net additionality so that an impermanent
intervention can be viewed as to be equivalent to geologically permanent
carbon sequestration. This is achieved through the use of an ex-ante but
conservative release schedule which models the rate at which the net
additional carbon in the project is released in to the atmosphere.

As the additionality calculation is ex-post, the statistical counterfactual is
constructed with observational ground-truth data that permits for a
mechanised, reproducible digital process.

###  IV-B Integration of blockchain data oracles

The mechanisation of the $(A-L)*eP$ evaluation allows for the implementation
of a fully digital evaluation pipeline that functions as a data oracle [41].
The evaluation pipeline processes and publishes evaluation data on a per-
project basis in such a way that all of the original inputs are tracked,
ensuring transparency and verifiability throughout the project evaluation
process.

For each project, the pipeline publishes and pins the following components to
the InterPlanetary File System (IPFS) [42].

####  IV-B1 Ground Truth Data

All data used for the construction of statistical counterfactuals used in
additionality and leakage calculations. This puts restrictions on the types
and availability of the data used as this necessarily needs to be freely
available under a license that permits for reproduction.

####  IV-B2 Statistical Counterfactuals

The calculated counterfactuals are made available. Whilst they could be
reconstructed from the ground truth data, the step of producing them is
computationally intensive and so their availability permits for lighterweight
verification, as well as additional tooling that allows for visualisation.

####  IV-B3 eP Release Schedules

As each methodology and potentially project has their own release schedule
used for the calculation of equivalent permanence, these must be made
available for reproduction as well as annual reccalculation of permanence and
credit adjustment.

The hashes of these artefacts are recorded alongside the evaluation results,
ensuring immutability and traceability of a given evaluation resulting and
also permitting independent third-party verification by reproducing the (open
source) computation pipeline.

###  IV-C Mechanisms for pooling co-benefits

As described earlier (§III-B), in addition to their primary climate benefit,
projects often yield significant other co-benefits including improvements in
biodiversity, local livelihoods, and social justice. Our pipeline tracks co-
benefits as follows.

####  IV-C1 Quantification of co-benefits

Where there are robust methods to do so, we quantitatively assess the co-
benefits of projects, which allows for comparison between projects. If a
numerical assessment is not yet feasible, then a qualitative assessment is
sufficient and assigned an A/B/C rating by human experts. Our most commonly
tracked co-benefits include biodiversity, livelihoods and justice – while
there are emerging mechanisms for quantifying biodiversity [43] and livelihood
impact [44], the most robust state-of-the-art for these is still qualitative
assessment.

####  IV-C2 Categorisation and Pooling

Projects are categorised into groups based on their expert-rated co-benefits.
This permits the construction of distinct PACT tokens each backed by pools
containing credits from evaluated projects with similar co-benefits. These
tokens, denominated in CO2e tonnes, are thus fungible whilst preserving the
value of project co-benefits.

Through this approach we can balance the benefits of fungibility whilst still
reflecting the value of project co-benefits.

###  IV-D Credit issuance and tracking

To manage issuance, trading, and retirement of PACT carbon credits in an
emissions-efficient way, we use a smart contract-based blockchain system. We
are pragmatic as to the manner in which the majority of credits are transacted
currently and so the system is designed to support both on-chain and off-chain
trading activities. The PACT system comprises three key contracts.

####  IV-D1 Central Registry Contract

At the core is a central registry contract responsible for tracking the
issuance, retirement and ownership of credits. Ownership is tracked in this
contract against an on-chain wallet or smart contract address, facilitating
integration with existing blockchain token interfaces (e.g FA2 on Tezos or
ERC20 on Ethereum) and thereby enables interoperability with wallets and
decentralised finance (DeFi) systems.

The registry also includes a “retirement” function to enable the offsetting of
credits against climate damage. With the potential requirement for billions of
tonnes of carbon credits [1] by 2030, we need an efficient way retire credits
that does not itself cause significant carbon emissions. While any retirements
system could be made more emissions efficient by coarsening the units of
retirement, this hinders detailed checking of organisation’s offsetting
claims. Thus, our mechanism for retirement minimises the additional on-chain
storage required due to the significant carbon footprint involved in on-chain
storage[45] by providing a specialised retirement entrypoint (and not, for
example, issuing NFTs per retirement, which would increase the on-chain
storage requirements).

Figure 2: Stages in carbon credit lifecycle

####  IV-D2 Pooled Credit Contract

A specialised contract is proposed for pooling project credits by their
categorised co-benefits, this creating pooled PACT credits. This contract
mirrors the interface of the central registry, ensuring interoperation with
existing blockchain and DeFi infrastructure and enabling the management and
trading of pooled credits.

####  IV-D3 Custodian Contract

To bridge the gap between on-chain and off-chain financial systems, a
’custodian’ contract is proposed. This contract is designed to hold both
individual project PACT credits and pooled PACT credits on behalf of off-chain
entities. It serves as a link, allowing traditional finance systems to engage
in trading activities that are reflected and tracked on the blockchain.

Through this system we aim to establish an emissions-efficient and transparent
system for the management of carbon credits. This approach not only addresses
the immediate needs of credit issuance and retirement but also pragmatically
integrates with existing financial ecosystems, thus making wider-adoption a
more realistic prospect.

##  V Evaluating the PACT carbon stablecoin

Figure 3: A visualisation of the counterfactual pixel-matching pipeline to
assess the additionality of an avoided deforestation project in Sierra Leone.
Pixels in green are from the project and they are matched to similar locations
in blue.

In order to test the efficacy of our architecture, we have built a prototype
of the PACT system architecture (§IV), with a focus on avoided deforestation
projects for tropic rainforests. Our implementation work has been focused on
three core areas, each corresponding to a key component of the proposed
solution.

####  V-1 Development of an Evaluation Pipeline

We have developed an open-source software pipeline that evaluates suitable
projects using this approach. The pipeline serves as the core of the proposed
data oracle, capable of processing and publishing project data. It is designed
to allow for full reproducibility, ensuring that third parties can
independently verify and replicate evaluations. Figure 3 shows an example
screenshot from the evaluation project browser, which is one of the forestry
projects from Table I.

We implemented the PACT Tropical Moist Forest methodology [40] for our
pipeline. The methodology uses multiple sources of publicly available data to
make the assessment based on comparison tens of thousands of treatment pixels
(samples) in both the project zone and its surrounding leakage zone to
corresponding paired control pixels in the surrounding region. Pairing is done
based on similarity of physical properties of the pixels (country, biome type,
elevation, slope, and proximity to human habitation), along with similar
historic behaviour in terms of land usage [46] up until the project start
point. Once the project starts, we then examine how the land usage changes
over time for the treatment pixels versus the counterfactual control pixels,
which indicate behaviour had the intervention not taken place. By combining
the local land usage data with AGB data [47], we calculate the carbon density
of the area and assess both the additionality of the project area (i.e.,
carbon saved compared to the control counterfactual pixels) and leakage (signs
of activity displaced into a buffer around the project) to create an overall
permanence evaluation for the project.

To enable adoption of the assessment methodology, we have provided a reference
pipeline implementation written in Python and controlled by the OCurrent
workflow library. The bulk of the work is done a series of Python scripts,
each performing one step in the methodology: the language choice and the
breaking down of the methodology into individual steps was made to make the
implementation scrutable to ecologists. These individual steps are then
orchestrated by an OCaml-based workflow engine, which provides a way to ensure
the scripts not only run in the right order, but unnecessary repeated work is
avoided, by tracking result dependancies we can avoid re-computing old results
where those individual scripts or their inputs don’t update. A typical
computation pipeline where a large project is involved can take up to a day to
process on a fast machine.

####  V-2 Smart Contracts

The blockchain piece of our implementation is a suite of open-source contracts
on the Proof-of-Stake Tezos blockchain [48]. These contracts implement the
registry and custodian functionalities, designed to manage the issuance,
trading and retirement of carbon credits efficiently and securely. The choice
of the Tezos blockchain and implementation reflect the requirements of
minimising the environmental impact of the proposed systems.

We chose the Tezos blockchain for the implementation of our proposed system
due to its low carbon footprint[49] and potential to deliver significant
transactional throughput for carbon stablecoin transactions at low gas cost
[50]. Tezos also has a novel self-amending distributed governance mechanism
built into the chain, allowing for technological upgrades to be voted on by
users [51]. This mechanism builds confidence in the longevity of the
underlying blockchain itself to run for decades, to match the carbon credits
projects that it is tracking.

The registry contract performs the following key functions:

  * •

Issuance: The registry issues PACT tokens on instructions from the data oracle
associated with the particular contract instantiation

  * •

Tracking of ownership: Transfer of PACT tokens between on-chain entities and
the querying of balances

  * •

Retirement: Tokens can be burned in order to retire and offset them. Each
retirement can only happen once.

The registry also implements the Tezos FA2 token standard [52] which enables
interoperability with existing Tezos wallets, marketplaces and automated
market-makers (AMMs). Each instance of the contract on-chain is associated
with a single data oracle that can mint and update contract metadata. The
contract allows for transfer of oracle to provide for evaluation updates.

Each contract contains one or more token types, numerated by their token id.
The contracts contain a metadata mapping against each token id, which in the
proposed system would contain immutable references to data on the project
itself, geographic information, project durations and finally the categorised
assessments of co-benefits.

####  V-3 Issuance Smart Contracts

The mint entrypoint enables the oracle to issue PACT tokens to an on-chain
address which are added to the addresses’ balance in the contract. A
transactional call to the mint entrypoint, e.g from a project developer
issuing a new set of credits, can contain structured metadata and this is the
mechanism used for recording the hashes of the evaluation source code, its
inputs and outputs. This data is “emitted’ by the smart contract but not added
to on-chain storage – this means it will be accessible from chain explorers
and archival nodes. This mechanism, in contrast to on-chain storage, does not
necessitate fast rapidly-accessible storage and so significantly lowers the
emissions involved in minting. This same mechanism is used for retirement.

The contract contains two entrypoints for tracking of token ownership:
Transfer and Balance. Transfer moves tokens between the balances of two on-
chain addresses and balance simply returns the total balance of a given token
at an address, in the contract. Due to adhering to the FA2 token
specification, the contract also supports operators which enables delegating
authority to transfer tokens belonging to an address to another address. This
is similar to the the allowance functionality in Etheruem’s ERC20[53].

####  V-4 Retirement Smart Contracts

The retirement entrypoint allows an address (or their operator) holding PACT
tokens in the registry to destroy part of their balance and do so with an
associated set of metadata. This is used to “offset” the tokens against a
claimed carbon emission and through specific details in the metadata as to the
cause of that carbon emission organisations can more precisely show their use
of offsets is in addition to their decarbonisation work.

Retirements of PACT tokens are designed to be emissions efficient, that is
they minimise the climate damage involved in the retirement itself. To do this
they “emit” metadata during retirement operations, which makes the data
available to indexers and archival nodes but does not occupy on-chain storage.

####  V-5 Custodian Smart Contracts

The custodian contract is intended to act as a bridge between on- and off-
chain transactions of PACT tokens. Each instance of the custodian contract
enables an on-chain entity to hold tokens on behalf of off-chain entities and
issue, manage and retire on their behalf. An off-chain entity is represented
by a set of Know Your Customer (KYC) metadata specific to the custodian
instance. It has the following main entrypoints:

  * •

Transfer internal/external: Transfers PACT token balances between two off-
chain entities (internal) or from the custodian to an on-chain entity
(external). Trades of PACT tokens between off-chain entities (e.g through an
existing financial exchange or bilaterally) are required to be reported to the
custodian, who in turn issues an internal transfer of the tokens between the
entities in the smart contract.

  * •

Mint/Retire Facilitates issuance and retirement of PACT tokens to an off-chain
entity, such as a project developer or corporate buyer. These are ultimately
carried out at the registry, with the custodian acting as a proxy.

Thus the custodian contract enables interoperation with existing carbon credit
trading venues, facilitating the reporting of transactions on-chain and
maintaining transparency.

##  VI Discussion

The combined properties of the proposed PACT carbon stablecoin enable it to
address the scale and trust issues currently plaguing the voluntary carbon
market.

Scale is achieved through:

  * •

data-driven project baselines that use freely available remote sensing data,
enabling low-cost project evaluations and monitoring

  * •

automated evaluation pipelines that serve as data oracles for the issuing of
on-chain tokens

  * •

pool mechanisms that group underlying projects and permit fungible tokens that
increase liquidity and enable automated trading

  * •

smart contracts that provide on-chain emissions-efficient registration and
custodianship of credits

We believe trust is also achieved via:

  * •

statistical and robust project baselines derived from remote sensing data and
thus avoids pessimistic baselines provided by projects themselves

  * •

reproducible open-source computational pipelines for evaluation and monitoring
that permit cross-checking by third parties

Name | Comparable for valuation | Fungibility | Liquidity
---|---|---|---
Verra | ✗(incomparable baselines) | ✗ | ✗
Toucan | ✗(incomparable baselines) | ✗(pooled but incomparable) | ✓
Flowcarbon | ✗(incomparable baselines) | ✗(pooled but incomparable) | ✓
Moss | ✗(incomparable baselines) | ✗(pooled but no co-benefits) | ✗
TABLE II: Related carbon asset systems

###  VI-A Related Work

Table II shows several of the most prominent initiatives to bring carbon
credits on to various blockchains. The largest is Toucan protocol[54] which
tokenizes existing carbon credits in off-chain registries via a bridge. It
originally provided this for Verra credits though this was prohibited in
2022[55]. It currently bridges credits from Puro Earth[56], a newer voluntary
standards body that only provides carbon removal credits that have at least
100 year permanence. This precludes nature-based projects such as Avoided
Deforestation or Afforestation, Reforestation and Revegetation (ARR) which
form major parts of many countries climate-change goals, especially in the
global south.

For bridged Verra credits, Toucan pools tokens in two separate pools: Base
Carbon Tonne (BCT) and Nature Carbon Tonne (NCT). While this does create
fungible BCT and NCT tokens, thus improving liquidity, it has significant
drawbacks. The credits forming both pools are not comparable \- they have
differing baselines and permanence [57]. This makes valuing the credits a
complex, manual process and indeed, has resulted in both pools containing
significant numbers of non-additional ”junk” credits [58]. Several other
projects, such as Flowcarbon and Moss also provided credits from Verra before
being prohibited from doing so. Table II shows how these tokens compare to the
PACT stablecoins, particularly around their comparability.

###  VI-B Future Work

There are many potential areas for future work on the proposed system, in
addition to the significant amounts of implementation work still to be carried
out.

#### Retirement

Carbon offsets should be used only for climate damaging activities that are
unavoidable and which can not currently be decarbonised or historic emissions.
That currently this is not always the case opens up even good actors to
accusations of ”greenwashing”. In order to avoid these reputational risks many
organisations simply choose not to offset but this need not be the case if
there were systems available to enable these organisations to transparently
show they were using offsets correctly. It may be possible to use techniques
like commitment schemes and verifiable computation to attach metadata to
retirement of offsets that enables scrutiny of their use while revealing
little information that could be of use to competitors.

#### Further decentralisation

As proposed the current system centralises the evaluation of projects, the
assessment of co-benefits and the issuance of credits with a single data
oracle. An alternative design might be that an arbitrary number of unit-less
credits are issued for a single project intervention and time period, with
evaluations of carbon and co-benefits being added as “layers” from multiple
participants in the ecosystem. Under this model, one’s available carbon
offsets in PACTs would be the PACT evaluation layer for the project’s
intervention in that time period multiplied by one’s fraction of total issued
tokens for that project intervention and time period. With multiple evaluation
layers on a project, buyers could have significant confidence in the true
carbon reduction or removals from the project, as well as the co-benefits.
There are many open questions for how this market could be structured and the
various incentive mechanisms that would need to be in place to encourage
evaluators to come forward without burdening project developers with greater
costs.

#### Improved fungibility

Whilst categorising projects by their co-benefits and jurisdiction controls
for the major sources of value and risk, it could fail to distinguish very
high quality projects as there is a necessary trade-off between the broadness
of categorisation and the liquidity of the resulting tokens for those pools.
Recent research on structured pools[59] could be one approach but more radical
could be to separate co-benefits from the carbon benefits of projects
themselves, in a manner similar to Renewable Energy Certificates[60]. If an
organisation puts a premium on biodiversity but has no current offsetting
needs, they could purchase the biodiversity components of existing projects -
which ultimately results in a higher return for the project. This may be
impractical without mechanisms to quantitatively assess co-benefits however.

##  VII Conclusion

We tackle the problem of carbon credit valuation through the adoption and
implementation of econometric techniques [24, 40] for assessing additionality
and leakage through statistical counterfactual analyses that provide dynamic
project baselines. We adopt conservative discounting techniques [37] for
determining the equivalent permanence of emissions reduced or removed by a
project. Together these techniques enable projects to be assessed in Permanent
Additional Carbon Tonnes (PACTs) which along with the base price per tonne
being offered enables comparable valuation across very diverse carbon credit
projects. Further we developed a reproducible computational pipeline for
estimating the climate benefits of carbon offset projects using these data-
driven dynamic baselines. This pipeline can serve as a data oracle, enabling
reliable and transparent valuation of projects on the blockchain.

With PACT tokens offering comparable climate benefit, we identify the co-
benefits attracting buyer premiums (biodiversity, livelihood impact and social
justice) as well as the main risk factor of jurisdiction, and pool tokens by
their biodiversity/justice/jurisdiction attributes. This within-pool
fungibility allows for the issuance of tokens backed by each pool and which
can be traded on any exchange or automated market maker (AMM).

In summary, we believe the contributions made by this paper solve key issues
that limit the effective use of carbon credits as digital assets, such as on
the blockchain. By widening market participation we can ensure that more
entities fully balance their climate damage with climate benefit, and together
we can limit the worst effects of climate change.

##### Acknowledgements

This research was funded by a donation to the University of Cambridge from the
Tezos Foundation (NRAG/719). We thank Andrew Balmford, David Coomes, Harriet
Hunnable, Eleanor Toye Scott and Bas Spitters.

## References

  * [1] C. Blaufelder, C. Levy, P. Mannion, and D. Pinner, “A blueprint for scaling voluntary carbon markets to meet the climate challenge,” _McKinsey_ , vol. 5, 2021.
  * [2] S. Gossling, P. Hanna, J. Higham, S. Cohen, and D. Hopkins, “Can we fly less? Evaluating the necessity of air travel,” _Journal of Air Transport Management_ , vol. 81, p. 101722, 2019.
  * [3] N. McQueen, K. V. Gomes, C. McCormick, K. Blumanthal, M. Pisciotta, and J. Wilcox, “A review of direct air capture (DAC): scaling up commercial technologies and innovating for the future,” _Progress in Energy_ , vol. 3, no. 3, p. 032001, 2021.
  * [4] B. Sohngen, R. H. Beach, and K. Andrasko, “Avoided deforestation as a greenhouse gas mitigation tool: Economic issues,” _Journal of Environmental Quality_ , vol. 37, no. 4, pp. 1368–1375, 2008.
  * [5] P. Greenfield, “Carbon offsets used by major airlines based on flawed system, warn experts,” _The Guardian_ , May 2021.
  * [6] C. Hodgson, “Surge of investment into carbon credits creates boom time for brokers,” _Financial Times_ , May 2022.
  * [7] S. Twidale and S. McFarlane. (2023, Sep) Carbon credit market confidence ebbs as big names retreat. Reuters.
  * [8] G. A. Karolyi and J. Tobin-de la Puente, “Biodiversity finance: A call for research into financing nature,” _Financial Management_ , 2023.
  * [9] G. Baughman, F. Carapella, J. Gerszten, and D. Mills, “The stable in stablecoins,” FEDS Notes, Washington, December 16 2022. [Online]. Available: https://doi.org/10.17016/2380-7172.3224
  * [10] K. Sandor. (2024, January) Tether reports record $2.85b profit as biggest stablecoin nears $100b market cap. Coindesk. Accessed on March 13, 2024. [Online]. Available: https://www.coindesk.com/business/2024/01/31/tether-reports-record-285b-profit-as-biggest-stablecoin-nears-100b-market-cap/
  * [11] A. S. Goudie, _Human impact on the natural environment_. John Wiley & Sons, 2018.
  * [12] United Nations Reducing Emissions from Deforestation and Forest Degradation (UN-REDD), “Forest carbon pricing brief,” Nov 2022. [Online]. Available: https://www.un-redd.org/sites/default/files/2022-11/Forest%20carbon%20pricing%20brief%20-%20FINAL.pdf
  * [13] P. Greenfield, “Revealed: more than 90% of rainforest carbon offsets by biggest certifier are worthless, analysis shows,” _The Guardian_ , Jan 2023. [Online]. Available: https://www.theguardian.com/environment/2023/jan/18/revealed-forest-carbon-offsets-biggest-provider-worthless-verra-aoe
  * [14] Climate Focus, “Vcm dashboard 2022 overview,” Jan 2023. [Online]. Available: https://climatefocus.com/wp-content/uploads/2023/01/VCM-Dashboard-2022-Overview-1.pdf
  * [15] N. Lakhani, “Revealed: top carbon offset projects may not cut planet-heating emissions,” _The Guardian_ , Sep 2023. [Online]. Available: https://www.theguardian.com/environment/2023/sep/19/do-carbon-credit-reduce-emissions-greenhouse-gases
  * [16] Verra, “VM0007 REDD methodology framework (REDD-MF), v1.6,” 2023. [Online]. Available: https://verra.org/methodologies/vm0007-redd-methodology-framework-redd-mf-v1-6/
  * [17] ——, “Vm0015 methodology for avoided unplanned deforestation v1.1,” 2023. [Online]. Available: https://verra.org/methodologies/vm0015-methodology-for-avoided-unplanned-deforestation-v1-1/
  * [18] ——, “Vm0009 methodology for avoided ecosystem conversion v3.0,” 2023. [Online]. Available: https://verra.org/methodologies/vm0009-methodology-for-avoided-ecosystem-conversion-v3-0/
  * [19] Patrick Greenfield, “Biggest carbon credit certifier to replace rainforest offsets scheme,” _The Guardian_ , Mar 2023. [Online]. Available: https://www.theguardian.com/environment/2023/mar/10/biggest-carbon-credit-certifier-replace-rainforest-offsets-scheme-verra-aoe
  * [20] F. Lewsey, “Carbon credits: hot air? millions of carbon credits are generated by overestimating forest preservation,” University of Cambridge - Stories, Aug 2023. [Online]. Available: https://www.cam.ac.uk/stories/carbon-credits-hot-air
  * [21] J. C. A. Mboma, “Alternative livelihoods of forest edge communities around the gola rain forest national park in malema chiefdom, kailahun district.” _International Journal of Innovative Science, Engineering and Technology_ , vol. 8, Oct. 2021.
  * [22] L. Schneider, “Assessing the additionality of cdm projects: practical experiences and lessons learned,” _Climate Policy_ , vol. 9, no. 3, pp. 242–254, 2009.
  * [23] J. Bennett, “Event causation: The counterfactual analysis,” _Philosophical perspectives_ , vol. 1, pp. 367–386, 1987.
  * [24] T. Swinfield and A. Balmford, “Cambridge carbon impact: Evaluating carbon credit claims and co-benefits,” _Cambridge Open Engage_ , 2023.
  * [25] A. Guizar-Coutiño, J. P. G. Jones, A. Balmford, R. Carmenta, and D. A. Coomes, “A global evaluation of the effectiveness of voluntary REDD+ projects at reducing deforestation and degradation in the moist tropics,” _Conservation Biology_ , vol. 36, no. 6, p. e13970, 2022. [Online]. Available: https://conbio.onlinelibrary.wiley.com/doi/abs/10.1111/cobi.13970
  * [26] T. A. P. West, S. Wunder, E. O. Sills, J. Börner, S. W. Rifai, A. N. Neidermeier, G. P. Frey, and A. Kontoleon, “Action needed to make carbon offsets from forest conservation work for climate change mitigation,” _Science_ , vol. 381, no. 6660, pp. 873–877, 2023. [Online]. Available: https://www.science.org/doi/abs/10.1126/science.ade3535
  * [27] H. C. Teo, N. H. L. Tan, Q. Zheng, A. J. Y. Lim, R. Sreekar, X. Chen, Y. Zhou, T. V. Sarira, J. D. T. De Alban, H. Tang _et al._ , “Uncertainties in deforestation emission baseline methodologies and implications for carbon markets,” _Nature Communications_ , vol. 14, no. 1, p. 8277, 2023.
  * [28] S. Wunder, “How do we deal with leakage,” _Moving ahead with REDD: issues, options and implications_ , vol. 1, pp. 65–75, 2008.
  * [29] J. Gan and B. A. McCarl, “Measuring transnational leakage of forest conservation,” _Ecological Economics_ , vol. 64, no. 2, pp. 423–432, 2007.
  * [30] H. Herzog, K. Caldeira, and J. Reilly, “An issue of permanence: Assessing the effectiveness of temporary carbon storage,” _Climatic Change_ , vol. 59, no. 3, pp. 293–310, 2003.
  * [31] J. Phelps, E. L. Webb, and W. M. Adams, “Biodiversity co-benefits of policies to reduce forest-carbon emissions,” _Nature Climate Change_ , vol. 2, no. 7, pp. 497–503, 2012.
  * [32] H. W. Fischer, A. Chhatre, A. Duddu, N. Pradhan, and A. Agrawal, “Community forest governance and synergies among carbon, biodiversity and livelihoods,” _Nature Climate Change_ , pp. 1–8, 2023.
  * [33] L. Godden and M. Tehan, “REDD+: climate justice and indigenous and local community rights in an era of climate disruption,” _Journal of Energy & Natural Resources Law_, vol. 34, no. 1, pp. 95–108, 2016.
  * [34] L. Song and P. Moura, “An (even more) inconvenient truth: why carbon credits for forest preservation may be worse than nothing,” _ProPublica_ , 2019.
  * [35] L. Peskett, K. Schreckenberg, and J. Brown, “Institutional approaches for carbon financing in the forest sector: learning lessons for REDD+ from forest carbon projects in uganda,” _Environmental science & policy_, vol. 14, no. 2, pp. 216–229, 2011.
  * [36] W. van der Gaast, R. Sikkema, and M. Vohrer, “The contribution of forest carbon credit projects to addressing the climate change challenge,” _Climate Policy_ , vol. 18, no. 1, pp. 42–48, 2018.
  * [37] A. Balmford, S. Keshav, F. Venmans, D. Coomes, B. Groom, A. Madhavapeddy, and T. Swinfield, “Realizing the social value of impermanent carbon credits,” _Nature Climate Change_ , vol. 13, no. 11, p. 1172–1178, 2023.
  * [38] A. Rakatama, R. Pandit, C. Ma, and S. Iftekhar, “The costs and benefits of REDD+: A review of the literature,” _Forest Policy and Economics_ , vol. 75, pp. 103–111, 2017.
  * [39] N. Chingono. (2023, Aug) Zimbabwe to take 30
  * [40] A. Balmford, D. Coomes, M. Dales, P. Ferris, J. Hartup, S. Jaffer, S. Keshav, M. Lam, A. Madhavapeddy, R. Message, and et al., “PACT Tropical Moist Forest accreditation methodology v2.0,” _Cambridge Open Engage_ , 2023.
  * [41] Chainlink, “What is a blockchain oracle?” Chainlink Education, Nov 2023, last Updated Date: November 29, 2023. [Online]. Available: https://chain.link/education/blockchain-oracles
  * [42] J. Benet, “Ipfs - content addressed, versioned, p2p file system,” 2014.
  * [43] A. Eyres, T. Ball, M. Dales, T. Swinfield, A. Arnell, D. Baisero, A. P. Durán, J. Green, A. Madhavapeddy, and A. Balmford, “LIFE: A metric for quantitively mapping the impact of land-cover change on global extinctions,” Nov. 2023. [Online]. Available: https://www.cambridge.org/engage/coe/article-details/65648bdbcf8b3c3cd73bbe64
  * [44] M. Burke, A. Driscoll, D. B. Lobell, and S. Ermon, “Using satellite imagery to understand and promote sustainable development,” _Science_ , vol. 371, no. 6535, p. eabe8628, 2021.
  * [45] S. Tannu and P. J. Nair, “The dirty secret of ssds: Embodied carbon,” 2023.
  * [46] C. Vancutsem, F. Achard, J.-F. Pekel, G. Vieilledent, S. Carboni, D. Simonetti, J. Gallego, L. E. O. C. Aragão, and R. Nasi, “Long-term (1990–2019) monitoring of forest cover changes in the humid tropics,” _Science Advances_ , vol. 7, no. 10, p. eabe1603, 2021. [Online]. Available: https://www.science.org/doi/abs/10.1126/sciadv.abe1603
  * [47] L. Duncanson, J. R. Kellner, J. Armston _et al._ , “Aboveground biomass density models for nasa’s global ecosystem dynamics investigation (gedi) lidar mission,” _Remote Sensing of Environment_ , vol. 270, p. 112845, 2022. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0034425721005654
  * [48] L. Goodman, “Tezos: A self-amending crypto-ledger position paper,” _Aug_ , vol. 3, p. 2014, 2014.
  * [49] PricewaterhouseCoopers, “Study of the environmental impact of the tezos blockchain: Life cycle assessment of the tezos blockchain protocol,” https://tezos.com/2021-12-06-Tezos-LCA-Final.pdf . Accessed November 2023.
  * [50] https://research-development.nomadic-labs.com/million-tps-demo.html. Accessed on 06.11.2023.
  * [51] V. Allombert, M. Bourgoin, and J. Tesson, “Introduction to the tezos blockchain,” in _2019 International Conference on High Performance Computing & Simulation (HPCS)_. IEEE, 2019, pp. 1–10.
  * [52] M. Gabbay, A. Jakobsson, and K. Sojakova, “Money grows on (proof-) trees: the formal fa1. 2 ledger standard,” _arXiv preprint arXiv:2109.09451_ , 2021.
  * [53] M. Di Angelo and G. Salzer, “Tokens, types, and standards: identification and utilization in ethereum,” in _2020 IEEE International Conference on Decentralized Applications and Infrastructures (DAPPS)_. IEEE, 2020, pp. 1–10.
  * [54] “Toucan Whitepaper,” https://docs.toucan.earth/. Accessed November 2023.
  * [55] B. Mulder, “As Verra halts tokenization of carbon credits, Toucan vows to ’keep web3 ethos alive’,” S&P Global - Commodity Insights, May 2022. [Online]. Available: https://blog.toucan.earth/verra-consultation-summary/
  * [56] “Puro earth,” https://puro.earth/, 2023, accessed: 2023-12-11.
  * [57] D. Sorensen, “Tokenized carbon credits,” _Ledger_ , 2023.
  * [58] G. Badgley and D. Cullenward, “Zombies on the blockchain,” CarbonPlan, Apr 2022. [Online]. Available: https://carbonplan.org/research/toucan-crypto-offsets
  * [59] D. Sorensen, “Structured pools for tokenized carbon credits,” in _2023 IEEE International Conference on Blockchain and Cryptocurrency (ICBC)_. IEEE, 2023, pp. 1–6.
  * [60] Environmental Protection Agency (EPA), “Renewable energy certificates (recs),” EPA Green Power Markets, 2023, accessed online. [Online]. Available: https://www.epa.gov/green-power-markets/renewable-energy-certificates-recs


* Kogut (1979) J. B. Kogut, Rev. Mod. Phys. 51, 659 (1979).
  * Hahn (1950) E. L. Hahn, Phys. Rev. 80, 580 (1950).
  * Suter and Álvarez (2016) D. Suter and G. A. Álvarez, Rev. Mod. Phys. 88, 041001 (2016).
  * Coleman and Weinberg (1973) S. Coleman and E. Weinberg, Phys. Rev. D 7, 1888 (1973).
  * Jackiw (1974) R. Jackiw, Phys. Rev. D 9, 1686 (1974).
  * Dolan and Jackiw (1974) L. Dolan and R. Jackiw, Phys. Rev. D 9, 3320 (1974).
  * Weinberg (1974) S. Weinberg, Phys. Rev. D 9, 3357 (1974).
  * Wilson and Fisher (1972) K. G. Wilson and M. E. Fisher, Phys. Rev. Lett. 28, 240 (1972).
  * Fisher (1998) M. E. Fisher, Rev. Mod. Phys. 70, 653 (1998).
  * Glimm and Jaffe (1968) J. Glimm and A. Jaffe, Phys. Rev. 176, 1945 (1968).
  * Glimm and Jaffe (1973) J. Glimm and A. Jaffe, Fortschritte der Physik 21, 327 (1973).
  * Feldman and Osterwalder (1976) J. S. Feldman and K. Osterwalder, Annals of Physics 97, 80 (1976).
  * Glimm and Jaffe (1974) J. Glimm and A. Jaffe, Phys. Rev. Lett. 33, 440 (1974).
  * Lüscher and Weisz (1987) M. Lüscher and P. Weisz, Nuclear Physics B 290, 25 (1987).
  * Aizenman (1981) M. Aizenman, Phys. Rev. Lett. 47, 1 (1981).
  * Fröhlich (1982) J. Fröhlich, Nuclear Physics B 200, 281 (1982).
  * Radcliffe (1971) J. M. Radcliffe, Journal of Physics A: General Physics 4, 313 (1971).
  * Haldane (1983) F. Haldane, Physics Letters A 93, 464 (1983).
  * Fradkin and Stone (1988) E. Fradkin and M. Stone, Phys. Rev. B 38, 7215 (1988).
  * Gell-Mann and Lévy (1960) M. Gell-Mann and M. Lévy, Il Nuovo Cimento (1955-1965) 16, 705 (1960).
  * Shankar (1994) R. Shankar, Rev. Mod. Phys. 66, 129 (1994).
  * Ghosh (1995) P. K. Ghosh,  _Ion traps_ (Clarendon Press, 1995).
  * Dubin and O’Neil (1999) D. H. E. Dubin and T. M. O’Neil, Rev. Mod. Phys. 71, 87 (1999).
  * Wineland and Itano (1979) D. J. Wineland and W. M. Itano, Phys. Rev. A 20, 1521 (1979).
  * Itano and Wineland (1982) W. M. Itano and D. J. Wineland, Phys. Rev. A 25, 35 (1982).
  * Wineland  _et al._ (1987a) D. J. Wineland, W. M. Itano, J. C. Bergquist, and R. G. Hulet, Phys. Rev. A 36, 2220 (1987a).
  * Cirac  _et al._ (1992) J. I. Cirac, R. Blatt, P. Zoller, and W. D. Phillips, Phys. Rev. A 46, 2668 (1992).
  * Morigi  _et al._ (2000) G. Morigi, J. Eschner, and C. H. Keitel, Phys. Rev. Lett. 85, 4458 (2000).
  * Eschner  _et al._ (2003) J. Eschner, G. Morigi, F. Schmidt-Kaler, and R. Blatt, J. Opt. Soc. Am. B 20, 1003 (2003).
  * Diedrich  _et al._ (1987) F. Diedrich, E. Peik, J. M. Chen, W. Quint, and H. Walther, Phys. Rev. Lett. 59, 2931 (1987).
  * Wineland  _et al._ (1987b) D. J. Wineland, J. C. Bergquist, W. M. Itano, J. J. Bollinger, and C. H. Manney, Phys. Rev. Lett. 59, 2935 (1987b).
  * Raizen  _et al._ (1992) M. G. Raizen, J. M. Gilligan, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Phys. Rev. A 45, 6493 (1992).
  * Gilbert  _et al._ (1988) S. L. Gilbert, J. J. Bollinger, and D. J. Wineland, Phys. Rev. Lett. 60, 2022 (1988).
  * Birkl  _et al._ (1992) G. Birkl, S. Kassner, and H. Walther, Nature 357, 310 (1992).
  * Leibfried  _et al._ (2003a) D. Leibfried, R. Blatt, C. Monroe, and D. Wineland, Rev. Mod. Phys. 75, 281 (2003a).
  * Berkeland  _et al._ (1998) D. J. Berkeland, J. D. Miller, J. C. Bergquist, W. M. Itano, and D. J. Wineland, Journal of Applied Physics 83, 5025 (1998).
  * Bermudez  _et al._ (2017b) A. Bermudez, P. Schindler, T. Monz, R. Blatt, and M. Müller, New Journal of Physics 19, 113038 (2017b).
  * James (1998) D. F. V. James, Applied Physics B 66, 181 (1998).
  * Hohenberg (1967) P. C. Hohenberg, Phys. Rev. 158, 383 (1967).
  * Mermin and Wagner (1966) N. D. Mermin and H. Wagner, Phys. Rev. Lett. 17, 1133 (1966).
  * Coleman (1973) S. Coleman, Communications in Mathematical Physics 31, 259 (1973).
  * Morigi and Fishman (2004a) G. Morigi and S. Fishman, Phys. Rev. Lett. 93, 170602 (2004a).
  * Morigi and Fishman (2004b) G. Morigi and S. Fishman, Phys. Rev. E 70, 066141 (2004b).
  * Deng  _et al._ (2005) X.-L. Deng, D. Porras, and J. I. Cirac, Phys. Rev. A 72, 063407 (2005).
  * Goodstein (2017) D. L. Goodstein,  _States of matter_ (Dover Publications, Inc., 2017).
  * Ashcroft (2016) M. Ashcroft,  _Solid State Physics: Revised Edition_ (Cengage Learning, 2016).
  * Affleck (1990) I. Affleck,  _Field theory methods and quantum critical phenomena Course 10_ (North-Holland, Netherlands, 1990).
  * (173) R. Shankar,  _Bosonization: How to make it work for you in condensed matter_ (World Scientific) pp. 353–387.
  * Shimshoni  _et al._ (2011) E. Shimshoni, G. Morigi, and S. Fishman, Phys. Rev. Lett. 106, 010401 (2011).
  * Bermudez and Plenio (2012) A. Bermudez and M. B. Plenio, Phys. Rev. Lett. 109, 010501 (2012).
  * Haldane (1981a) F. D. M. Haldane, Phys. Rev. Lett. 47, 1840 (1981a).
  * Giamarchi (2010) T. Giamarchi,  _Quantum physics in one dimension_ (Clarendon Press, 2010).
  * Luther and Peschel (1975) A. Luther and I. Peschel, Phys. Rev. B 12, 3908 (1975).
  * Emery (1976) V. J. Emery, Phys. Rev. B 14, 2989 (1976).
  * Haldane (1980) F. D. M. Haldane, Phys. Rev. Lett. 45, 1358 (1980).
  * Tomonaga (1950) S.-I. Tomonaga, Progress of Theoretical Physics 5, 544 (1950).
  * Luttinger (1963) J. M. Luttinger, Journal of Mathematical Physics 4, 1154 (1963).
  * Haldane (1981b) F. D. M. Haldane, Journal of Physics C: Solid State Physics 14, 2585 (1981b).
  * Coleman (1975) S. Coleman, Phys. Rev. D 11, 2088 (1975).
  * Senechal in (2004) D. Senechal in,  _Theoretical methods for strongly correlated electrons_ (Eds. Bourbonnais, C., Senechal, D. and Tremblay, A.-M., Springer, 2004) pp. 139–186.
  * von Delft and Schoeller (1998) J. von Delft and H. Schoeller, Annalen der Physik 7, 225 (1998).
  * Emery in (1993) V. J. Emery in,  _Correlated Electron Systems_ ((Ed. V. J. Emery), World Scientific, 1993) pp. 166–198.
  * Gonzalez in (1995) J. Gonzalez in,  _Quantum electron liquids and high-Tc superconductivity_ (Eds. Gonzalez, J., Martin-Delgado, M.A., Sierra, G., Vozmediano, A.H. Springer, 1995) pp. 109–124.
  * Sørensen and Mølmer (1999) A. Sørensen and K. Mølmer, Phys. Rev. Lett. 82, 1971 (1999).
  * Leibfried  _et al._ (2003b) D. Leibfried, B. DeMarco, V. Meyer, D. Lucas, M. Barrett, J. Britton, W. M. Itano, B. Jelenković, C. Langer, T. Rosenband, and D. J. Wineland, Nature 422, 412 (2003b).
  * Soderberg and Monroe (2010) K.-A. B. Soderberg and C. Monroe, Reports on Progress in Physics 73, 036401 (2010).
  * Landau and Lifshitz (2008) L. D. Landau and E. M. Lifshitz,  _Theory of elasticity_ (Butterworth-Heinemann, 2008).
  * Thorne and Blandford (2017) K. S. Thorne and R. D. Blandford,  _Modern classical physics: optics, fluids, plasmas, elasticity, relativity, and statistical physics_ (Princeton University Press, 2017).
  * Britton  _et al._ (2012) J. W. Britton, B. C. Sawyer, A. C. Keith, C.-C. J. Wang, J. K. Freericks, H. Uys, M. J. Biercuk, and J. J. Bollinger, Nature 484, 489 (2012).
  * Islam  _et al._ (2013) R. Islam, C. Senko, W. C. Campbell, S. Korenblit, J. Smith, A. Lee, E. E. Edwards, C.-C. J. Wang, J. K. Freericks, and C. Monroe, Science 340, 583 (2013).
  * Richerme  _et al._ (2014) P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Nature 511, 198 (2014).
  * Jurcevic  _et al._ (2014) P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, Nature 511, 202 (2014).
  * Smith  _et al._ (2016) J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Nature Physics 12, 907 (2016).
  * Lanyon  _et al._ (2017) B. P. Lanyon, C. Maier, M. Holzäpfel, T. Baumgratz, C. Hempel, P. Jurcevic, I. Dhand, A. S. Buyskikh, A. J. Daley, M. Cramer, M. B. Plenio, R. Blatt, and C. F. Roos, Nature Physics 13, 1158 (2017).
  * Friis  _et al._ (2018) N. Friis, O. Marty, C. Maier, C. Hempel, M. Holzäpfel, P. Jurcevic, M. B. Plenio, M. Huber, C. Roos, R. Blatt, and B. Lanyon, Phys. Rev. X 8, 021012 (2018).
  * Monroe  _et al._ (2015) C. Monroe, W. Campbell, E. Edwards, R. Islam, D. Kafri, S. Korenblit, A. Lee, P. Richerme, C. Senko, J. Smith, and et al., IOS Press Ebooks (2015).
  * Nevado and Porras (2016) P. Nevado and D. Porras, Phys. Rev. A 93, 013625 (2016).
  * Bermudez  _et al._ (2017c) A. Bermudez, L. Tagliacozzo, G. Sierra, and P. Richerme, Phys. Rev. B 95, 024431 (2017c).
  * Bermudez  _et al._ (2011a) A. Bermudez, J. Almeida, F. Schmidt-Kaler, A. Retzker, and M. B. Plenio, Phys. Rev. Lett. 107, 207209 (2011a).
  * Bermudez  _et al._ (2012) A. Bermudez, J. Almeida, K. Ott, H. Kaufmann, S. Ulm, U. Poschinger, F. Schmidt-Kaler, A. Retzker, and M. B. Plenio, New Journal of Physics 14, 093042 (2012).
  * Källén (1952) G. Källén, Helvetica Physica Acta 25, 417 (1952).
  * Lehmann (1954) H. Lehmann, Il Nuovo Cimento (1943-1954) 11, 342 (1954).
  * Zwicky (2016) R. Zwicky, “A brief introduction to dispersion relations and analyticity,” (2016), arXiv:1610.06090 [hep-ph] .
  * Stein and Shakarchi (2005) E. M. Stein and R. Shakarchi,  _Real analysis: measure theory, integration, and Hilbert spaces_ (Princeton University Press, 2005).
  * Schiffer (1993) J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993).
  * Ulm  _et al._ (2013) S. Ulm, J. Roßnagel, G. Jacob, C. Degünther, S. T. Dawkins, U. G. Poschinger, R. Nigmatullin, A. Retzker, M. B. Plenio, F. Schmidt-Kaler, and K. Singer, Nature Communications 4, 2290 (2013).
  * Pyka  _et al._ (2013) K. Pyka, J. Keller, H. L. Partner, R. Nigmatullin, T. Burgermeister, D. M. Meier, K. Kuhlmann, A. Retzker, M. B. Plenio, W. H. Zurek, A. del Campo, and T. E. Mehlstäubler, Nature Communications 4, 2291 (2013).
  * Mielenz  _et al._ (2013) M. Mielenz, J. Brox, S. Kahra, G. Leschhorn, M. Albert, T. Schaetz, H. Landa, and B. Reznik, Phys. Rev. Lett. 110, 133004 (2013).
  * Ejtemaee and Haljan (2013) S. Ejtemaee and P. C. Haljan, Phys. Rev. A 87, 051401 (2013).
  * Brox  _et al._ (2017) J. Brox, P. Kiefer, M. Bujak, T. Schaetz, and H. Landa, Phys. Rev. Lett. 119, 153602 (2017).
  * Kadanoff (1966) L. P. Kadanoff, Physics Physique Fizika 2, 263 (1966).
  * Podolsky  _et al._ (2014) D. Podolsky, E. Shimshoni, P. Silvi, S. Montangero, T. Calarco, G. Morigi, and S. Fishman, Phys. Rev. B 89, 214408 (2014).
  * Silvi  _et al._ (2013) P. Silvi, G. De Chiara, T. Calarco, G. Morigi, and S. Montangero, Annalen der Physik 525, 827 (2013), https://onlinelibrary.wiley.com/doi/pdf/10.1002/andp.201300090 .
  * Porras and Cirac (2004b) D. Porras and J. I. Cirac, Phys. Rev. Lett. 93, 263602 (2004b).
  * Brown  _et al._ (2011) K. R. Brown, C. Ospelkaus, Y. Colombe, A. C. Wilson, D. Leibfried, and D. J. Wineland, Nature 471, 196 (2011).
  * Harlander  _et al._ (2011) M. Harlander, R. Lechner, M. Brownnutt, R. Blatt, and W. Hänsel, Nature 471, 200 (2011).
  * Haze  _et al._ (2012) S. Haze, Y. Tateishi, A. Noguchi, K. Toyoda, and S. Urabe, Phys. Rev. A 85, 031401 (2012).
  * Ramm  _et al._ (2014) M. Ramm, T. Pruttivarasin, and H. Häffner, New Journal of Physics 16, 063062 (2014).
  * Debnath  _et al._ (2018) S. Debnath, N. M. Linke, S.-T. Wang, C. Figgatt, K. A. Landsman, L.-M. Duan, and C. Monroe, Phys. Rev. Lett. 120, 073001 (2018).
  * Toyoda  _et al._ (2013) K. Toyoda, Y. Matsuno, A. Noguchi, S. Haze, and S. Urabe, Phys. Rev. Lett. 111, 160501 (2013).
  * Abdelrahman  _et al._ (2017) A. Abdelrahman, O. Khosravani, M. Gessner, A. Buchleitner, H.-P. Breuer, D. Gorman, R. Masuda, T. Pruttivarasin, M. Ramm, P. Schindler, and H. Häffner, Nature Communications 8, 15712 (2017).
  * Hakelberg  _et al._ (2019) F. Hakelberg, P. Kiefer, M. Wittemer, U. Warring, and T. Schaetz, Phys. Rev. Lett. 123, 100504 (2019).
  * Eckardt (2017) A. Eckardt, Rev. Mod. Phys. 89, 011004 (2017).
  * Dunlap and Kenkre (1986) D. H. Dunlap and V. M. Kenkre, Phys. Rev. B 34, 3625 (1986).
  * Bermudez  _et al._ (2011b) A. Bermudez, T. Schaetz, and D. Porras, Phys. Rev. Lett. 107, 150501 (2011b).
  * Kiefer  _et al._ (2019) P. Kiefer, F. Hakelberg, M. Wittemer, A. Bermúdez, D. Porras, U. Warring, and T. Schaetz, Phys. Rev. Lett. 123, 213605 (2019).
  * Schwinger (1951c) J. Schwinger, Proceedings of the National Academy of Sciences 37, 452 (1951c).
  * Achilles and Bonfiglioli (2012) R. Achilles and A. Bonfiglioli, Archive for History of Exact Sciences 66, 295 (2012).
  * Abers and Lee (1973) E. Abers and B. Lee, Physics Reports 9, 1 (1973).
  * Ryder (1996) L. H. Ryder,  _QUANTUM FIELD THEORY_ (Cambridge University Press, 1996).
  * Dyson (1949) F. J. Dyson, Phys. Rev. 75, 1736 (1949).
  * Debye (1912) P. Debye, Annalen der Physik 344, 789 (1912).
  * Wilson (1974) K. G. Wilson, Phys. Rev. D 10, 2445 (1974).
  * Holstein (1959) T. Holstein, Annals of Physics 8, 325 (1959).
  * Sachdev (2011) S. Sachdev,  _Quantum Phase Transitions_, 2nd ed. (Cambridge University Press, 2011).


# A deep learning classifier for local ancestry inference

Matthew Aguirre
Department of Biomedical Data Science
Stanford University
<EMAIL_ADDRESS>
Jan Sokol
Department of Biomedical Data Science
Stanford University
<EMAIL_ADDRESS>
Guhan Venkataraman
Department of Biomedical Data Science
Stanford University
<EMAIL_ADDRESS>
Alexander Ioannidis
Department of Biomedical Data Science
Stanford University
<EMAIL_ADDRESS>
###### Abstract

Local ancestry inference (LAI) identifies the ancestry of each segment of an
individual’s genome and is an important step in medical and population genetic
studies of diverse cohorts. Several techniques have been used for LAI,
including Hidden Markov Models and Random Forests. Here, we formulate the LAI
task as an image segmentation problem and develop a new LAI tool using a deep
convolutional neural network with an encoder-decoder architecture. We train
our model using complete genome sequences from 982 unadmixed individuals from
each of five continental ancestry groups, and we evaluate it using simulated
admixed data derived from an additional 279 individuals selected from the same
populations. We show that our model is able to learn admixture as a zero-shot
task, yielding ancestry assignments that are nearly as accurate as those from
the existing gold standard tool, RFMix.

##  1 Introduction

Ancestry inference refers to the task of assigning genetic ancestry labels
given an individual’s genomic sequence. Two forms are of note: global ancestry
inference, which performs this task at an individual level, and local ancestry
inference (LAI), which further segments an individual’s genetic ancestry into
assignments that can differ across the genome.

Many models of ancestry inference have been proposed, spurring significant
statistical methods development. The first model of global ancestry inference,
STRUCTURE, was an independent discovery of Latent Dirichlet Allocation (LDA),
and is still the preferred method for this task [1, 2, 3]. Early models for
local ancestry inference, such as HAPMIX, followed in the tradition of the
Kingman coalescent and used extensions of a haplotype-based model of linkage
disequilibrium due to Li and Stephens [4, 5, 6, 7]. Other approaches to LAI
have used Hidden Markov Models [8] or discriminative models over windows of
chromosomal sequence [9, 10]. These tools have been reviewed in greater depth
by Liu, et. al. [11].

For most modern studies, however, LAI is a pure prediction problem in that
model parameters are not of interest: the goal is the ancestry assignments
themselves. Further, the LAI task can also be framed as image segmentation. In
this formulation, the genome sequence is a one-dimensional image. Each variant
site constitutes a pixel, with two complementary channels for reference and
alternate alleles relative to a genome standard. Here, we describe a deep
learning model for LAI using a convolutional neural network (CNN) designed for
image segmentation, and benchmark it against the existing gold standard LAI
tool, RFMix [10]. A schematic of our model is shown in Figure 1.

Figure 1: Model overview. Input is a two-channel bit vector that encodes
whether a sample’s maternal or paternal allele varies from the reference
genome at a given site. Data are fed into a CNN based on the Segnet
architecture [12], which consists of several conv/maxpool and conv/upsampling
blocks. The output is a segmentation of the input sequence, in which each
letter is assigned to a genetic ancestry group.

##  2 Dataset

We assembled a dataset of whole genome sequences from real individuals in the
1000 Genomes Project (1kG, $n=2,540$), Human Genome Diversity Project (HGDP,
$n=929$), and Simons Genome Diversity Project (SGDP, $n=279$) [13, 14, 15].
These data were harmonized using standard bioinformatic tools such as PLINK
and bcftools (to filter and merge genetic data), liftOver (to map variants to
a common reference genome), and Beagle (to infer haplotypes from unphased
samples) [16, 17, 18, 19].

We used ADMIXTURE, a tool which implements the STRUCTURE algorithm, to produce
unsupervised genetic ancestry clusters, referencing metadata to interpret the
resulting cluster assignments [3]. At $K=8$ clusters, we find genetic clusters
consistent with African (AFR), East Asian (EAS), European (EUR), Native
American (NAT), Oceanian (OCE), South Asian (SAS), San-Mbuti (SMB), and West
Asian (WAS) ancestries. We removed individuals in the three least common
cluster groups, as well as admixed individual (having $<99\%$ assignment to a
single cluster), yielding a final dataset ($n=2,522$ haplotypes) of five
continental ancestries (AFR, EAS, EUR, NAT, SAS), which we split into train,
development (dev), and test sets (Table 1). Related individuals were removed
to avoid data leakage. For computational tractability, we subset the genetic
data to include only biallelic (one alternate allele) single nucleotide
polymorphisms (SNPs) on chromosome 20 that are present in the train set
($p=475,328$ variant positions).

Population | AFR | EAS | EUR | NAT | SAS
---|---|---|---|---|---
Train | 289 | 389 | 118 | 51 | 135
Dev | 52 | 70 | 24 | 16 | 24
Test | 26 | 35 | 12 | 8 | 12
Table 1: Number of individuals of each ancestral composition in the train,
dev, and test sets.

To evaluate our models under realistic scenarios of admixture, we simulated
the progeny of the real dev and test set individuals using RFMix [10]. We
varied the number of generations of mixture and ancestral diversity of the
founding members of the population so as to create a comprehensive set of
benchmark datasets. For model selection (see Methods), we used a dev set
consisting of 200 genotypes simulated by 10 generations of admixture across
all five ancestries of dev set individuals.

##  3 Methods

SegNet is a convolutional encoder-decoder neural network architecture designed
for semantic segmentation [12]. In its original instance SegNet consists of
five “down” blocks containing two or three convolutional operators and a
pooling layer, then five “up” blocks containing an up-sampling layer followed
by two or three convolutional layers. Three SegNet hyperparameters are of
interest: the number of blocks, the number of filters in the input layer, and
the filter width. The number of filters increases by a factor of two in each
down/up block, and filter width is fixed throughout.

We conducted a grid search to select an optimal network architecture using
these three hyperparameters. Filter width and filter count values were roughly
spaced exponentially in the range $[2^{1},2^{6}]$, and the number of blocks
was 3, 4, or 5. All models were trained using categorical cross-entropy loss,
evaluated over genetic variants and individuals. The best performing model
(with minimal dev set loss) had 4 blocks, with 16 filters with width 16.
Complete results are available as a table on the project GitHub
(www.github.com/maguirre1/deepLAI/).

As baseline, we evaluated RFMix on the same test data. This method is fully
described by Maples et. al. [10]; in brief, it uses several independent random
forest classifiers to predict ancestry within chromosomal windows. Classifier
output is then smoothed by a conditional random field (CRF) layer to yield
final predictions. We used a version of RFMix (v2.03) from bioconda [20].

##  4 Results

In all, we trained about 50 models to select optimal hyperparameters. Several
perform moderately well, achieving base-pair level accuracy above 80% on the
dev set (see Dataset), with the best model (see Methods) reaching 85.6%
accuracy. We also found that our model predictions are, in places, noisy
(Figure 2). We therefore post-processed model output with a mode filter,
replacing the output for each position with the most common prediction within
$k$ positions on either side. We let $k=2000$, for an overall window size of
4000, and found that this increased the accuracy of our predictions by a few
percentage points.

Figure 2: LAI Example. Genetic ancestry ground truth labels (top), with SegNet
(middle) and RFMix predictions (bottom). $x$-axis values are position indexes.
SegNet output is subject to a mode filter.

In an independent test set of individuals simulated under the same conditions
as the dev set, our model achieves 88.2% accuracy. Relative to the baseline
method, RFMix, however, our model compares rather unfavorably (Table 2). The
test set accuracy of RFMix, fit using the same training set as our model, is
97.2%. While both models do quite well identifying regions of African (AFR)
and East Asian (EAS) ancestries, the SegNet model fares much worse with the
other populations. This is not surprising, as AFR and EAS are over-represented
classes in the training set (Table 1). Moreover, the errors made by our model
(e.g. confusion between EUR/SAS, and between NAT/EAS) tend to reflect the more
recent common ancestry between those groups.

SegNet | AFR | EAS | EUR | NAT | SAS
---|---|---|---|---|---
AFR | 0.973 | 0.009 | 0.010 | 0.000 | 0.007
EAS | 0.005 | 0.949 | 0.006 | 0.002 | 0.039
EUR | 0.042 | 0.037 | 0.710 | 0.006 | 0.204
NAT | 0.004 | 0.182 | 0.010 | 0.739 | 0.066
SAS | 0.028 | 0.185 | 0.153 | 0.009 | 0.626

RFMix | AFR | EAS | EUR | NAT | SAS
---|---|---|---|---|---
AFR | 0.981 | 0.004 | 0.013 | 0.000 | 0.002
EAS | 0.003 | 0.989 | 0.002 | 0.002 | 0.004
EUR | 0.006 | 0.026 | 0.939 | 0.005 | 0.025
NAT | 0.001 | 0.011 | 0.029 | 0.954 | 0.004
SAS | 0.003 | 0.037 | 0.021 | 0.003 | 0.937

Table 2: Model performance. Ground truth genotypes (rows) were generated by 10
generations of admixture between test set individuals. Confusion with output
labels (columns) is normalized across rows. Diagonal entries are ancestry-
specific sensitivity. All values rounded to thousandths.

Our model also generalizes across varied cohort demography. In another series
of experiments, we generated 100 simulated individuals from 10 generations of
admixture between founding populations of two ancestry groups at an unequally
sampled (80:20) ratio. In Table 3, we highlight results from a cohort of 80%
African and 20% South Asian ancestry. While RFMix achieves 98.4% accuracy
after fitting a new model, our SegNet model reaches 89.8% without the need for
retraining. We conducted similar experiments across all pairs of ancestry
groups and find that model performance (i.e. class confusions from Table 2) is
broadly consistent across the cohorts (full results on GitHub).

SegNet | AFR | EAS | EUR | NAT | SAS
---|---|---|---|---|---
AFR | 0.989 | 0.001 | 0.004 | 0.000 | 0.006
SAS | 0.018 | 0.143 | 0.202 | 0.003 | 0.634

RFMix | AFR | EAS | EUR | NAT | SAS
---|---|---|---|---|---
AFR | 0.989 | 0.001 | 0.009 | 0.000 | 0.001
SAS | 0.007 | 0.015 | 0.002 | 0.015 | 0.961

Table 3: Model performance in 80/20 ancestry composition cohort. Ground truth
genotypes (rows) are assigned output labels (columns), with values normalized
across rows. Diagonal entries are ancestry-specific sensitivity. All values
rounded to thousandths.

##  5 Discussion

Here, we formulate the local ancestry inference task as a one-dimensional
image segmentation problem, and develop a new LAI tool based on a deep
convolutional neural network (SegNet). While there is a clear performance gap
between the method we present here and the current gold standard, we foresee
several ways to improve our model. One is data augmentation. This includes
incorporating admixed genotypes during training, which may be generated on the
fly within each epoch during training (as RFMix does), or which may be pre-
computed. Another is adding data “channels” for biologically relevant
quantities – such as recombination rate between sites (also considered by
RFMix), or population-specific allele frequencies for each input variant.
Architectural changes, including adding a conditional random field output
layer to smooth output predictions, could also be helpful. Finally, more
extensive use of regularization techniques like dropout may also improve
performance, as most genetic variants are not informative with respect to
ancestry.

Though work remains to make our model viable, we note that our approach is not
without benefits or novelty. First, while the models in this work are not very
resource-hungry (all run to completion in under two days on a single NVIDIA
RTX 2080 Ti), the “train once, use anywhere” paradigm is immensely important
for analyses of large or growing datasets [21]. The portability of the model
allows ancestry learned on a privacy-protected or proprietary dataset to be
applied by external users lacking access, something that is not possible with
RFMix. Second, it warrants mention that deep learning techniques are
underutilized in population genetics, and many popular genomics tools are not
optimized for graphical processing resources. We believe there is significant
room for methods development in this space, particularly for purely predictive
tasks such as LAI. We anticipate this will be of interest as the size and
scope of genomic data continue to grow.

##  6 Broader Impacts

Several commercial entities offer generic ancestry inference as a direct-to-
consumer enterprise, which has remained largely uncontroversial, aside from
data privacy concerns and occasional unexpected family discoveries. However,
we must acknowledge that the field of genetics – in particular, genetic
studies of differences between individuals of diverse backgrounds – has had a
problematic past with respect to data collection (e.g. participant consent)
and to propagating systems of racial hierarchy and racism (e.g. eugenics).
Even today, there remains significant risk that certain individuals will
promote misreadings of genetic studies to further personal or political
agendas. In this respect, let us be very clear: we believe that race, as a
social construct, has no biological basis and therefore no meaningful place in
population genetic studies like this one.

Population genetic studies, using tools such as the ones we propose, can
reveal a great deal about our origins and history as a species: our
migrations, our interactions, and our families. For some, these stories may be
a source of pride, or a tool to reclaim a lost, colonized past, while for
others, they may be reminders of times where our ancestors have been less
kind. These realities do not negate the ways we choose to describe ourselves
in the present, and they do not foretell the type of people we may become.

## References

  * [1] Jonathan K Pritchard, Matthew Stephens, and Peter Donnelly.  Inference of population structure using multilocus genotype data.  Genetics, 155(2):945–959, 2000.
  * [2] David M Blei, Andrew Y Ng, and Michael I Jordan.  Latent dirichlet allocation.  Journal of machine Learning research, 3(Jan):993–1022, 2003.
  * [3] David H Alexander and Kenneth Lange.  Enhancements to the admixture algorithm for individual ancestry estimation.  BMC bioinformatics, 12(1):246, 2011.
  * [4] Alkes L Price, Arti Tandon, Nick Patterson, Kathleen C Barnes, Nicholas Rafaels, Ingo Ruczinski, Terri H Beaty, Rasika Mathias, David Reich, and Simon Myers.  Sensitive detection of chromosomal segments of distinct ancestry in admixed populations.  PLoS genetics, 5(6):e1000519, 2009.
  * [5] John Frank Charles Kingman.  The coalescent.  Stochastic processes and their applications, 13(3):235–248, 1982\.
  * [6] Richard R Hudson.  Properties of a neutral allele model with intragenic recombination.  Theoretical population biology, 23(2):183–201, 1983.
  * [7] Na Li and Matthew Stephens.  Modeling linkage disequilibrium and identifying recombination hotspots using single-nucleotide polymorphism data.  Genetics, 165(4):2213–2233, 2003.
  * [8] Nick Patterson, Neil Hattangadi, Barton Lane, Kirk E Lohmueller, David A Hafler, Jorge R Oksenberg, Stephen L Hauser, Michael W Smith, Stephen J O’Brien, David Altshuler, et al.  Methods for high-density admixture mapping of disease genes.  The American Journal of Human Genetics, 74(5):979–1000, 2004.
  * [9] Sriram Sankararaman, Srinath Sridhar, Gad Kimmel, and Eran Halperin.  Estimating local ancestry in admixed populations.  The American Journal of Human Genetics, 82(2):290–303, 2008.
  * [10] Brian K Maples, Simon Gravel, Eimear E Kenny, and Carlos D Bustamante.  Rfmix: a discriminative modeling approach for rapid and robust local-ancestry inference.  The American Journal of Human Genetics, 93(2):278–288, 2013.
  * [11] Yushi Liu, Toru Nyunoya, Shuguang Leng, Steven A Belinsky, Yohannes Tesfaigzi, and Shannon Bruse.  Softwares and methods for estimating genetic ancestry in human populations.  Human genomics, 7(1):1, 2013.
  * [12] Vijay Badrinarayanan, Alex Kendall, and Roberto Cipolla.  Segnet: A deep convolutional encoder-decoder architecture for image segmentation.  IEEE transactions on pattern analysis and machine intelligence, 39(12):2481–2495, 2017.
  * [13] 1000 Genomes Project Consortium.  A global reference for human genetic variation.  Nature, 526(7571):68, 2015.
  * [14] Anders Bergström, Shane A McCarthy, Ruoyun Hui, Mohamed A Almarri, Qasim Ayub, Petr Danecek, Yuan Chen, Sabine Felkel, Pille Hallast, Jack Kamm, et al.  Insights into human genetic variation and population history from 929 diverse genomes.  Science, 367(6484), 2020.
  * [15] Swapan Mallick, Heng Li, Mark Lipson, Iain Mathieson, Melissa Gymrek, Fernando Racimo, Mengyao Zhao, Niru Chennagiri, Susanne Nordenfelt, Arti Tandon, et al.  The simons genome diversity project: 300 genomes from 142 diverse populations.  Nature, 538(7624):201–206, 2016.
  * [16] Christopher C Chang, Carson C Chow, Laurent CAM Tellier, Shashaank Vattikuti, Shaun M Purcell, and James J Lee.  Second-generation plink: rising to the challenge of larger and richer datasets.  Gigascience, 4(1):s13742–015, 2015.
  * [17] Heng Li, Bob Handsaker, Alec Wysoker, Tim Fennell, Jue Ruan, Nils Homer, Gabor Marth, Goncalo Abecasis, and Richard Durbin.  The sequence alignment/map format and samtools.  Bioinformatics, 25(16):2078–2079, 2009.
  * [18] Robert M Kuhn, David Haussler, and W James Kent.  The ucsc genome browser and associated tools.  Briefings in bioinformatics, 14(2):144–161, 2013.
  * [19] Sharon R Browning and Brian L Browning.  Rapid and accurate haplotype phasing and missing-data inference for whole-genome association studies by use of localized haplotype clustering.  The American Journal of Human Genetics, 81(5):1084–1097, 2007.
  * [20] Björn Grüning, Ryan Dale, Andreas Sjödin, Brad A Chapman, Jillian Rowe, Christopher H Tomkins-Tinch, Renan Valieris, and Johannes Köster.  Bioconda: sustainable and comprehensive software distribution for the life sciences.  Nature methods, 15(7):475–476, 2018.
  * [21] Keith Noto, Yong Wang, Shiya Song, Joshua G Schraiber, Alisa Sedghifar, Jake K Byrnes, David A Turissini, Eurie L Hong, and Catherine A Ball.  Ancestry inference using reference labeled clusters of haplotypes.  bioRxiv, 2020.