# Social-ecological feedbacks drive tipping points in farming system
diversification

Melissa S. Chapman
University of California, Berkeley
Berkeley, California, USA
<EMAIL_ADDRESS>
Serge Wiltshire
University of California, Berkeley
Berkeley, California, USA

Patrick Baur
University of Rhode Island
Kingston, Rhode Island, USA

Timothy Bowles
University of California, Berkeley
Berkeley, California, USA

Liz Carlisle
University of California, Santa Barbara
Santa Barbara, California, USA

Federico Castillo
University of California, Berkeley
Berkeley, California, USA

Kenzo Esquivel
University of California, Berkeley
Berkeley, California, USA

Sasha Gennet
The Nature Conservancy
Arlington, Virginia, USA

Alastair Iles
University of California, Berkeley
Berkeley, California, USA

Daniel Karp
University of California, Davis
Davis, California, USA

Claire Kremen
University of British Columbia
Vancouver, BC, Canada

Jeffrey Liebert
Cornell University
Ithaca, New York, USA

Elissa M. Olimpi
Virginia Tech
Blacksburg, Virginia, USA

Joanna Ory
University of California, Berkeley
Berkeley, California, USA

Matthew Ryan
Cornell University
Ithaca, New York, USA

Amber Sciligo
The Organic Center
Washington, DC, USA

Jennifer Thompson
University of California, Berkeley
Berkeley, California, USA

Hannah Waterhouse
University of California, Berkeley
Berkeley, California, USA

Carl Boettiger
University of California, Berkeley
Berkeley, California, USA
<EMAIL_ADDRESS>

###### Abstract

The emergence and impact of tipping points have garnered significant interest
in both the social and natural sciences. Despite widespread recognition of the
importance of feedbacks between human and natural systems, it is often assumed
that the observed nonlinear dynamics in these coupled systems rests within
either underlying human or natural processes, rather than the rates at which
they interact. Using adoption of agricultural diversification practices as a
case study, we show how two stable management paradigms (one dominated by
conventional, homogeneous practices, the other by diversified practices) can
emerge purely from temporal feedbacks between human decisions and ecological
responses. We explore how this temporal mechanism of tipping points provides
insight into designing more effective interventions that promote farmers’
transitions towards sustainable agriculture. Moreover, our flexible modeling
framework could be applied to other cases to provide insight into numerous
questions in social-ecological systems research and environmental policy.

_K_ eywords ecosystem services $\cdot$ tipping points, $\cdot$ agriculture
$\cdot$ diversification practices $\cdot$ decision-making $\cdot$ tipping
points

##  1 Science for Society

Understanding the mechanisms of tipping points in social-ecological systems is
critical to designing effective policy interventions in numerous environmental
contexts. Using adoption of agricultural diversification practices as a case
study, we show how tipping points in social-ecological systems can emerge
purely from the temporal feedbacks between human decisions and ecological
responses. Further, we explore why these finding matters for designing
incentive programs to promote farmers’ transitions towards sustainable
agriculture. We present a flexible modeling framework that can be built on to
address numerous questions in social-ecological systems and environmental
policy.

##  2 Introduction

Both ecosystems and social systems can change states abruptly as the result of
crossing critical thresholds. These critical thresholds (“tipping points”, or
states of a system where small perturbations can trigger large responses) have
garnered extensive academic and public attention (Gladwell 2006; Rockström et
al. 2009). However, mechanisms of tipping points in social-ecological systems
(SES) remain largely explained by complex assumptions about either the
ecological or social system dynamics (Dai et al. 2012; Mumby, Hastings, and
Edwards 2007; Scheffer 2010; Horan et al. 2011b), rather than the ways in
which these systems interact.

In social-ecological systems, human actions impact ecological processes, and
the resultant ecological changes create feedbacks that alter future management
actions (Liu et al. 2007; Ostrom 2009; Walker et al. 2004). These systems
become challenging to model when the temporal dynamics of ecological processes
and their feedbacks to human systems (i.e., benefits from ecosystems services)
do not align with the temporal scale of human decision-making (Cumming,
Cumming, and Redman 2006). Techniques previously used to investigate both
dynamic ecological processes and decision-making in SES have mostly overlooked
the temporal complexity of decision-making (Lippe et al. 2019). For instance,
agent-based models are commonly used to explore complex emergent phenomena in
SES. However, these models often use single time-step, or user-defined,
decision rules rather than allowing for emergent decision strategies that
maximize expected rewards over longer time horizons (Lippe et al. 2019).
Similarly, economic models, which typically explicitly consider the time
horizons of decisions, often overlook ecological lags (J. H. Vandermeer and
Perfecto 2012). While temporal attributes are central drivers of emergent
dynamics in SES, social scientists have regularly pointed to their importance
for decision making processes as well (e.g., land tenure affects decision-
making by creating long-term incentives for management (Fraser 2004; Long et
al. 2017; Richardson Jr 2015; Soule, Tegene, and Wiebe 2000)). New modeling
approaches that can integrate temporal attributes for both ecological change
and human decision-making are needed.

Agriculture is a particularly interesting case for exploring time lags in
social-ecological systems because many ecological responses to management
actions in these systems (such as planting hedgerows or building up organic
matter in soils) happen slowly, often taking years to return ecological and/or
financial benefits, which can exceed the time frame of investment planning.
Further, the duration of land tenure varies considerably among farmers, which
creates variation in, and constraints on, horizons over which decisions
strategies are optimized (Soule, Tegene, and Wiebe 2000). Farmers on owned
land may be able to plan for payoffs that occur over the course of multiple
decades or generations. Tenant farmers who lease their farmland, by contrast,
may be constrained to the decisions that pay off during the length of lease
agreements. In the US, leases are most often short-term single-year contracts
but can extend up to 10 years (Bigelow, Borchers, and Hubbs 2016). Finally,
while agriculture is regularly cited as a key driver of anthropogenic
ecological change (Foley et al. 2005, 2011; Stoate et al. 2009), different
types of agriculture have radically different effects on ecosystems. Some
forms of agriculture rely on promoting ecological processes that regenerate
ecosystem services for their productivity and are less input intensive
(diversified farming systems), while others rely primarily on external inputs,
such as chemical fertilizers and pesticides that often degrade the surrounding
water, soil, and air quality (Kremen, Iles, and Bacon 2012). In the context of
diversified farming systems, diversification practices include hedgerows, crop
rotation, intercrops, the use of compost, growing multiple crop types, reduced
tillage, and cover crops. This type of diversification is distinct from the
concept of operational diversification (i.e., increasing the range of revenue
streams produced on a given farm, such as tourism or value-added products) and
has been shown to promote ecosystem services that benefit farmers, including
soil fertility and water-holding capacity, pest and disease control,
pollination and productivity, thus providing an economically-viable
alternative to chemically-intensive methods of crop production (Tamburini et
al. 2020; Kremen and Miles 2012; Rosa-Schleich et al. 2019; Beillouin et al.
2021).

While adoption of diversified farm management practices encompasses a
continuum of actions and outcomes, suites of practices are often used together
in a package, coalescing around distinct stable states or “syndromes” (Andow
and Hidaka 1989; Ong and Liao 2020; J. Vandermeer 1997a). The mechanisms used
to explain and explore these patterns in agricultural systems mathematically
have relied on the assumption that both ecological (or production) and
decision (or economic) dynamics are non-monotonic (a function that both
increases and decreases) (J. Vandermeer 1997a; J. H. Vandermeer and Perfecto
2012). In coupled dynamic equations, if either of these systems is
approximated as monotonic (a function that only increases or only decreases),
the larger social-ecological system is characterized by a single stable point
(or no stable point), making multiple syndromes of production impossible to
explain with dynamic equations (J. Vandermeer 1997a; J. Vandermeer and
Perfecto 2012). In other words, the existence of distinct stable states in
agriculture – defined by high levels of biodiversity and associated ecosystem
services on one hand and low-levels of biodiversity and comparatively high
synthetic inputs on the other – cannot be explained in conventional models
without assuming complex structural dynamics. While non-monotonic assumptions
are often reasonable, equilibrium explanations overlook the temporal component
of both the ecological and decision processes central to agricultural SES.

Markov Decision Processes (MDP) provide a convenient mathematical framework
for modeling decision making (Bellman 1957) in SES because they allow for: (1)
formulation of situations in which environments (in this case, agroecosystems)
change slowly and stochastically and (2) land management decisions are forward
looking and based on predictions about how those decisions will impact a
farmer’s productivity and vitality in the future. While MDPs have been widely
used in a variety of environmental control problems (Marescot et al. 2013),
they are rarely applied to modeling and exploring the dynamics of social-
ecological systems. Additionally, like other modeling approaches, these
methods are scarcely informed by, or ground truthed with, social science data.
Leveraging social science data, such as interviews or surveys, can help inform
critical features of social-ecological models.

This paper presents a stylized Markov Decision Process model of the adoption
of agricultural diversification practices to explore the ecosystem service
patterns that result specifically from interactions between forward looking
decision-making and a slowly-changing environment(see Experimental Procedures
for further details). Our modeling work is inspired by patterns and system
characteristics (e.g. the concept of forward-looking decision-making) that
emerged from the extensive empirical fieldwork with farmers that our research
team has conducted on commercial farms in California (see Experimental
Procedures for further details) (Gonthier et al. 2019; E. Olimpi et al. 2020;
E. M. Olimpi et al. 2019) and through an iterative, collaborative process with
an interdisciplinary team comprising plant and soil scientists, agricultural
economists, ecologists, agricultural sociologists, modelers, policy analysts,
and farmers. Using this model, we explore a mechanism leading to the two
prevailing management paradigms (i.e. relying primarily on ecosystem services
versus external chemical inputs) that is the result not of complex structural
assumptions within either the human or ecological system, but rather the rates
at which the two systems interact. While our model necessarily simplifies both
decision-making and environmental processes, it provides a useful framework to
explore emergent properties in social-ecological systems. We show that our
findings have important implications, both for agricultural policy
implementation (such as incentive design) and social-ecological systems
theory.

##  3 Results

We observe the behavior of farmers’ sequential choices and the resultant
environmental outcomes through time. The decision strategy, $\pi^{*}$,
describes the emergent optimal course of action for a given ecosystem service
state (the stationary optimal state-dependent decision strategy; see
Experimental Procedures for further details). Figure 1A shows this optimal
strategy when the farmer plans over a discounted infinite time horizon.
Notably, it shows that at some ecosystem service state, the optimal decision
strategy displays a tipping point in which it becomes advantageous to adopt
diversification practices (Figure 1A).

We find that following the optimal decision strategy from Figure 1A, farms
have largely settled into two stable ecosystem service states, with some farms
transitioning to more simplified (lower levels of ecosystem services) farming
systems, and others to more diversified (higher levels of ecosystem services)
systems (Figures 1B and 1C).

Figure 1: Initial ecosystem states (dark blue) are distributed normally (mean
= 0.5; S.D. = 0.2; truncated at [0,1]). (A) Optimal decision strategy $\pi$
for discounted infinite decision horizon. (B) Ecosystem state of each agent
following decision strategy from (A) over 20 decision cycles (500
simulations). (C) Initial ecosystem state density (dark blue) and final
bimodal ecosystem state density at $t=20$ (light blue). Density represents the
probability density of a given ecosystem service state.

###  3.1 Importance of temporal dynamics in coupled systems

Our baseline model shows how a simple coupling of human choices and ecological
responses can result in bistable landscapes of high and low diversification
practice adoption and, as a result, high and low levels of ecosystem services
(Figure 1). By varying the time horizon of the decision process, the rate of
ecological response, and the cost/benefit ratio, we find that this tipping
point in decision strategy disappears when the speed of response of either the
ecological system or decision-making process overwhelms the coupling (we use
this as a proxy for decoupling) (Figure 2A).

With temporal human/environment interactions, there exists a region of cost-
benefit ratio within which various decision tipping points and bimodal
ecosystem service state distributions exist, as in Figure 2A and Figure 1).
Intuitively, at low enough cost-benefit ratios, bimodality disappears because
farmers are expected to always invest (Figure 2A bottom panel). Similarly, at
high enough cost-benefit rations, biomodality disappears because farmers are
expected to always divest (Figure 2A bottom panel). However, within a range of
cost-benefit ratios, decision strategies are expected to drive bimodal
ecosystem patterns (Figure 2A bottom panel between red dotted lines).
Shortening the time horizon of decisions (Fig 2B) or increasing the rate of
ecological processes (Fig 2C) necessarily changes the ratio of benefits to
costs required to make investing in practices worthwhile. However, when
decisions become temporally myopic (in this case, with a time horizon of 2
decision cycles), the potential for bistability in adoption trajectories
disappears (Fig 2B bottom panel). Unlike Figure 1A, there does not exist a
region of cost-benefit space for this case in which bistable patterns of
ecosystem states exist (Figure 2B bottom panel). Similarly, when ecological
processes become fast enough that the ecosystem responds almost immediately to
farmer actions ($r=0.95$), alternate stable states fail to emerge, regardless
of cost-benefit ratios (Figure 2C bottom panel). Only when both a gradually
changing environment and a forward-looking decision-maker (i.e. a farmer who
takes into account potential benefits over the long term) are coupled, do
tipping point phenomena emerge in the decision strategy, leading to two
predominant ecosystem service states (Figure 2A, Figure 1). This bimodal
pattern matches farmers’ experiences based on quotes from our interview data
(Figure 7; see Experimental Procedures for further details), as well as other
real world agricultural systems (J. H. Vandermeer and Perfecto 2012).

Figure 2: For three scenarios (coupled human/natural system, overly-myopic
decision maker, and overly-fast ecological change), cost/benefit ratio was
varied incrementally over 40 values, indicated by color shade, across a $c:b$
range of width 0.15, encompassing the transition between a ’never invest’ to
an ’always invest’ policy. For each $c:b$, 500 replicate simulations were
conducted as in Fig 3. Upper plots show distribution of final ecosystem
service state for each $c:b$. Lower plots show density curve peak(s). Where
overlap is observed in the lower graphs indicates the c:b ratios associated
with bistability. (A) By coupling a forward-looking decision-maker (e.g., a
farmer who takes into account potential benefits over the long term) and a
slowly-adapting environment, complex dynamics like alternate stable states can
emerge (seen in cost benefit ratios between the red dotted lines). Bistable
states do not exist at all cost-benefit ratios in this case (i.e., at a high
enough cost to benefit ratio no adoption will occur, leading to a single low
adoption state). Further, with (B) a short-term decision strategy (solving the
MDP over a 2-year time horizon), or (C) a fast ecological change rate
($r=0.95$), no bimodality is observed. In the cases of (B) and (C), the shift
from no adoption to all-in adoption exists at some cost benefit ratio,
removing the possibility of bistability in (A)

###  3.2 Influence of land tenure policy on ecosystem service states

Given that temporal factors emerged as central themes from our interview data
on diversified farming adoption patterns (Figure 7), and that such factors are
more broadly relevant to understanding decision making patterns on rented land
(Soule, Tegene, and Wiebe 2000), we investigated the impact of land tenure
policy on farmer decision making.

We solved the MDP from Figure 1 on a constrained time horizon (10-decision
cycles, in comparison to an infinite time horizon in Fig 1), representing the
shorter horizon on which tenant farmers might make decisions.

Comparing the final state distribution of the long-tenure (baseline) versus
the short-tenure model shows that, as a farmer’s expected land tenure duration
decreases, it becomes optimal to reduce diversification adoption across a
wider range of ecosystem states (Figure 3). This results in ecosystem state
degradation even among farm sites with an initially high ecosystem service
value, with all farms ending up in the simplified state after 20 decision
cycles (which might represent two separate 10 year leases) (Figure 3C).
However, the duration of land tenure may not be the sole factor defining
decision horizons. Numerous economic and cultural factors – for example,
whether farmers are highly motivated to seek sustainability as a goal in
itself rather than solely for individual economic reasons – might also impact
the time frame over which a farmer is willing to wait for ecological benefit.

Figure 3: (A) The simulation is identical to that in Fig 3B, and represents
long, stable land tenure. (B) The model from (A) is solved under a finite,
10-decision time horizon (rather than an infinite time horizon) to represent
short-tenure. (C) Comparison between final state distribution of short- vs.
long-tenure model runs. Figure 4: Starting from the same initial states as Fig
3, ecosystem service state time series are shown for (A) a large, abrupt
incentive (100% of adoption expenses are covered for two years) vs. (B) a
smaller, more sustained incentive (i.e. adoption cost is 80% of baseline for
10 years). Before discounting, both packages have the same total cost to the
funder (the equivalent of 2 years’ worth of full adoption cost offsets). With
discounting, (C) scenario is cheaper. After the incentive period, farmers
(agents) adjust their decision rules to that of the base case (i.e. no
incentive) until $t=20$. (D) Shows that the sustained incentive ultimately
drove more DP adoption.

###  3.3 Temporal dynamics and incentive structures

Our coupled social-ecological system model also allows for exploration of how
incentives that shift cost-benefit structures influence management practices.
Based on feedback from the farmers we interviewed (Figure 7), we explore the
impact of incentive duration on the efficacy of policies to promote adoption
of diversification practices by comparing two different publicly funded
incentive scheme designs: a short-term (two-time step) incentive which fully
covers the cost of adoption, versus a longer-term (ten-time step) incentive
that only partially offsets the adoption cost. Both schemes offer the same
total amount of financial support. Within the model, farmers adapt their
optimal decision strategies for the given cost-benefit ratio during the
incentive period, and at its conclusion they revert to the baseline strategy
(i.e. without payments).

We find longer, more sustained incentive programs to be more effective at
pushing the farmer over the critical threshold toward diversified farming
(Figure 4). Once a farmer has crossed the viable ecosystem service state
threshold (or optimal decision strategy tipping point), it becomes less likely
that they will return to simplified systems, even after incentives are
removed. Because it takes a series of investment actions for the ecosystem
service state to cross this threshold, longer-term incentives ultimately
result in more adoption of diversification practices. Additionally, because
the agent is forward-looking, they are able to assess the entire expected
reward of a long term incentive.

##  4 Discussion

Our analysis suggests a mechanism for tipping points in social-ecological
systems that does not rely on complex assumptions about the structure of the
social or ecological systems alone. Instead, these tipping points emerge from
the temporal interactions between forward-looking decisions (i.e., a farmer
who considers potential benefits over the long term) and slowly emerging
ecological outcomes. While alternate stable states within social-ecological
systems, including farming systems, have been previously explored and observed
(Horan et al. 2011a; J. Vandermeer 1997b; J. H. Vandermeer and Perfecto 2012),
our results shed light specifically on temporal feedbacks that might
contribute to this pattern (Figure 2). We also show how path dependence can
result in self-perpetuating low ecosystem states and low adoption of
diversification practices (Figure 1) and why this provides novel insights not
only for social-ecological research (Figure 2), but also for agricultural
policy (Figure 3 and Figure 4).

In contrast to equilibrium models (J. H. Vandermeer and Perfecto 2012), our
model assumes (Experimental Procedures; Figure 6) that ecological and
environmental processes take time to respond to the adoption of a diversified
practice. For example, soil organic matter and its benefits (such as improved
water retention and storage of essential nutrients) take years to build after
starting practices like cover cropping and compost additions (Poeplau and Don
2015). Our interviews with farmers support this reality.
One farmer explains:

> “I’ll use five years, which seems like a long time, but I mean, that’s only
> potentially 5 or 10 crop cycles depending how heavy you crop…There’s
> probably some very good soils that can be turned around relatively quickly
> if everything works right. Somebody might see some pretty dramatic benefits
> in a year or two, depending how bold they wanted to do things. But I think
> the changes in soil in my mind, they’re not immediate. You don’t make grand
> changes right away. So I mean, if you get started doing some reduced tillage
> using more cover crops, if you have a good source of compost and start
> incorporating those practices, I would hope that you would see something in
> five years.”

We show how time delays in ecosystem responses to management decisions, as
exemplified above, can explain patterns of multiple stable ecosystem service
states (Figure 5 P1). While existing explanations of multiple stable states in
SES provided by equilibrium models (J. H. Vandermeer and Perfecto 2012) are
not necessarily wrong, temporal explanations for this pattern reflect key
system attributes described by farmers (Figure 7) and allow for the
exploration of intervention strategies that are temporally constrained (e.g.
land tenure, incentives, etc.). While not addressed in this analysis, the
interaction of nonmonotonic (or generally more complex) subsystem dynamics and
the temporal interactions of those subsystems will be an important path for
future research.

Figure 5: (Table 1) Table of the main model predictions, evidence in support
of the pattern, value added of the temporal mechanism and minimal assumptions.

Our results also have important implications for understanding farmer
decision-making and agricultural policy design. Our model explains why the
land tenure status of a farmer can significantly influence their willingness
and ability to adopt diversification practices (Figure 1; Figure 5 P2). This
finding accords with a large body of sociological research documenting how
security and length of land tenure affect the adoption of sustainable
agricultural practices (Fraser 2004; Long et al. 2017; Richardson Jr 2015;
Soule, Tegene, and Wiebe 2000), suggesting that our model captures emergent
socio-ecological dynamics of farming systems. As another farmer explains, “We
do have hedgerows on several of the ranches, more where we have long-term
leases.” Growers who hold shorter leases are more likely to decide that
adopting diversification practices will not benefit them. They may lose their
investment if their lease ends forcibly or may have insufficient time to learn
how to use practices in the particular ecological and geographical conditions
of their farm (Calo and De Master 2016; Calo 2018). Immigrant farmers and
farmers of color, especially those new or beginning, often struggle to achieve
stable land tenure due to racial discrimination, poverty, or language barriers
in farmer networks, policy, and finance (Minkoff-Zern 2019).
Thus, policies which specifically aim to increase land tenure, for example by
supporting ownership and generational succession, may be powerful levers to
effect positive change in this area.

Finally, our model suggests that existing incentive programs to promote
agricultural sustainability and ecosystem services by reducing the costs of
practice adoption may need significant redesign (Figure 4; Figure 5 P3). Such
policies have become an integral part of farming over the past half-century
(Batáry et al. 2015; Graddy-Lovelace and Diamond 2017). They are particularly
interesting to explore with a Markov Decision Process due to their often
sequential but time-limited nature. Incentive policies rolled out over a given
time frame are challenging to study with equilibrium analyses or simple
decision rules.

Our results suggest that long-term sustained incentives, even when only
partially covering the cost of adoption, may be more effective in shifting
farmers from simplified ecological states to diversified states than more
concentrated short-term incentives. We show that the cost of interventions and
the social-environmental benefit of those interventions are not necessarily
equivalent. Rather, the perceived stability of incentive programs may be an
important driver of adoption. This dynamic can be overlooked when the temporal
rates of coupled dynamics in social-environmental systems are not considered.
If farmers expect a stable source of support over a known time period, they
may decide it is worthwhile to experiment and persist with a new practice that
may not provide observable benefits for many years (Claassen et al. 2014).
Unstable support, by contrast, may lead to farmers abandoning practices after
a short time, or may prevent farmers from trying new conservation practices
(Dayer et al. 2018). Moreover, the reduced transaction costs that come with
farmers making a longer-term commitment, while not captured in our model,
would only further suggest the higher efficacy of sustained incentives
compared to concentrated incentives.

This finding is particularly relevant to the design of government payment
programs and suggests that smaller payments can be highly effective in
encouraging the adoption of diversification practices (or other ecosystem
service promoting practices) when distributed over long time horizons. Small
payments over a longer time frame also constitute a lower total cost to the
government when considering even modest discount rates. Yet, the relationship
between the length of incentive programs and the persistence of changes in
land manager behavior once payments end remains unclear. One study found that
when landowners were unable to re-enroll in a waterbird habitat program in
northern California due to three-year period limits, participant numbers
declined and farmers persisted less with their practices (Dayer et al. 2018).
Other studies have found that growers tend to switch back land that is left
unused in return for payments via the federal Conservation Reserve Program to
‘more valuable’ productive uses (e.g., corn ethanol (Roberts and Lubowski
2007)). It is possible, as our model suggests, that steady, if somewhat lower,
conservation payments might result in more favorable outcomes when compared to
fluctuating or short-term payments.

Several federal government programs provide incentives to farmers over long
time periods. For example, the US Department of Agriculture (USDA) manages a
Conservation Stewardship Program (CSP) which is a 5-year contract –
potentially renewed for 5 more years – that pays farmers an annual sum in
return for agreeing to implement a customized conservation plan co-created
with a USDA agent. The plan allows growers to build on their existing
conservation practices by implementing practices that improve a wide range of
on-farm conditions, from soils to biodiversity. USDA also manages the
Environmental Quality Improvement Program (EQIP), which similarly supports on-
farm diversification practices with contracts that typically last 1-3 years
but may extend to 10 years. Payment rates are reviewed and changed annually;
certain practices may receive sizable assistance but rates can be unstable
over time (Agriculture 2021). While both CSP and EQIP are heavily in demand by
farmers in many states, including California (Wyant 2020), researchers have
not yet examined whether the differing longevity of the incentives provided
via these programs could impact the durability of diversification practice
implementation.

In conclusion, by combining semi-structured interview data with a modeling
approach that captures complex temporal dynamics in a stylized social-
ecological system model, we offer insights into important agricultural
management patterns and their implications for ecological outcomes and public
policy. While tipping points have been extensively studied throughout the
social-ecological systems literature, including agriculture, we suggest a
novel mechanism for these tipping points that makes minimal assumptions about
system-specific behavior. Further, we present a flexible model framework that
can be built on to address critical questions in social-ecological systems
research and policy design.

##  5 Experimental Procedures

###  5.1 Conceptual model description

We explore the transition to and from diversified farming systems (low and
high ecosystem service provisioning states) using a Markov Decision Process
(MDP) in which a farmer makes a series of decisions about whether or not to
employ agricultural diversification practices over time (Figure 1). In the
context of diversified farming systems, diversification practices include
hedgerows, crop rotation, intercrops, the use of compost, growing multiple
crop types, reduced tillage, and cover crops. These practices have often been
shown to promote ecosystem services that benefit farmers, including soil
fertility and water-holding capacity, pest and disease control, pollination
and productivity, thus providing an economically-viable alternative to
chemically-intensive methods of crop production (Tamburini et al. 2020; Kremen
and Miles 2012; Rosa-Schleich et al. 2019; Beillouin et al. 2021). This type
of diversification is distinct from the concept of operational diversification
(i.e., increasing the range of revenue streams produced on a given farm, such
as tourism or value-added products). The model was developed through an
iterative, collaborative process with an interdisciplinary team comprising
plant and soil scientists, agricultural economists, ecologists, agricultural
sociologists, modelers, policy analysts, and farmers with the goal of
capturing patterns stemming from the coupled human and natural dynamics of the
modeled system.

###  5.2 Conceptual model description

We explore the transition to and from diversified farming systems (low and
high ecosystem service provisioning states) using a Markov Decision Process
(MDP) in which a farmer makes a series of decisions about whether or not to
employ agricultural diversification practices over time (Figure 6). Modeling
the adoption of diversification practices and the resultant ecosystem services
as a Markov Decision Process requires that we first define a set of available
“actions” (or decisions) and a set of possible system states. In our model, at
each time step, the farmer takes an “action” of 0% to 100% investment in
adopting or maintaining diversification practices. The “system state”
corresponds to the level of benefit derived from the ecosystem services that
result from those adoption decisions. While higher ecological states are
beneficial, investments in diversification practices also come with higher
associated costs (Figure 6 A1). Costs and benefits may be financial, social,
ideological, and/or aesthetic, and we approximate that relationship as linear
(Figure 6 A2). A greater percent investment in diversification practices
corresponds to a greater probability of transitioning to a higher (more
beneficial) ecological state within the next decision cycle (Figure 6 A3). Our
model makes minimal assumptions about the relationships between actions and
costs (Figure 6 A1), states and benefits (Figure 6 A2), and actions and state
changes (Figure 6 A3). While additional assumptions could be integrated into
this MDP framework (e.g., nonlinear functions for Figure 6 A1-A3), we focus
our study on the impact of the interactions between ecological rates and time
horizons of decisions by minimizing assumptions around the functional forms of
these subsystems. The rate at which that ecological response occurs depends on
parameter r, but importantly is not instantaneous (Figure 6 A4). By defining
parameter values for cost, benefit, transition stochasticity, ecological
change rate, and future discounting, a Markov Decision Process allows the
optimal action strategy for the farmer (agent) to emerge based on expected
rewards (benefits minus costs) over either a finite (to represent short-tenure
leased farms) or infinite (to represent longer-term leases and land ownership)
time horizon (Figure 6 A5). We use a ten-year time horizon to represent
shorter term decision-making, essentially the longest frame of reference that
tenant farmers tend to work within and a conservative way of looking at the
impact of lease length for tenant farmers (Bigelow, Borchers, and Hubbs 2016).
This frame of reference is suggested not only in the agrarian sociology
literature but in the farmer interviews we conducted. Discounted infinite
decision horizons are meant to represent landowners and other farmers with the
capacity to account for the economic viability of an action over the long run.

Figure 6: Conceptual diagram and model assumptions. The farmer’s choice of how
much to invest (time and money) into the adoption of diversification practices
is shown in blue, and the resulting ecosystem services state in green, with a
more diversified ecosystem state at the top, and a more simplified ecosystem
state at bottom. Each time step, the farmer chooses the optimal action for
their current ecosystem service state based on the perceived utility function,
u, and state transition probability function, p. For a given ecosystem service
state and action at time t, p describes how the ecosystem responds
stochastically to result in an updated state at t + 1. The updated ecosystem
service state then feeds back to influence the farmer’s future choices,
leading to tradeoffs arising from the coupling of ecological processes with
consecutive diversification practice adoption decisions over time. Main model
assumptions (A1-A5) are outlined along with a brief rationale for each
approximation.

###  5.3 Interview data

As part of the larger project that our modeling work contributes to, between
February 2018 - August 2020, the agricultural sociologists in our team
interviewed 25 lettuce growers and 17 almond growers from California using a
snowball sampling method. We developed an interview guide with questions that
focused on the barriers and motivations for using diversification practices
such as cover cropping, planting hedgerows, and diverse crop rotations. We
focused on almonds and leafy greens/lettuce because these are among the most
economically valuable and regionally prevalent crops in California, represent
different farming systems and environmental conditions, and their increased
diversification could have major impacts (for almonds, a very large acreage
could benefit; for leafy greens, their requirements for fertilizer and
pesticide applications could be reduced greatly). We selected interviewees to
represent a range of growers (small to large scale; organic to conventional;
early adopters of diversification practices to late adopters; family run to
corporate management; and direct-to-consumer marketing to wholesale).
Interviews were conducted in person or over the phone when in-person
interviews were not possible due to farmer schedules or the need to social
distance during COVID-19 restrictions. Most interviews were audio-recorded and
transcribed. If recording was not possible, careful notes were taken to create
a transcript.

We performed deductive coding for central themes and keywords of the
transcripts to inform structural attributes of our model. Specifically, our
interview coding informed the relationships among costs, benefits and actions
in diversified farming systems, the integration of time horizons into decision
strategies, and the gradual rate of ecological change in response to
management actions (Figure 7). Additionally, interviews provided quotes to
contextualize model findings.

Figure 7: Key quotes from farmers suggest that the temporal horizons of
decision making and the rate at which farmers receive ecosystem benefits as a
result of those decisions are important factors in the adoption of
diversification practices

###  5.4 Mathematical description

The Markov Decision Process is composed of two coupled models: a model of the
biological/ecological processes, $s_{t+1}=f(s_{t},a_{t})$, and a model of how
the farmer views those processes, expressed as the utility function of the
biological state and the cost of the farming actions/decisions
$u(s_{t},a_{t})$. Both models incorporate temporal dynamics. The biological
model has a notion of time which says that actions don’t immediately change
the biological environment, but instead change it over time at rate $r$.
Meanwhile, the farmer pays the cost of action $a_{t}$ as soon as that action
is taken. However, unlike common alternative frameworks, such as most agent-
based (‘individual-based-simulation’) models, the farmer does not choose the
sequence of actions one at a time. Instead, the farmer plans ahead over the
future, by considering actions which may be costly now but pay off in years to
come given the utility of a strategy (i.e. a sequence of actions, the
discounted sum of the utility of all the individual actions in the strategy).
This decision model can be formulated as

$\max_{\\{a_{t}\in
A\\}}\mathbb{E}\left[\sum_{t}^{T}u(s_{t},a_{t})\gamma^{t}\right]$

where $\\{a_{t}\\}$ is chosen from the set of available actions, $\mathbb{E}$
the expected utility operator, $u(s_{t},a_{t})$ the utility which the farmer
associates with being in state $s_{t}$ and taking action $a_{t}$ at time $t$,
$\gamma$ the myopic discount factor, and $T$ the time horizon of the decision,
which in this case represents the land tenure of the farm. In our study we set
$T=10$ to represent tenant farms and $T\to\infty$ to represent a farmer who
owns the land or has a long lease. The farmer takes action $a_{t}$ to get the
highest expected return over either an infinite decision horizon or a given
finite decision horizon (methods to solve for the action policy are outlined
in Marescot et al., 2013 (@ Marescot et al. 2013)).

We assume a simple model of the farmer’s perceived utility $u(s_{t},a_{t})$ as
a function of the difference between the cost $c_{a}$ associated with
diversification practice action $a_{t}$, versus expected benefits $b_{s}$
derived from ecosystem state $s_{t}$, at time $t$, such that

$u(s_{t},a_{t})=b_{s}s_{t}-c_{a}a_{t}$

where farmers’ initial ecosystem states were distributed normally around a
mean of $s_{0}=0.5$. The ecosystem state is also dynamic, evolving according
to the transition probability function $p(s_{t},a_{t})$, such that

$s_{t+1}=p(s_{t},a_{t}):=s_{t}+r\left(a_{t}-s_{t}\right)+\epsilon$

where $\epsilon\sim N(0,\sigma)$. This provides a minimal state transition
model in which the parameter $r$ sets the natural timescale at which the
ecosystem can respond to changes in land management decisions, and $\sigma$
defines the width of the state transition probability distribution, capturing
the noise inherent to ecological system change.

While we have assumed very basic transition and utility functions for this
stylized model, in general more complicated nonlinear functions for both the
ecosystem state transition and perceived utility could be substituted into
this framework. # Model implementation

The model was developed in the _R_ programming language (R Core Team 2019).
The _MDPtoolbox_ library was used to set up and solve the MDP (Chades et al.
2017). Code for our model and the experiments conducted in this paper is
available freely at https://github.com/boettiger-lab/dfs-mdp.

##  6 Acknowledgments

Funding for this research was provided by the National Science Foundation
grant number CNH-1824871

##  7 Author Contributions:

Conceptualization CB, MC, SW, PB, TB, LC, FC, KE, SG, AI, DK, CK, JL, EO, JO,
MR, AS, JT, HW; Data curation: MC, SW, CB; Formal Analysis: MC, SW, CB;
Funding acquisition: TB, AI, CK, DK, CB; Methodology: CB, MC, SW, PB, TB, LC,
FC, KE, AI, DK, CK, EO, JT, HW; Code: MC, SW, CB; Visualization: MC, SW, CB;
Writing – original draft: MC, SW, CB, LC, AI; Writing – review & editing: CB,
MC, SW, PB, TB, LC, FC, KE, SG, AI, DK, CK, JL, EO, JO, MR, AS, JT, HW

##  8 Competing Interests:

The authors declare no competing interests.

##  9 Diversity and Inclusion Statement:

We worked to ensure ethnic or other types of diversity in the recruitment of
human subjects. We worked to ensure that the study questionnaires were
prepared in an inclusive way. One or more of the authors of this paper self-
identifies as an underrepresented ethnic minority in science. One or more of
the authors of this paper self-identifies as a member of the LGBTQ+ community.
One or more of the authors of this paper self-identifies as living with a
disability.

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