Higher yields and more biodiversity on smaller farms

Abstract

Small farms constitute most of the world’s farms and are a central focus of sustainable agricultural development. However, the relationship between farm size and production, profitability, biodiversity and greenhouse gas emissions remains contested. Here, we synthesize current knowledge through an evidence review and meta-analysis and show that smaller farms, on average, have higher yields and harbour greater crop and non-crop biodiversity at the farm and landscape scales than do larger farms. We find little conclusive evidence for differences in resource-use efficiency, greenhouse gas emission intensity and profits. Our findings highlight the importance of farm size in mediating some environmental and social outcomes relevant to sustainable development. We identify a series of research priorities to inform land- and market-based policies that affect smallholders globally.

Full text

AnAlysis
https://doi.org/10.1038/s41893-021-00699-2
1School of Public Policy and Global Affairs, University of British Columbia, Vancouver, British Columbia, Canada. 2Institute for Resources, Environment and
Sustainability, University of British Columbia, Vancouver, British Columbia, Canada. 3Center for Sustainable Food Systems, University of British Columbia,
Vancouver, British Columbia, Canada. ✉e-mail: vinnyricciardi@gmail.com
Farm size has become a key variable of interest in discussions
surrounding food security, development, and the environ-
ment1. Most of the world’s farms are small—of the 570 million
farms in the world, 84% are <2 ha in size2. Smallholders are facing
growing pressure on their livelihoods from low prices in global mar-
kets and climate change-induced production losses3. Accordingly,
smallholders have been the target of global development policies
such as the Sustainable Development Goal (SDG) target 2.3, which
seeks to support smallholders by increasing their productivity,
incomes, and access to land. Many countries’ Intended Nationally
Determined Contributions (INDCs) of the UN Conference of
Parties on Climate Change (COP21) also aim to bolster smallhold-
ers’ adaptive capacity.
Numerous scholars argue that smaller farms perform better than
larger farms in terms of production, environmental, and socioeco-
nomic outcomes4. On the basis of these arguments, scholars, policy
makers, and social movements argue in favour of land reforms to
redistribute farmland5,6. Although 84% of the world’s farms are
<2 ha in size, they only constitute 12% of farmland—increasing the
proportion of farmland in smaller farms will arguably increase its
benefits. At the same time, consumers have increased their willing-
ness to pay for products with labels associated with smaller farms7,8.
Thus, there is a growing call for support for small farms. While this
support is important, the performance of small farms in terms of
productivity, resource efficiency, biodiversity, and greenhouse gas
(GHG) emissions has itself remained highly contested9–14.
Here, we synthesize the relationship between farm size and six
socioeconomic and environmental outcomes, leveraging the past
50 yr of empirical evidence that directly assessed crop production,
environmental performance, and economic outcomes as they relate
to farm size. Our systematic assessment of the multidimensional
outcomes related to farm size builds on past reviews that focused
on single outcomes (for example, yield, economic performance,
or biodiversity metrics for specific species)15–18, non-systematic
reviews15,16, studies based on indirect measurements of farm size
and the outcome variables of interest19–21, and studies with specific
regional foci15,17. We present evidence from 118 studies (318 obser-
vations) from 51 countries on the relationship between relative farm
size (along a continuum) and: (1) yields as value of crop output per
area (value ha–1) or total crop production per area (kg ha–1), (2) crop
diversity at species and varietal levels, (3) non-crop biodiversity at
field and landscape levels, (4) resource-use efficiency as measured
in terms of technical efficiency22, (5) GHG emissions per unit out-
put, and (6) profit per unit area.
Results
Our analysis finds that smaller farms have higher yields and har-
bour greater crop diversity and higher levels of non-crop biodiver-
sity at the field and landscape scales than larger farms (Table 1). We
find no conclusive evidence for a relationship between farm size and
resource-use efficiency, GHG emissions, or profit. In the remainder
of this article, we will address each of these key findings in turn and
discuss their implications for policy initiatives and consumer sup-
port for small farms globally.
Smaller farms have higher yields. Our synthesis shows that, in
the literature, when primary studies assess yield across farm sizes,
79% (95% confidence interval, CI = 58–100%) of them report that
smaller farms have higher yields (in either weight ha–1 and value ha–1
terms) (Fig. 1). We also find that yields typically decrease by 5% for
each hectare increase in farm size (−5% mean effect; 95% CI = −9
to −1%; Fig. 2a and Fig. 3), within the range of studied observa-
tions (mean = 7.5 ha; s.d. = 22.7 ha). While the distribution of effects
includes deviant cases (Fig. 3 and Supplementary Fig. 1), these new
findings show that, on average, the available evidence supports the
idea—which originated in the 1920s and has been studied exten-
sively since the 1960s—that smaller farms are higher yielding than
larger farms14,23,24. Moreover, we find that controlling for labour
removed the effect—our model not controlling for labour has
stronger effect size (although not statistically different from zero at
the 95% confidence level) than the one that does. This result is in
line with Sen’s 1964 prediction24 and subsequent literature25, that
Higher yields and more biodiversity on
smaller farms
Vincent Ricciardi 1,2 ✉ , Zia Mehrabi 1,2,3, Hannah Wittman2,3, Dana James 2,3 and
Navin Ramankutty 1,2,3
Small farms constitute most of the world’s farms and are a central focus of sustainable agricultural development. However, the
relationship between farm size and production, profitability, biodiversity and greenhouse gas emissions remains contested.
Here, we synthesize current knowledge through an evidence review and meta-analysis and show that smaller farms, on average,
have higher yields and harbour greater crop and non-crop biodiversity at the farm and landscape scales than do larger farms.
We find little conclusive evidence for differences in resource-use efficiency, greenhouse gas emission intensity and profits. Our
findings highlight the importance of farm size in mediating some environmental and social outcomes relevant to sustainable
development. We identify a series of research priorities to inform land- and market-based policies that affect smallholders
globally.
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AnAlysis NaTure SuSTaiNabiliTy
suggests that labour markets are an important reason for the inverse
farm size–productivity relationship (Fig. 2b).
Smaller farms have greater crop diversity. While many field studies
have explored in situ crop diversity on small farms26–28, few directly
measured the relationship between farm size and crop diversity.
In our review, four studies show higher crop diversity on smaller
farms, while three found the opposite; much too small a sample for
statistical inference. But we previously conducted an in-depth quan-
titative analysis on the relationship between crop diversity and farm
size across 55 countries and 154 crops using a newly harmonized
dataset of nationality representative farmer surveys and agricul-
tural censuses29. We found that, except for an unexplained dip in
the 2–5 ha size range, there is a strong inverse relationship globally
between farm size and the number of crop species found across the
landscape—with higher species diversity within smaller farms than
larger farms when controlling for area (Supplementary Fig. 2). Crop
diversity on small farms is selected by farmers for a range of reasons
such as improved nutrition30, market diversification31 and mitiga-
tion of drought risk32.
Smaller farms harbour greater non-crop biodiversity. There
are three key pathways by which smaller farms could be benefi-
cial for non-crop biodiversity covered in the literature. The first is
through ecological management practices, such as limited insecti-
cide use and use of organic management practices. The second is
through increased field edges (increased margin-to-field area ratio);
increased field edges can lead to larger available breeding habi-
tats for arthropods33,34, provide refuge for arthropods and smaller
species to colonize after escaping recently disturbed fields35,36,
increase the number of pollinators and beneficial predators within
fields4,34 and act as conservation corridors for arthropods and small
mammals37,38. The third is through landscape composition, with
small-farm-dominated landscapes harbouring diverse land cover
types such as forests and wetlands, fields of different crops or fields
in different phenological stages of production39,40. In the studies we
reviewed, there is evidence for all of these effects. When combined,
77% of studies (95% CI = 61–99%) reported that smaller farms and
fields have greater biodiversity at the farm and landscape levels
compared to larger farms and fields (Fig. 1).
The three remaining variables we tested—GHG emissions,
resource-use efficiency, and profits—did not show conclusive
relationships for the effect size magnitude and sign (Figs. 2, 4,
and 5), even though the majority of studies concluded that larger
farms had greater resource efficiency than smaller farms (Fig. 1).
For example, while the evidence we reviewed shows that GHG
Table 1 | Main results and mechanisms
Variable Result Mechanisms favouring small farms Mechanisms favouring large farms
Yield Smaller farms have
higher yields Reliance on family labour (for example, Fig. 2). Mechanization enables higher yields with less
labour but is only cost-effective on larger fields57.
Biodiversity
(non-crop) Smaller farms have
higher biodiversity Smaller fields have more edges that provide
habitat5,36,58.
Independently managed smaller fields and farms
may create a more heterogeneous landscape59.
The link between field and farm size is relatively
understudied; large farms with small fields may also
benefit biodiversity but this was untested in the
reviewed literature.
Crop diversity Smaller farms have
higher crop diversity Subsistence farmers plant a greater diversity of
traditional crops to meet nutritional needs30.
Small farms are incentivized to cultivate landraces
when there are niche markets for traditional crops31.
Varietal diversity requires a minimum amount of
space to prevent genetic erosion for wind-pollinated
crops60,61.
Diversified crops can reduce long-term risk at the
expense of short-term profit, which may require
financial buffers62,63.
Resource-use
efficiency Inconclusive evidence In contexts where off-farm labour opportunities
were greater, there was less available on-farm
family labour and, in turn, greater technical
efficiency64.
Increased access to information from extension
and advisory services was associated with
greater technical efficiency, which is often only
cost-effective on larger fields64–67.
GHG emissions Inconclusive evidence Smaller farms may use less input-intensive
production methods but this was untested in the
reviewed literature.
Agricultural mechanization can enable higher yields
with less input use, and mechanization is often only
cost-effective on larger fields57.
Profit Inconclusive evidence Specialty markets for traditional foods offer higher
prices31.
Smallholder credit access can increase access to
inputs and markets68.
Better market access for larger farms69,70.
Recovering fixed costs requires a minimum scale69,71.
Better access to land-based subsidies72.
Yields
(n = 69)
Biodiversity
(n = 87)
Profitability
(n = 20)
Resource efficiency
(n = 34)
100
75
50
25
0
100
75
50
25
0
Probability of finding (%)
Small farms
are better
No trend No trendLarge farms
are better
Small farms
are better
Large farms
are better
a b
dc
Fig. 1 | The probability of studies finding relationships between farm size
and each outcome variable. Results are as per the vote count findings
(for example, small farms have more biodiversity when compared to larger
farms, compared to no trend emerging between farm size and profitability).
a–d, Results are shown for the following outcome variables: yield (a),
biodiversity (b), resource efficiency (c), and profitability (d). The average
and 95% CIs are given (see Supplementary Table 3 for underlying data).
Note, GHG emission studies were typically on individual farms so we could
not conduct vote counts on this variable.
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emissions per unit output tend to be higher on smaller farms, sug-
gesting that smaller farms might be less efficient per unit output,
the confidence intervals around this effect crossed zero (−4% mean
effect; 95% CI = −10–2%). We found no clear difference between
small or large farms in technical efficiency (our proxy for resource
efficiency per unit output with 0% mean effect; 95% CI = −1–2%),
even after controlling for a variety of moderating factors, such as
access to credit, extension services or cooperative membership
(Fig. 2c). See the Supplementary Information for further discus-
sion of these results. Similarly, while profitability per unit area also
declined with increasing farm size, statistical confidence in the
effect was also low (−2% mean effect; 95% CI = −10–5%) (Fig. 2a).
Discussion
Our evidence review and meta-analysis of the current evidence base
for these six outcomes associated with farm size finds strong sup-
port for the inverse farm size–productivity and farm size–diversity
relationship (empirical findings that both have strong theoretical
support24,41–43). While a couple of emerging studies44,45, with limited
coverage, suggest that the inverse size–productivity relationship
might simply be a result of measurement errors and while we were
unable to rule out this possibility, our synthesis did find the inverse
farm size–yield effect was removed when controlling for labour,
suggesting that smaller farms may be more productive due to the
availability of family labour24. Similarly, we recognize that socio-
political context is important and small farms may not always be
more biodiverse46 but most of the evidence base across a broad geo-
graphic range of agricultural systems is in support of this positive
relationship.
An important caveat to interpreting the past literature for each of
these outcomes are regional biases and variation. Regional biases are
most evident in the biodiversity literature that has predominantly
focused on higher-income countries, mainly in North America and
Europe (Supplementary Fig. 4). Different regions may contain spe-
cies that prefer environments that larger farms foster, either through
their larger fields or different farm management techniques (Table
1). While we could not test for these factors explicitly due to our
sample size, a dominant theme in the literature for other indica-
tors (yield, profitability, and resource efficiency) was that a farm’s
political, socioeconomic, and geographic context (a farmer’s access
to training, credit, machinery, insurance, inputs, markets, and/or
subsidies) may explain the farm size to outcome relationships. For
instance, the relationships between farm size, resource efficiency,
and profit were the most spatially heterogeneous across all variables
examined. For certain smallholder-dominant countries (for exam-
ple, India and Ethiopia) we found that smaller farms were more
profitable, whereas larger farms were more profitable in countries
dominated by large farms, higher incomes, and better rural infra-
structure (for example, the United States). This may suggest that
smallholders have better access to markets, inputs, and technolo-
gies in a smallholder-dominant system that may affect their profit-
ability and resource efficiency (see Supplementary Information for
expanded discussion).
Systematic evidence syntheses, such as meta-analyses, are an
iterative process47. For some of the outcomes (such as GHG emis-
sions, profits, and resource-use efficiency) we were unable to
identify consistent or confident outcomes from the existing liter-
ature. This may be due to the small number of included studies,
limited cross-country analyses, or that these relationships are too
context-specific to be generalized. Future work should continue
to assess these outcomes and build on this study to include other
important outcomes, such as mental and physical health of workers
and farmers, employment opportunities, pesticide or fertilizer use
efficiency, and other key ecosystem services, such as pollination, in
Yields (n = 33)
Profitability (n = 15)
Resource efficiency (n = 18)
Resource efficiency (n = 18)
Resource efficiency
GHG emissions (n = 100)
–10 –5 0 5 10 –10 0 10
Percentage change Percentage change
Yields (n = 33)
Yields
Management not controlled (n = 16)
Extension not controlled (n = 7)
Extension controlled (n = 11)
Cooperative not controlled (n = 14)
Cooperative controlled (n = 4)
Credit not controlled (n = 8)
Credit controlled (n = 10)
Management controlled (n = 17)
Labour not controlled (n = 17)
Labour controlled (n = 16)
Institutions not controlled (n = 26)
Institutions controlled (n = 7)
a b
c
–10 0 10
Fig. 2 | The pooled effect sizes for each outcome variable that show the percent change per 1ha increase in farm size. a, Pooled effect size per variable
as derived from the random effect meta-regressions. The vertical black line indicates the 1:1 response ratio where, for a 1-ha change in farm size, there is
no change in the outcome variable. A response ratio <0 suggests that smaller farms have a higher effect (for example, smaller farms have higher yields)
and, if it is >0, then larger farms have a higher effect. The number of observations (n) and 95% CIs are given per variable. b, For yield, sensitivity analyses
fit separate models to explore heterogeneity in the effect for studies that controlled for common explanations for the inverse farm size–yield relationship:
institutional characteristics, farm management and family labour. c, For resource-use efficiency, separate models were fit to test if the effect was
moderated by common development interventions to improve smallholder resource-use efficiency: extension access, farmer cooperatives/groups, and
credit access. Profit and GHG emissions had no additional models. Note, biodiversity studies typically did not include regression coefficients, so we could
not conduct a random effects meta-regression. (See Supplementary Table 4 for underlying data).
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AnAlysis NaTure SuSTaiNabiliTy
addition to examining literature in languages other than English.
New primary work is also needed to further explore the functional
form of the effects we present here, and to explore how different
socioecological and political conditions and measurement methods
may mediate positive or negative outcomes across farm size classes.
This could further inform policies on land reform (such as redistri-
bution or consolidation) that address market failures so that such
policies can maximize the multidimensional benefits of farming
systems to society48.
To support sustainable transitions in farming practices across
a range of farm sizes, more evidence-based synthesis is needed at
broad regional scales. Until recently, the role of farm size in the
global food system has been largely assessed by independent case
studies. As international commitments (for example, SDGs and
COP21 INDCs) begin to evolve into actionable funding plans and
as countries continue to decide on land use policies that directly
affect the size of farms, it is critical to identify how farm size affects
different social, economic and environmental outcomes.
Our study lends evidence to boost support for policies target-
ing smallholders. Most of the world’s farms (84%) are operated
by smallholders2 and smallholders in lower-income countries are
also among the poorest people on the planet49. Our study shows
that smallholders are both productive and stewards of biodiversity.
Rewarding smaller farms for their conservation benefits may be
one policy pathway towards supporting smallholders. Biodiversity
could be promoted on larger farms by promoting more ecologically
friendly management practices and increasing biodiversity refuges
such as buffer strips and increased natural perimeters.
These findings come at a time where donor countries need to
invest an estimated US$14 billion annually to achieve the goal of
SDG 2.3 to double the incomes and productivity of smallholders49.
Our review adds to the motivation for these investments. We found
that, despite smallholders’ increased yields and role in provision of
ecosystem services, there is not enough evidence for equivalent gains
in smallholders’ profits. Thus, development support for smallhold-
ers is imperative from multiple viewpoints: the data not only show
that investing in smallholders could lead to humanitarian benefits
but also to increases in food production and benefits to biodiversity.
Haji, 2007 − Ethiopia (many) (n = 150)
Majumder, 2016 − Bangladesh (Rice) (n = 944)
Majumder, 2016 − Bangladesh (rice) (n = 944)
Binici, 2006 − Turkey (cotton) (n = 54)
Abedullah, 2007 − Pakistan (rice) (n = 200)
Wang, 2010 − China (wheat) (n = 432)
Tolga, 2009 − Turkey (rice) (n = 70)
Bojnec, 2013 − Slovenia (many) (n = 1,784)
Kilic, 2009 − Turkey (hazelnut) (n = 78)
Bakhshoodeh, 2001 − Iran (wheat) (n = 164)
Hussien, 2011 − Ethiopia (many) (n = 252)
Omonona, 2010 − Nigeria (cowpea) (n = 120)
Alene, 2003 − Ethiopia (maize) (n = 60)
Majumder, 2016 − Bangladesh (rice) (n = 944)
Kulekci, 2010 − Turkey (sunflower) (n = 117)
Majumder, 2016 − Bangladesh (rice) (n = 944)
Majumder, 2016 − Bangladesh (rice) (n = 944)
Abdallah, 2016 − India (cotton) (n = 569)
Pooled effect 0 (−0.01 to 0.02)
−20 0 20
Percentage change per 1 ha
increase in farm size
Fig. 4 | Forest plot for resource efficiency, where observations are in
standardized form and 95% CI are given. The size of each point estimate
relates to the inverse standard error. The pooled effect and 95% CI are
given in the lower plot. The country, crop name, and sample size (n) for
each observation are given on the y axis. ‘National’ sample sizes indicate
that the author used tabulated national statistics and did not include the
sample size. Please see the source data in the Supplementary Information
for complete list of references shown in the figure.
Pooled effect −0.05 (−0.09 to −0.01)
−75 −50 −25 0 25
Percentage change per 1 ha
increase in farm size
Headey, 2014 − Ethiopia (Teff) (n = 1,240)
Headey, 2014 − Ethiopia (Maize) (n = 1,240)
Li, 2013 − China (Many) (n = 2,155)
Heltberg, 1998 − Pakistan (Many) (n = 930)
Carletto, 2013 − Uganda (Maize) (n = 107)
Stifel, 2008 − Madagascar (Rice) (n = 163)
Benjamin, 1995 − Indonesia (Many) (n = 4,605)
Rada, 2015 − China (Wheat) (n = 6,964)
Rada, 2015 − China (Maize) (n = 12,478)
Rada, 2015 − China (Rice) (n = 8,589)
Benjamin, 1995 − Indonesia (Rice) (n = 4,605)
Assuncao, 2007 − India (Many) (n = 3,973)
Newell, 1997 − India (Many) (n = 400)
Ghose, 1979 − India (Many) (n = 100)
Carter, 1984 − India (Many) (n = 406)
Kagin, 2016 − Mexico (Many) (n = 1,361)
Ghose, 1979 − India (Many) (n = 148)
Khan, 1977 − Pakistan (Rice) (n = National)
Ghose, 1979 − India (Many) (n = 85)
Henderson, 2015 − Nicaragua (Many) (n = 5,743)
Chen, 2011 − China (Many) (n = 386)
Barrett, 2010 − Madagascar (Rice) (n = 286)
Ghose, 1979 − India (Many) (n = 149)
Khan, 1977 − Pakistan (Rice) (n = National)
Garrett, 2013 − Brazil (Soy) (n = 2,155)
Khan, 1977 − Pakistan (Cotton) (n = National)
Ghose, 1979 − India (Many) (n = 100)
Khan, 1977 − Pakistan (Wheat) (n = National)
Khan, 1977 − Pakistan (Cotton) (n = National)
Ghose, 1979 − India (Many) (n = 150)
Khan, 1977 − Pakistan (Wheat) (n = National)
Ghose, 1979 − India (Many) (n = 94)
Dorward, 1999 − Malawi (Many) (n = National)
Fig. 3 | Forest plot for yields, where observations are in standardized
form and 95% CI are given. The size of each point estimate relates to the
inverse standard error. The pooled effect and 95% CI are given in the lower
plot. The country, crop name, and sample size (n) for each observation are
given on the y axis. ‘National’ sample sizes indicate that the author used
tabulated national statistics and did not include the sample size. Please
see the source data in the Supplementary Information for complete list of
references shown in the figure.
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Such a triple reward confirms that support for smallholders globally
is an essential pathway for sustainable development.
Methods
A meta-analysis was conducted using the PRISMA guidelines50 (see Supplementary
Fig. 3 for inclusions/omissions and Supplementary Table 1 for Boolean search
terms). Below, we outline our data collection and synthesis methods.
Data. We searched the Web of Science and Scopus databases for studies in
English published before December 2017. We used four inclusion criteria:
(1) peer-reviewed; (2) directly measured farm size and the outcome variable(s) of
interest; (3) reported error estimates/significance tests in determining effect size;
and (4) compared farms with similar management systems (for example, compared
small and large cereal farms, not small vegetable farms to large cereal farms) or
controlled for the cropping systems’ differences (for example, converted different
crops to their value amount and/or controlled for the different types of crop species
planted). The inclusion of studies that compared farms with similar management
systems enabled us to examine if policies should target certain farm sizes to
grow particular crops. Future research may want to omit this inclusion criteria to
examine policy questions relevant to which types of crops should a country grow
given their farm size distribution.
Studies were coded at the observational level to analyse multiple crops, years
and locations per study; studies had multiple observations if they separately
reported different crops, years and/or locations per outcome variable. The main
conclusions were categorically coded as vote counts, where an increase in farm
size was associated with a decrease, increase or null relationship to the variable of
interest (we found no nonlinear results in the literature). For yield, resource-use
efficiency and profit, we extracted several additional variables to calculate pooled
effect sizes of regression model coefficients. To augment the sparse crop diversity
and GHG emission literature on farm size, we used results from Ricciardi et al.29 and
Clark & Tilman’s (2017)51 dataset, respectively. We leveraged the Clark & Tilman
meta-analysis database containing 742 agricultural life-cycle analysis observations
from 152 unique studies51; we coded observations that reported average farm size to
construct a dataset containing crop species, GHG emissions per unit output (in CO2
equivalents), average farm size and sample size for 100 observations (11 studies)
that met our inclusion criteria. As part of our systematic assessment we extracted
information from the broader literature on causal mechanisms behind the main
trends, as well as factors that caused deviations from the main trends (Table 1).
Our search yielded 1,474 studies. In total, we identified 118 studies (318
observations) that met our inclusion criteria. From these, we included seven solely
in the life-cycle analysis and coded 111 studies (218 observations) as vote counts,
of which we extracted regression coefficients from 40 studies (66 observations)
(Supplementary Table 2 shows summary statistics).
Synthesis of results. We ran three types of meta-regressions to synthesize the vote
count findings, extracted regression slopes and the GHG emission estimates. Due
to differing data availability across variables (for example, biodiversity studies did
not typically report regression coefficients), not all variables were analysed in each
meta-regression. First, we used cumulative link multilevel models (CLMM) to
synthesize the ordinal vote count findings for yield, resource-use efficiency, profit
and biodiversity52,53. We used CLMMs to examine the probability of the ordinal
outcome variable (observation finding negative, null or positive relationships
with farm size). For all CLMM and subsequent models (detailed in the following
paragraphs), we set the study as a random effect. Hierarchical models are
commonplace in meta-analyses and applied in our study because of the a priori
expectation that observations within studies and across similar crop types would
be correlated in the response, with random effects allowing us to account for
non-independence. In addition, as used in meta-analyses, random effects estimate
a variance component in addition to the sampling variance that fixed effects
models assume; this extra variance component has enabled meta-analyses
using random effects to be applied more generally and allows data to be
interpreted as a random population of outcomes instead of a single ‘true effect’,
as is a common interpretation of fixed effects meta-analyses47. For yields and
non-crop biodiversity, we also set crop type as random effects. For non-crop
biodiversity, we also set non-crop species type as a random effect. We tested if the
additional random effects used for yields and non-crop biodiversity changed the
results compared to using only studies as random effects and found no differences
in our conclusions.
Second, we used hierarchical meta-regressions of the standardized regression
slopes and standard errors54,55 to calculate pooled effects for yield, resource-use
efficiency and profit. Since certain variables contained multiple currencies,
efficiency units or measurement metrics, we relied on the Rodríguez-Barranco
et al. technique to convert farm size regression coefficients and standard errors
into standardized regression coefficients56. Our standardized coefficients represent
a relative change in the outcome variable per 1-ha change in farm size (we note
that these coefficients are limited by the range of the underlying farm sizes in
each study and should not be extrapolated). We used a linear model to synthesize
results because the literature predominantly provided linear coefficients. We used
the same random effects variable set up as in the CLMM models. Sensitivity tests
were conducted through cumulative meta-regressions for continuous variables
(for example, year of study and average farm size study observed) and subsetted
meta-regression for categorical variables (for example, type of diversity metric
used, if yield was defined by weight ha–1 or value ha–1, if resource efficiency was
derived from data envelopment analysis or stochastic frontier and so on). All
sensitivity tests found no differences in results. Forest plots are given in Figs. 3–5.
An inclusion of bias analysis was conducted through funnel plots that compare the
observed outcomes to standard errors. There were no clear biases for yields and
resource efficiency but a slight positive bias for profit (Supplementary Fig. 5).
This meta-regression framework also enabled us to further test if the variation
in findings between different studies could be attributed to the inclusion/omission
of variables that authors used when estimating the relationship between farm size
and the variable of interest, through sensitivity analyses using moderators. For
yield, we assessed the importance of moderators such as the types of production
methods, institutional characteristics (credit markets and access, extension access
and involvement in farmer cooperatives) and types of labour (general labour
market imperfections, family labour and household size). Our logic was that, if the
relationship is moderated by these factors (for example, if the main relationship
became null), it would indicate that there is a systematic variable omission bias in
the literature that, once corrected for, could explain the inverse farm size to yield
relationship. For resource-use efficiency, we conducted similar sensitivity analyses,
by including moderators that described development interventions (credit access,
extension access or farmer group membership). Our key hypothesis was that
having similar access to credit, extension or inputs and markets (through farmer
groups) may enable small farms to be equally or more efficient than large farms.
Heltberg, 1998 − Pakistan (many) (n = 930)
Gaurav, 2015 − India (Many) (n = 51,770)
Rada, 2015 − China (maize) (n = 33,369)
Rada, 2015 − China (rice) (n = 20,584)
Deininger, 2003 − Nicaragua (many) (n = 1,352)
Rada, 2015 − China (wheat) (n = 17,794)
Myyra, 2002 − Finland (cereals) (n = 962)
Lamb, 2003 − India (many) (n = 1,060)
Li, 2013 − China (many) (n = 2,155)
Sewando, 2014 − Tanzania (cassava) (n = 98)
Rahman, 2016 − Nigeria (yam) (n = 400)
Rahman, 2016 − Nigeria (cassava) (n = 400)
Savastano, 2009 − Kyrgyzstan (many) (n = 114)
Dauda, 2009 − Nigeria (many) (n = 250)
Rahman, 2016 − Nigeria (rice) (n = 400)
Pooled effect −0.02 (−0.1 to 0.05)
040 80 120
Percentage change per 1 ha
increase in farm size
Fig. 5 | Forest plot for profitability, where observations are in standardized
form and 95% CI are given. The size of each point estimate relates to the
inverse standard error. The pooled effect and 95% CI are given in the lower
plot. The country, crop name, and sample size (n) for each observation
are given on the y axis. Please see the source data in the Supplementary
Information for complete list of references shown in the figure.
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AnAlysis NaTure SuSTaiNabiliTy
Third, for the GHG emission observations, we used robust linear mixed-effects
models where we set the study and crop type as random effects. To estimate GHG
emissions per unit output, we used the log average farm size of a study as a fixed
effect. The key difference in the GHG emission model is that the data are at the
aggregated farm level, as opposed to extracted regression coefficients for the yield,
resource-use efficiency and profit models. (Formulas and further detail on each
meta-regression used are available in the Supplementary information.)
Data availability
The data that support the findings of this study are available in the Supplementary
Information. Source data are provided with this paper.
Code availability
The computer code that support the findings of this study is available in the
Supplementary Information.
Received: 14 July 2020; Accepted: 18 February 2021;
Published: xx xx xxxx
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Acknowledgements
We acknowledge funding from the University of British Columbia 4-Year Doctoral
Fellowship & Social Sciences and Humanities Research Council (SSHRC) Insight grant
no. 435-2016-0154.
Author contributions
V.R., N.R. and H.W. conceived the idea and designed the data collection process. V.R.
collected and coded the data. V.R., Z.M. and N.R. designed the analysis. V.R. and Z.M.
conducted the analysis. V.R., Z.M., N.R., H.W. and D.J. contributed interpretations of
results. All authors wrote the paper.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41893-021-00699-2.
Correspondence and requests for materials should be addressed to V.R.
Peer review information Nature Sustainability thanks Michael Clark and the other,
anonymous, reviewer(s) for their contribution to the peer review of this work.
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