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10.1002/ecy.2034 
This article is protected by copyright. All rights reserved 
 1 
PROF. DUNCAN NICHOLAS LUBCHENCO MENGE (Orcid ID : 0000-0003-4736-9844) 2 
MS. WENYING  LIAO (Orcid ID : 0000-0001-8777-1817) 3 
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Article type      : Articles 6 
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Why are nitrogen-fixing trees rare at higher compared to lower latitudes? 9 
Duncan N. L. Menge1,5, Sarah A. Batterman2,3,4, Lars O. Hedin2, Wenying Liao1,2, Stephen W. 10 
Pacala2, and Benton N. Taylor1 11 
1Department of Ecology, Evolution, and Environmental Biology, Columbia University 12 
2Department of Ecology and Evolutionary Biology, Princeton University 13 
3School of Geography and Priestley International Centre for Climate, University of Leeds  14 
4Smithsonian Tropical Research Institute, Ancon, Panama 15 
5Corresponding Author. Email: dm2972@columbia.edu  16 
 17 
Running head: N-fixing trees across latitude 18 
 19 
Article in Ecology  20 
Manuscript received 20 June 2017; revised 8 September 2017; accepted 18 September 2017. 21 
Corresponding Editor: Serita D. Frey 22 
 Abstract  23 
Symbiotic nitrogen (N) fixation provides a dominant source of new N to the terrestrial biosphere, 24 
yet in many cases the abundance of N-fixing trees appears paradoxical. N-fixing trees, which 25 
should be favored when N is limiting, are rare in higher-latitude forests where N limitation is 26 
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common, but are abundant in lower-latitude forests where N limitation is rare. Here, we develop 27 
a graphical and mathematical model to resolve the paradox. We use the model to demonstrate 28 
that N fixation is not necessarily cost-effective under all degrees of N limitation, as intuition 29 
suggests. Rather, N fixation is only cost-effective when N limitation is sufficiently severe. This 30 
general finding, specific versions of which have also emerged from other models, would explain 31 
sustained moderate N limitation because N-fixing trees would either turn N fixation off or be 32 
outcompeted under moderate N limitation. From this finding, four general hypothesis classes 33 
emerge to resolve the apparent paradox of N limitation and N-fixing tree abundance. The first 34 
hypothesis is that N limitation is less common at higher latitudes. This hypothesis contradicts 35 
prevailing evidence, so is unlikely, but the following three hypotheses all seem likely. The 36 
second hypothesis, which is new, is that even if N limitation is more common at higher latitudes, 37 
more severe N limitation might be more common at lower latitudes because of the capacity for 38 
higher N demand. Third, N fixation might be cost-effective under milder N limitation at lower 39 
latitudes but only under more severe N limitation at higher latitudes. This third hypothesis class 40 
generalizes previous hypotheses and suggests new specific hypotheses. For example, greater 41 
tradeoffs between N fixation and N use efficiency, soil N uptake, or plant turnover at higher 42 
compared to lower latitudes would make N fixation cost-effective only under more severe N 43 
limitation at higher latitudes. Fourth, N-fixing trees might adjust N fixation more at lower than at 44 
higher latitudes. This framework provides new hypotheses to explain the latitudinal abundance 45 
distribution of N-fixing trees, and also provides a new way to visualize them. Therefore, it can 46 
help explain the seemingly paradoxical persistence of N limitation in many higher latitude 47 
forests. 48 
Keywords: Nitrogen, nitrogen fixation, legume, latitude, tree, ecosystem, theory, limitation, 49 
facultative, obligate 50 
Introduction 51 
 Biological nitrogen (N) fixation is the largest natural N input to the terrestrial biosphere 52 
(Vitousek et al. 2013), and unlike other N inputs, has the capacity to respond to biotic N demand 53 
(Vitousek et al. 2002). This capacity is exceptionally high for symbioses between N-fixing 54 
bacteria and angiosperms (“rhizobial” legume species and “actinorhizal” species in other 55 
families), which can fix >100 kg N ha-1 y-1 (Binkley et al. 1994, Ruess et al. 2009). However, at 56 
the ecosystem scale, N-fixers (we call the plants “N-fixers” or “N-fixing plants” regardless of 57 
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whether they are actively engaged in N-fixing symbioses) can only fix N at high rates if they are 58 
relatively abundant, which they often are not. 59 
 The abundance distribution of N-fixing trees across latitude in the Americas is 60 
particularly intriguing. Forests at higher latitudes are more frequently N limited (i.e., N demand 61 
exceeds N supply) than those at lower latitudes (Vitousek & Sanford 1986, Vitousek & Howarth 62 
1991, Hedin et al. 2009, Brookshire et al. 2012). Given that N-fixing trees can access a vast N 63 
pool that other plants cannot (atmospheric N2
 High N-fixing tree abundance does not necessarily indicate high rates of symbiotic N 69 
fixation (SNF), which remain poorly quantified. Global models (e.g., Houlton et al. 2008, 70 
Wieder et al. 2015, Ri & Prentice 2017) typically suggest that SNF rates are high (tens of kg N 71 
ha
), it seems reasonable that they should have a 64 
competitive advantage in N-limited habitats, and therefore be more abundant at higher latitudes. 65 
However, according to systematic government forest inventories and plot-level data from many 66 
millions of trees, N-fixing trees are 10-fold less abundant at higher (>35°N) than lower latitudes 67 
in the Americas (<35°N; ter Steege et al. 2006, Menge et al. 2010, 2014, 2017). 68 
-1 yr-1) at lower latitudes. However, these models are typically parameterized based either on 72 
an early data synthesis (Cleveland et al. 1999) or no N fixation data at all (Wieder et al. 2015). 73 
The early data synthesis (Cleveland et al. 1999) included very few measurements of SNF at 74 
lower latitudes, and more recent studies suggest that many tropical forests with abundant N-75 
fixing trees have low to moderate rates of SNF (e.g., Barron et al. 2011, Batterman et al. 2013, 76 
Sullivan et al. 2014). Regardless of SNF rates, however, the pattern of N-fixing tree abundance 77 
in the Americas is exceptionally strong, and although abundance itself does not indicate SNF, it 78 
does control the capacity for SNF. The capacity for SNF—not the current rates—will help 79 
determine how forests respond to changing environmental conditions. One quarter of 80 
anthropogenic CO2
 Why are N-fixing trees rare at higher compared to lower latitudes? Hans Jenny wrote, 86 
“The question yet to be answered is whether the frequency of leguminous trees in the tropical 87 
forests studied and the related high nitrogen gains are conditioned by equatorial climate or by the 88 
 emissions are currently absorbed by forests (Ciais et al. 2013), but the extent 81 
to which this will continue may depend on N availability (Hungate et al. 2003, Thornton et al. 82 
2007, Sokolov et al. 2008, Gerber et al. 2010, Wårlind et al. 2014). Therefore, vastly different 83 
capacities for SNF at higher vs. lower latitudes could help determine future carbon storage 84 
(Batterman et al. 2013). 85 A
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history of plant evolution” (Jenny 1950). The plant evolutionary history argument was 89 
crystallized by Crews (1999). Noting that woody legumes are much more speciose in the tropics, 90 
he suggested that something unrelated to N might constrain legume trees to lower latitudes. 91 
However, trait evolution rates suggest that over 2,500 species of higher-latitude woody N-fixing 92 
legumes would be extant if SNF were widely adaptive at higher latitudes (Menge & Crews 93 
2016). Furthermore, legumes (rhizobial symbioses) are not the only N-fixing trees. When 94 
actinorhizal and rhizobial trees are considered together, N-fixing trees comprise only a slightly 95 
lower fraction of taxonomic diversity at higher compared to lower latitudes in the Americas 96 
(Menge et al. 2017). Overall, plant evolutionary history is likely not the explanation. 97 
 If plant evolutionary history is not the explanation, then there must be one or more 98 
ecological explanations. Even though N-fixing trees are not necessarily fixing N all the time, 99 
their capacity for SNF is their distinguishing ecological feature, so we focus on explanations that 100 
favor SNF itself. The reasoning behind our focus draws on opposing ecological forces. On one 101 
hand, SNF must be advantageous in some environments, otherwise N-fixing plants would be 102 
outcompeted. On the other hand, there must be some constraints or costs of having the capacity 103 
to fix N, otherwise perfectly “facultative” N fixers—those that adjust SNF to balance their 104 
benefits and costs exactly—would outcompete all non-fixing plants (Menge et al. 2009a). 105 
 Among the ecological mechanisms that could drive the latitudinal pattern of N-fixing tree 106 
abundance, climate (Jenny’s other proposed driver) has often been invoked. N-fixing trees are 107 
more abundant in hotter (Liao et al. 2017) and more arid (Pellegrini et al. 2016, Liao et al. 2017) 108 
ecosystems, but the mechanisms underlying these patterns are not well established. One 109 
previously proposed possibility is that a direct temperature constraint on the process of N 110 
fixation confines N-fixing trees to lower latitudes (Houlton et al. 2008). However, there are 111 
reasons to question a direct temperature constraint. For instance, peak growing season 112 
temperatures, unlike mean annual temperatures, are similar across a range of latitudes. 113 
Additionally, although some nitrogenase enzymes are particularly sensitive to low temperatures 114 
(Ceuterick et al. 1978), nitrogenases from bacteria adapted to higher latitudes are less so (Prévost 115 
et al. 1987). At the organismal level, bacteria and plants have adapted to arctic conditions well 116 
enough to fix N at rates similar to their temperate counterparts (Bordeleau & Prévost 1994). We 117 
speculate that adaptation to colder temperatures, the success of herbaceous N-fixing legumes 118 
(Bordeleau & Prévost 1994, Sprent 2009) and actinorhizal N-fixing plants (Liao et al. 2017) at 119 
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higher latitudes, the high SNF rates in higher-latitude plants (Binkley et al. 1994, Ruess et al. 120 
2009), and the small temperature differences across latitude during peak growing season suggest 121 
a need to look beyond a direct temperature constraint. 122 
 Temperature could also constrain SNF indirectly. According to theory, N-fixers that can 123 
adjust SNF rapidly are more competitive than those with substantial time lags (Menge et al. 124 
2009a). Temperature, which influences biological kinetics, likely influences how quickly N-125 
fixers can adjust SNF, so plants that live at higher latitudes could have unavoidably longer time 126 
lags, particularly at the beginning of the growing season when temperatures are still low. 127 
Significant time lags, particularly in ecosystems with short growing seasons, might select for an 128 
“obligate” SNF strategy that maintains a constant rate of SNF, rather than a facultative SNF 129 
strategy that adjusts to N limitation (Menge et al. 2009a). Theory suggests that obligate N-fixers 130 
are rare at the landscape scale because they are only successful in early successional habitats, 131 
whereas facultative N-fixers are more abundant because they persist throughout succession 132 
(Menge et al. 2009a, 2014). Therefore, temperature and growing season constraints on 133 
facultative SNF could explain the rarity of N-fixing trees at higher latitudes. 134 
 A second indirect climate-related mechanism also favors obligate N-fixers at higher 135 
latitudes. Sheffer et al. (2015) observed that colder temperatures lead to higher soil C:N, 136 
corresponding to lower rates of decomposition and slower release of bioavailable N in soils. If 137 
colder climates cause higher-latitude forests to have larger N deficits and recover biomass more 138 
slowly, then N limitation lasts longer, favoring the evolution of an obligate SNF strategy. 139 
Tropical forests also experience N limitation, but the condition appears limited to transient 140 
periods of rapid biomass accretion that follow disturbances (Davidson et al. 2004, 2007, Barron 141 
et al. 2011, Batterman et al. 2013). The combination of transient N limitation and rapid growth 142 
favors facultative SNF at lower latitudes (Sheffer et al. 2015). 143 
 Myriad other ecological mechanisms have been proposed to limit N-fixer abundance, 144 
including preferential herbivory on N-fixers (Vitousek & Howarth 1991, Ritchie & Tilman 1995, 145 
Hulme 1996, Vitousek & Field 1999, Knops et al. 2000, Menge et al. 2008, Kurokawa et al. 146 
2010), greater demand for soil nutrients that the symbionts need to fix N (e.g., phosphorus (P) or 147 
molybdenum (Mo); Vitousek & Howarth 1991, Vitousek & Field 1999, Uliassi & Ruess 2002), 148 
greater energy demand to pay the symbionts (Vitousek & Howarth 1991, Vitousek & Field 1999, 149 
Rastetter et al. 2001), and lower N use efficiency (Menge et al. 2008). Studies addressing these 150 
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mechanisms have focused on why SNF is rare in N-limited ecosystems, in an effort to 151 
understand the paradox of sustained N limitation (Vitousek & Howarth 1991), but have not 152 
addressed how these mechanisms influence the latitudinal abundance distribution of N-fixing 153 
trees. Understanding the rarity of SNF in N-limited ecosystems is integral to the latitudinal issue, 154 
but only addresses the higher latitude end of the spectrum. Moreover, these studies focus on the 155 
process of SNF, rather than the abundance of trees capable of SNF. A full explanation for the 156 
latitudinal abundance pattern needs to address N-fixing tree abundance, and why N-fixing trees 157 
are abundant at lower latitudes as well as rare at higher latitudes. 158 
 Here, we introduce a graphical framework to understand the abundance of N-fixing trees 159 
across latitude. This framework starts by providing a general explanation for sustained N 160 
limitation to net primary productivity (synonymous with plant N demand exceeding soil N 161 
supply). Our framework then reveals four classes of hypotheses to explain the latitudinal 162 
abundance pattern of N-fixing trees. Two of these hypotheses are new, one generalizes a 163 
previously proposed mechanism and extends other previously proposed mechanisms to a 164 
latitudinal context, and the fourth is one we have previously developed and include here for 165 
completeness. The first hypothesis proposes that, contrary to current understanding, N limitation 166 
is more common at lower latitudes (N limitation frequency hypothesis). The second new 167 
hypothesis proposes that more severe N limitation is more common at lower latitudes, even if 168 
some degree of N limitation is more common at higher latitudes (N limitation severity 169 
hypothesis). We define N limitation severity as the degree of imbalance between plant N demand 170 
and soil N supply, so “more severe” and “more moderate” indicate directions along an N 171 
limitation axis. A third possibility is that SNF is cost-effective under more moderate N limitation 172 
at lower latitudes, whereas it is only cost-effective under more severe N limitation at higher 173 
latitudes (N fixation benefit-cost hypothesis). The N fixation benefit-cost hypothesis generalizes 174 
specific mechanisms (e.g., Houlton et al. 2008) and extends previously proposed mechanisms 175 
(e.g., preferential herbivory might limit N-fixers; Vitousek & Field 1999, Menge et al. 2008) to a 176 
latitudinal context (e.g., preferential herbivory might change across latitude). A fourth 177 
possibility, which we developed previously (Menge et al. 2009a, 2014, Sheffer et al. 2015), is 178 
that the regulation of SNF changes with latitude (Differential regulation hypothesis). These 179 
hypotheses are not mutually exclusive, and each could be driven by multiple specific 180 
mechanisms. 181 
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Methods 182 
Theoretical model 183 
 Our graphical theory is more general than one specific model, but we use a mathematical 184 
model to show how specific plant traits (in the mathematical model) determine the values of the 185 
graphical components. The mathematical model we use is simple by design, following a long 186 
tradition in theoretical ecology, not because we eschew the importance of other factors, but 187 
because including other factors would obfuscate our understanding. Because of its simplicity, our 188 
model might miss some of the specific details that more complex models would capture, but it 189 
can also give more general insights. Our results emerge from the model shown here, but they 190 
could also emerge from other models that include more realistic features. The theory we use 191 
builds on Menge et al. (2008, 2009a, 2009b), and tracks how plant populations, Bi (kg C ha
-1), a 192 
soil pool of plant-unavailable N, D (kg N ha-1), and a soil pool of plant-available N, A (kg N ha-193 
1����� = �� �min �� ��) � ��)� + ��), � ��)1+� ��)∑ ��� � − µ ��)�     (1) 195 ), change over time: 194 ���� = ∑ µ������� ��)� −�� − ��          (2) 196 ���� = � +�� − �� − ∑ ��� ��) �min ������������� + ���, �����1+�����∑ ��� � −���������  (3) 197 
The subscripts i, j, and k refer to different plant types. In this model (Fig. 1a) plant growth can be 198 
limited by N or another density-dependent factor such as light, P, or another resource. 199 
 Plant traits can vary with SNF, between non-fixing and N-fixing species regardless of 200 
fixation rate, or both. For simplicity we only consider trait variation with SNF in the main text, 201 
so parameter values are the same for non-fixers and for N-fixing species that are not fixing N 202 
(e.g., ���� = ���� () ≡ �0).  This feature makes the graphical presentation of our results 203 
simpler because both non-fixing N-fixers and non-fixers have the same N limitation threshold.  204 
A version of the model with species-level variation, where non-fixing and N-fixing species differ 205 
independently of SNF rates, is in Appendix S1. 206 
 All plants can take N from the plant-available soil pool via uptake, ν (ha kg C-1 yr-1), and 207 
N-fixers can also acquire N via fixation, F (kg N kg C-1 yr-1). Newly acquired N is converted to 208 
new biomass C via N use efficiency, ω (kg C kg N-1). When not N limited, the plant grows at a 209 
maximum per capita rate g (yr-1), dampened by its susceptibility to competition, γ (ha kg C-1) and 210 
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its competitors’ biomass C, ∑B. Plant biomass turns over to the soil (µ; yr-1). Plant-unavailable N 211 
is converted to plant-available N (m, yr-1), and lost (φ, yr-1). N comes into the plant-available soil 212 
N pool from external inputs such as N deposition (I, kg N ha-1 yr-1) and is lost (e.g., leaching or 213 
gas loss) at the rate k (yr-1
Previously proposed tradeoffs between SNF and plant traits 216 
). All parameters are strictly positive except for fixation (F), which can 214 
be 0. 215 
 Because a given amount of root tissue can be used for either SNF or N uptake, there is 217 
probably a tradeoff between SNF and soil N uptake (Rastetter et al. 2001, Menge et al. 2008, 218 
Sheffer et al. 2015; Fig. 1b): 
�� �)�� ≡ �′ < (. N-fixing plants have higher average tissue N 219 
concentrations than non-fixing plants (Fyllas et al. 2009, Nasto et al. 2014, Adams et al. 2016), 220 
which is driven in part by symbiotic bacteria, regardless of plant N demand (Wolf et al. 2017). 221 
Therefore, we assume that nutrient use efficiency decreases with SNF: 
�� �)�� ≡ �′ < (. As 222 
described in the introduction, N-fixers might suffer greater rates of herbivory-driven turnover 223 
than non-fixers because of their high N content 
�µ �)�� ≡ µ′ > (. On the contrary, N-fixing trees 224 
might use extra N to increase herbivore defenses (Vitousek & Field 1999, Menge et al. 2008, 225 
Menge & Chazdon 2016), which could balance or reverse the relationship between SNF and 226 
turnover: µ′ ≤ (. 227 
 A number of mechanisms connect SNF to energy, P, or other non-N nutrients (Vitousek 228 
& Howarth 1991, Vitousek & Field 1999, Rastetter et al. 2001, Houlton et al. 2008). Our model 229 
specifies that some other resource limits plant growth if N does not, so competition for other 230 
resources affects the non-N-limited maximum growth rate, �, or competition, �. Under 231 
conditions when both the non-fixer and the N-fixer are not N limited, greater demand for energy, 232 
P, Mo, or another resource would mean that N-fixers would experience a lower maximum 233 
growth rate or greater competition than non-fixers: 
�� �)�� ≡ �′ < (, �� �)�� ≡ �′ > (. On the 234 
contrary, if N-fixers use their higher N content to increase photosynthetic rates (Field & Mooney 235 
1986) or water use efficiency (Adams et al. 2016), or are better able than non-fixers to access P 236 
via phosphatase enzymes (Houlton et al. 2008), they could have higher maximum growth rates or 237 
a competitive advantage when both non-fixers and N-fixers are not N limited: �′ > (, �′ < (. 238 
Previously proposed latitudinal trends in plant traits and tradeoffs between SNF and plant traits 239 
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 If temperature constrains SNF directly (Houlton et al. 2008), then plants at higher 240 
latitudes (L) need to spend more carbon to get the same amount of N. Our model can incorporate 241 
this in two ways. First, turnover rates of N-fixers might increase more with SNF, or decrease less 242 
with SNF, at higher than at lower latitudes (Fig. 1c): 
��µ �)���� > (. Second, the temperature effect 243 
might require a greater investment in nodules to achieve a similar SNF rate, which would 244 
decrease the carbon available for soil N uptake via roots or mycorrhizae. In this case, the N 245 
uptake rates of N-fixers decrease more with SNF at higher than at lower latitudes (Fig. 1d): 246 ��� �)���� < (. A higher turnover cost of SNF at higher latitudes (��µ �)���� > () could also stem from N-247 
fixers being more palatable to herbivores than non-fixers at higher latitudes, but less palatable 248 
than non-fixers at lower latitudes (Fig. 1c). 249 
 The idea that SNF confers a greater phosphatase advantage (Houlton et al. 2008) at lower 250 
latitudes, where P is more limiting than at higher latitudes, would mean that effects of SNF on 251 
the non-N-limited growth parameters change across latitude. If P acquisition enhances the plant’s 252 
maximum growth rate more at lower latitudes (Fig. 1e), 
��� �)���� < (, whereas if P acquisition 253 
reduces competition with neighboring plants more at lower latitudes (Fig. 1c), 
��� �)���� > (. The 254 
final previously proposed mechanism involves the degree to which N-fixing plants regulate SNF 255 
in response to soil N supply vs. N demand. In this scenario, F is constant at high latitudes but 256 
variable at low latitudes. 257 
 The trends in this section represent what has been proposed previously. However, our 258 
analytical results do not depend on these assumptions, and one could evaluate the effect of other 259 
cases using our equations in Appendix S1. 260 
Analysis: A framework to classify mechanisms that can maintain N limitation 261 
 We show our graphical results in the main text as a function of our N limitation index, 262 
which is the difference between soil N supply flux (S = I + mD) and N demand at a snapshot in 263 
time (Appendix S1). Because this approach focuses on the difference between N demand and N 264 
supply, the absolute values of each do not influence the presentation. However, because it is of 265 
interest to examine changes in N demand and N supply independently, we also show our 266 
graphical results as a function of soil N supply in Appendix S2.  267 
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 Our approach requires three graphical components. The first is the “co-limitation 268 
threshold,” the N supply level (Sco) that divides N limitation from non-N limitation. The co-269 
limitation threshold is equivalent to N demand. The second component is the “N fixation benefit-270 
cost threshold,” the level of N supply (Scrit
 The pattern we want to explain concerns the relative abundance of N-fixing trees, which 282 
in our model is 
����∑� . However, we focus our analysis on three key quantities—the co-limitation 283 
threshold, the N fixation benefit-cost threshold, and the distribution of habitats—rather than 284 
relative abundance itself, for three reasons. First, these three quantities are the key determinants 285 
of the difference in relative growth rate between N-fixing trees and non-fixing trees, so they give 286 
a clear window into relative abundance, even if there is not a one-to-one correspondence. We are 287 
interested in qualitative patterns in this work (fewer N-fixing trees, not more, in an environment 288 
that is more N limited), not specific numbers. Second, studying these three quantities requires 289 
fewer assumptions than examining relative abundance itself. Modeling relative abundance 290 
requires not only a description of how the ecosystem changes (Eqns. 1-3), but also a description 291 
of the starting values and length of time since the ecosystem was at those starting values. The 292 
forest ecosystems we are modeling typically range up to a couple hundred years old (Menge et 293 
al. 2014), whereas this sort of ecosystem model takes thousands of years to approach equilibrium 294 
(Menge et al. 2009b). Explicitly modeling a mosaic of succession would be cumbersome and 295 
would not add qualitative understanding. Third, these three quantities facilitate the graphical 296 
framework that will clarify our hypotheses and the underlying mechanisms. 297 
) at which the benefit of SNF equals the cost. The 271 
benefits vs. costs of SNF are, respectively, the new biomass gained from newly fixed N vs. the 272 
new biomass lost due to the indirect effects of SNF on the other plant parameters. The N fixation 273 
benefit-cost threshold divides the region where N fixation is cost-effective from the region where 274 
it is not. In the main text we give the benefit-cost threshold results for perfectly facultative SNF. 275 
In Appendix S1 we also present results for obligate SNF and with an explicit cost of being 276 
facultative. To find the facultative SNF benefit-cost threshold, we evaluate how a small amount 277 
of fixation influences the relative plant population growth rate. A positive effect indicates a net 278 
SNF benefit, and a negative effect indicates a net SNF cost, so the threshold is where this 279 
quantity equals 0: 
�1�������  |�=0 = (. The third and final graphical component is the distribution of 280 
habitats across a gradient of N limitation. 281 
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 Once we have the graphical framework, we examine how the three components—the co-298 
limitation threshold, the N fixation benefit-cost threshold, and the distribution of habitats—might 299 
vary across latitude. Because our approach uses a simple model, and focuses on graphical and 300 
analytical (but not numerical simulation) techniques, there is no need for direct parameterization 301 
of our model or for numerical sensitivity analyses. Our model reveals hypotheses that could 302 
explain the latitudinal distribution of N-fixing trees, and how underlying plant and ecosystem 303 
traits influence these hypotheses. It does not attempt to assign quantitative probabilities to them, 304 
but in the discussion we draw on relevant literature to debate the relative likelihood of the 305 
different hypotheses. 306 
Results 307 
Sustained N limitation: Graphical theory 308 
 Sustained N limitation seems paradoxical because intuition says that SNF should be 309 
advantageous when N limits production, and should therefore alleviate N limitation (Vitousek & 310 
Howarth 1991). Graphically, we can show this intuitive statement as a distribution of habitats 311 
along an N limitation gradient (Fig. 2a; see Appendix S2: Fig. S1a for an N supply gradient). If 312 
SNF is cost-effective whenever N limits production, then N-fixers fix N in habitats to the left of 313 
the dashed line. After their newly fixed N is incorporated into the soil, N supply would increase, 314 
shifting the habitat distribution to the right. In reality many forests are N limited, as in Fig. 2a, 315 
but have no SNF, unlike Fig. 2a, which is why sustained N limitation seems paradoxical. A key 316 
assumption underlying this seeming paradox is that SNF is cost-effective whenever soil N supply 317 
alone is insufficient to meet N-fixers’ demand. As shown below (and elsewhere, e.g., Vitousek & 318 
Field 1999, Menge et al. 2008), this does not have to be true. Fig. 2b, Appendix S2: Fig. S1b 319 
show a scenario where most habitats are N limited but SNF is only cost-effective in habitats 320 
where N limitation is sufficiently severe. Next we derive the conditions under which the scenario 321 
in Fig. 2b occurs. 322 
Sustained N limitation: Mathematical results 323 
 The co-limitation threshold (Sco
 ��� = � � �)1+� �)∑�−� �)�� �+∑�� �))� �)� �)        (4) 325 
) is the soil N supply at which plants are co-limited: 324 
 The N fixation benefit-cost threshold (Scrit
 ����� = �µ0′−�0� �+∑��0)2�0′�0 �+∑��0+��0)+�0�0′  �+∑��0−��0)      (5) 327 ) for a facultative N-fixer is: 326 
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The “′” indicates a derivative with respect to F. The “0” subscripts indicate “evaluated at F = 0.” 328 
 The key point of Eqns. 4-5 is that the N fixation benefit-cost threshold (Scrit) does not 329 
have to be the same N supply level as the co-limitation threshold (Sco). To see this, note that 330 
many parameters appear in only one equation. Therefore, the intuitive scenario (Scrit = Sco; Fig. 331 
2a) is possible, but highly unlikely. By contrast, a range of N limitation where SNF is not cost-332 
effective (Scrit < Sco
Comparing across latitude 337 
; Fig. 2b) is likely, depending on the values of the plant and ecosystem traits 333 
that determine the co-limitation and N fixation benefit-cost thresholds (Appendix S1: Table S1). 334 
Stronger tradeoffs between SNF and N use efficiency (�), soil N uptake (�), or turnover (µ) 335 
lower the N fixation benefit-cost threshold, and therefore facilitate N limitation. 336 
 We now use this graphical framework to ask: Why are N-fixing trees rare at higher 338 
compared to lower latitudes? 339 
 N limitation frequency hypothesis: N limitation is more common at lower latitudes 340 
 The first explanation is that N limitation is more common at lower latitudes (Fig. 2c, 341 
Appendix S2: Fig. S1c), counter to our current understanding.  342 
N limitation severity hypothesis: More severe N limitation is more common at lower 343 
latitudes 344 
 If there is a range of N limitation over which SNF is not cost-effective (Scrit < Sco
 N fixation benefit-cost hypothesis: SNF is cost-effective over a wider range of N 353 
limitation at lower latitudes 354 
, as in 345 
Fig. 2b, Appendix S2: Fig. S1b), then only the proportion of habitat where N limitation is 346 
sufficiently severe (i.e., SNF is cost-effective)—not the proportion that is N limited at all—347 
predicts N-fixing tree success. The N limitation severity hypothesis states that even if N 348 
limitation is less common in lower- than higher-latitude forests, more severe N limitation is more 349 
common in lower- than higher-latitude forests (Fig. 2d, Appendix S2: Fig. S1d). Put another 350 
way, even if the mean trend is that higher latitudes are more N limited than lower latitudes, 351 
variance in the magnitude of N limitation across habitats could be greater at lower latitudes. 352 
 If SNF is only cost-effective when N limitation is severe enough (Scrit < Sco; Fig. 2b), the 355 
“severe enough” threshold itself (Sco – Scrit) might vary across latitude. The N fixation benefit-356 
cost hypothesis states that SNF is only cost-effective under more severe N limitation at higher 357 
latitudes, whereas it is cost-effective under more moderate N limitation at lower latitudes (Fig. 358 
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2e, Appendix S2: Fig. S1e). This general hypothesis class encompasses many specific 359 
mechanisms. Because plant traits modify the co-limitation threshold, the N fixation benefit-cost 360 
threshold, or both (Table S1), we can determine which specific mechanisms would support the N 361 
fixation benefit-cost hypothesis (Fig. 3, Appendix S1, Appendix S2: Fig. S2). Not all of these 362 
mechanisms are likely, but we list them for completeness. First, lower N use efficiency at higher 363 
latitudes would increase the co-limitation threshold but decrease the N fixation benefit-cost 364 
threshold compared to lower latitudes. Second, stronger tradeoffs between SNF and N use 365 
efficiency, soil N uptake, and turnover at higher latitudes decrease the N fixation benefit-cost 366 
threshold at higher latitudes. Third, a higher maximum growth rate, a lower susceptibility to non-367 
N-based competition, or a lower soil N uptake rate at higher latitudes compared to lower 368 
latitudes would increase ecosystem N demand at higher latitudes. 369 
Differential regulation hypothesis: The SNF strategy differs across latitude 370 
 The three hypotheses discussed above examine situations in which facultative N-fixers 371 
are more common at lower than at higher latitudes. If higher-latitude N-fixers are more obligate 372 
but lower-latitude N-fixers are more facultative (Menge et al. 2014, Sheffer et al. 2015), then a 373 
fourth hypothesis—the differential regulation hypothesis—emerges.  374 
Obligate N-fixers are less competitive under mild N limitation than facultative N-fixers, 375 
for two reasons. First, the N fixation benefit-cost threshold is closer to the co-limitation threshold 376 
for facultative (or over-regulating, under-regulating, or incompletely down-regulating; Menge et 377 
al. 2015) than for obligate N-fixers (Fig. 2f, Appendix S1, Appendix S2: Fig. S1f). The second 378 
reason concerns relative growth rates when SNF is not cost-effective. When SNF is not cost-379 
effective, obligate N-fixers have much lower relative population growth rates than non-fixers 380 
because they are wasting energy fixing N. On the contrary, facultative N-fixers that are not 381 
fixing have only slightly lower relative population growth rates than do non-fixers, depending on 382 
the costs of being facultative (Appendix S1). 383 
Discussion 384 
 Four general hypothesis classes emerge from our graphical framework, all of which could 385 
explain why N-fixing trees are much more abundant at lower latitudes than at higher latitudes, 386 
and all of which could act in concert. These general hypothesis classes relate to our finding that, 387 
contrary to the intuition that N fixation is cost-effective under all degrees of N limitation, it is 388 
only cost-effective under sufficiently severe N limitation. This finding, which has also been 389 
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shown or suggested in previous studies (e.g., Vitousek & Howarth 1991, Ritchie & Tilman 1995, 390 
Vitousek & Field 1999, Rastetter et al. 2001, Menge et al. 2008), provides a graphical 391 
explanation for sustained N limitation, which has long been viewed as a paradox in ecosystem 392 
ecology (Vitousek & Howarth 1991). Although this understanding of sustained N limitation 393 
opens doors to many questions, our focus here is on understanding the latitudinal abundance 394 
pattern of N-fixing trees in the Americas. In that vein, we now draw on the literature to evaluate 395 
how likely each general hypothesis class is and which of the specific mechanisms we have 396 
highlighted might underlie them. 397 
N limitation is probably not more common at lower latitudes 398 
 The latitudinal abundance pattern of N-fixing trees seems paradoxical (Houlton et al. 399 
2008, Hedin et al. 2009, Menge et al. 2014) precisely because N limitation is thought to be less 400 
common at lower latitudes, not more common (Vitousek & Sanford 1986, Hedin et al. 2009, 401 
Brookshire et al. 2012). The evidence for this, such as the 10-fold greater leaching of plant-402 
available N in tropical compared to temperate forests (Hedin et al. 2009, Brookshire et al. 2012), 403 
suggests that our first hypothesis—the N limitation frequency hypothesis—is unlikely. 404 
Somewhat surprisingly, a meta-analysis of N fertilization studies found that N limitation was at 405 
least as strong in tropical forests as in temperate forests (LeBauer & Treseder 2008), although 406 
three factors mitigate this finding. First, few fertilization studies have been conducted in tropical 407 
forests, particularly before 2008. Second, site selection bias towards young and successional 408 
tropical forests may have amplified the N limitation signal compared to the true distribution of 409 
tropical forest types (LeBauer et al. 2008). In particular, only one mature tropical forest was 410 
included in that meta-analysis, and it did not show an NPP response to N fertilization. Mature 411 
tropical forests, which comprise 58% of Latin American tropical forest area (Chazdon et al. 412 
2016), are the tropical forests typically thought to be N-rich (Hedin et al. 2009). Studies in 413 
mature tropical forest studies since 2008 have found no ecosystem-level response to N additions 414 
(Wright et al. 2011, Alvarez-Clare et al. 2013). Many other tropical forests, such as those 415 
growing on young substrates (Vitousek & Farrington 1997) or those in early successional stages 416 
(Davidson et al. 2004, Batterman et al. 2013), are often N limited. Third, the response metric 417 
used—the response ratio—does not distinguish between the frequency and severity of N 418 
limitation, and as we discuss below, tropical forests might be more severely but less frequently N 419 
limited. 420 
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More severe N limitation might be more common at lower latitudes 421 
 The N limitation severity hypothesis—more severe N limitation is more common in 422 
lower- than higher-latitude forests—is new, to our knowledge, and is an intriguing possibility. It 423 
could explain why tropical forests appeared at least as N limited as temperate forests in a meta-424 
analysis (LeBauer & Treseder 2008). Even if most tropical forests are not N limited, a few 425 
severely N-limited forests would inflate the average response to fertilization. On a mechanistic 426 
level, lower-latitude forests likely have a greater capacity for more severe N limitation than 427 
higher-latitude forests. Longer growing seasons, warmer temperatures, and ample rainfall 428 
stimulate N demand, so if N supply is greatly diminished—for example, due to large 429 
disturbance-mediated N losses—then lower-latitude forests can be more severely N limited than 430 
higher-latitude forests (Fig. 2d). For example, a recent modeling study (Ri & Prentice 2017) 431 
suggests that N demand that is unmet by recycling is much higher at lower than higher latitudes. 432 
 Variation in N limitation could occur at a variety of scales. On the successional timescale 433 
and the landscape spatial scale, a variety of studies suggest that N limitation—possibly severe N 434 
limitation—is common in young regenerating tropical forests (Davidson et al. 2004, 2007, 435 
Batterman et al. 2013), which comprise 22% of Neotropical forests (where “young” is <20 years 436 
old; Chazdon et al. 2016). However, N-fixing trees are also common in mature tropical forests 437 
(ter Steege et al. 2006, Batterman et al. 2013, Menge & Chazdon 2016). On smaller spatial 438 
scales, tree-fall gaps lead to greater understory light penetration at lower latitudes because of the 439 
sun angle (Canham et al. 1990). Greater light penetration—which increases N demand for the 440 
remaining trees—combined with reduced N supply in gaps (Vitousek and Denslow 1986) could 441 
drive a severe N demand-supply imbalance in gaps, even in mature forests. A study in Panama 442 
documented much higher nodulation rates in mature forest gaps than in the surrounding matrix 443 
(Barron et al. 2011), which could explain the continued success of N-fixing trees in mature 444 
tropical forests (Batterman et al. 2013). 445 
SNF might be cost-effective under a wider range of N limitation at lower latitudes 446 
 Most of the previously proposed mechanisms that could constrain N-fixers in N-limited 447 
environments are, in essence, explanations for why SNF is only cost-effective when N limitation 448 
is sufficiently severe. An allocation tradeoff between soil N uptake and SNF (Rastetter et al. 449 
2001, Menge et al. 2008), lower N use efficiency or higher turnover as a consequence of SNF 450 
(Menge et al. 2008), and energetic or other resource (e.g., P or Mo) costs of SNF (Vitousek & 451 
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Howarth 1991, Vitousek & Field 1999, Rastetter et al. 2001, Uliassi & Ruess 2002) all make 452 
SNF cost-effective under more severe but not more moderate N limitation (Fig. 2b). 453 
 If any of these specific mechanisms change across latitude, and the change is in the right 454 
direction, they could support the N fixation benefit-cost hypothesis, and help explain why N-455 
fixers are rare at higher latitudes. Two of these latitudinal changes relate to previously proposed 456 
mechanisms (Fig. 3). If temperature constrains the process of SNF (Houlton et al. 2008), then 457 
higher-latitude N-fixers would need to invest more carbon per unit N fixed than lower-latitude 458 
N-fixers. Such a carbon investment could strengthen the tradeoff between SNF and N uptake at 459 
higher latitudes because carbon used for SNF cannot be used for soil N uptake. Alternatively, 460 
such a carbon investment could make SNF more costly via an increased turnover rate. 461 
 The second previously proposed mechanism relates to herbivory. As explained above, N-462 
fixers’ higher N content could lead to higher herbivore pressure (if it is used for tasty, non-463 
defensive compounds; Vitousek & Howarth 1991), or it could enable a greater capacity for 464 
chemical defense, by using N-based defensive compounds, by using their higher photosynthetic 465 
rates to synthesize more C-based defensive compounds, or both. If herbivory is a stronger 466 
selective force at lower latitudes (Coley & Barone 1996), then lower latitude N-fixers might have 467 
been selected for greater investment in anti-herbivore defense than higher latitude N-fixers 468 
(Vitousek & Field 1999, Menge et al. 2008). In this case, N-fixers might have a higher turnover 469 
cost of SNF, corresponding to higher mortality rates than non-fixers, at higher latitudes, but vice 470 
versa at lower latitudes (Figs. 1c, 3). In support of this prediction, N-fixing trees in the 471 
coterminous U.S.A. had higher mortality rates than non-fixing trees (Liao & Menge 2016), 472 
whereas N-fixing trees in Costa Rica had lower mortality than non-fixing trees (Menge & 473 
Chazdon 2016). This empirical mortality pattern is consistent with an herbivory mechanism, but 474 
does not pinpoint herbivory as the mechanism because it was not measured. 475 
 Curiously, one previously proposed specific mechanism—that N-fixers have a greater 476 
ability to produce P-liberating phosphatases (Houlton et al. 2008)—cannot explain N-fixer 477 
abundance in our model. The model that produced that hypothesis (Wang et al. 2007, Houlton et 478 
al. 2008) is much more complex than ours, so it is not surprising that it allows for possibilities 479 
that ours does not, but we note that many other specific mechanisms emerge from our model 480 
despite its simplicity. 481 
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 In addition to the previously-proposed mechanisms that could underlie the N fixation 482 
benefit-cost hypothesis, three other possibilities emerge from our model (Fig. 3). First, the 483 
stronger the tradeoff between SNF and N use efficiency, the more severe N limitation must be to 484 
favor SNF (Fig. 3). Second, trees might experience weaker competition for non-N resources at 485 
higher latitudes. Third, trees might have lower soil N uptake rates at higher latitudes. However, 486 
even if these traits and tradeoffs change in the right direction, they can be offset by other trends. 487 
For example, trees are more N use efficient at higher latitudes (Vitousek 1984, McGroddy et al. 488 
2004), which lowers ecosystem-level N demand and enhances the benefit of fixed N (Fig. 3). 489 
  Although it is useful to think through these specific mechanisms, pinning down all the 490 
conditions needed to scale up to the overall balance of N fixation benefits and costs is 491 
challenging. The specific mechanisms interact, and trends for seemingly unrelated traits can 492 
cancel each other out (Appendix S1: Eqn. S11). Pursuing each of these specific mechanisms is a 493 
good goal, but a complementary way to evaluate the N fixation benefit-cost hypothesis is to test 494 
the theoretical predictions rather than the parameters. For example, Menge et al. (2015) found 495 
that a number of herbaceous plant species were “over-regulators.” These plants turned SNF off at 496 
N supply levels that were lower than their N demand, as predicted by our theory (Appendix S1, 497 
Appendix S1: Fig. S1). If these plants’ SNF rates accurately assess the cost-effectiveness of 498 
SNF, then “over-regulation” is evidence that the N fixation benefit-cost threshold is lower than 499 
the co-limitation threshold. 500 
N-fixing trees might be more facultative at lower latitudes 501 
 A variety of field observations suggest that higher latitude N-fixing trees are obligate 502 
(Mead & Preston 1992, Binkley et al. 1994, Menge & Hedin 2009), whereas lower latitude N-503 
fixing trees are facultative (Pearson & Vitousek 2001, Barron et al. 2011, Batterman et al. 2013, 504 
Sullivan et al. 2014, Bauters et al. 2016, see also Andrews et al. 2011). Modeling suggests that a 505 
strategy transition across latitude can explain the latitudinal trend (Menge et al. 2014). 506 
Underlying climate effects on soil N deficits (Sheffer et al. 2015) or on the constraints and costs 507 
of regulating SNF (Menge et al. 2009a) can explain a transition in strategy. Although 508 
experimental evidence is still scant, the differential regulation hypothesis is promising. 509 
Conclusions 510 
 Given current evidence, the most likely reasons that N-fixing trees are more abundant at 511 
lower latitudes in the Americas are: a greater prevalence of more severe N limitation at lower 512 
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latitudes (the N limitation severity hypothesis), lower costs of SNF compared with other forms of 513 
N uptake at lower latitudes (the N fixation benefit-cost hypothesis), and a transition in SNF 514 
strategy across latitude (the differential regulation hypothesis) (Fig. 4). Evolutionary constraints 515 
on the biogeography of N-fixing trees and a higher frequency of N limitation at lower latitudes 516 
are unlikely to explain the latitudinal trend of N-fixer abundance in the Americas. Disentangling 517 
the relative importance of N limitation severity, N fixation benefits vs. costs, and differential 518 
regulation, and determining the specific mechanisms that underlie them, will help resolve the 519 
seemingly paradoxical latitudinal distribution of N-fixers that has puzzled scientists for over 65 520 
years. Furthermore, given the importance of N fixation for ecosystems’ responses to rising 521 
atmospheric CO2
Acknowledgements 525 
 and temperature, testing these hypotheses will greatly improve our 522 
understanding of how the fixation and carbon sequestration responses differ across latitude, 523 
which will improve our predictions of global climate change. 524 
 This material is based upon work supported by the National Science Foundation under 526 
grant no. DEB-1457650. SAB was supported by a UK Natural Environment Research Council 527 
Independent Research Fellowship (NE/M019497/1). 528 
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Figure legends 703 
Figure 1. Structure of the theoretical model and previously proposed trends. Red and blue curves 704 
indicate lower and higher latitudes, respectively. (a) The model is an ecosystem model that tracks 705 
nitrogen (N) in plants and soils, and carbon in plants. Plant growth can be limited by N, by 706 
another implicit resource such as light or phosphorus, or co-limited. (b) Previously proposed 707 
relationships between N fixation and other plant traits. The vertical axis is a relative trait value 708 
axis for each trait, so the absolute value has no meaning. Question marks by traits indicate that 709 
there are mechanisms suggesting both directions (the trait value might increase or decrease with 710 
N fixation). (c)-(e): Previously proposed changes in the relationship between N fixation and plant 711 
traits across latitude. The changes indicated are changes in slope. Although some are shown as 712 
switches in the sign of the slope (e.g., up vs. down), they could also be changes in slope without 713 
a change in sign (e.g., less down vs. more down). See text for specific mechanisms underlying 714 
these trends. 715 
Figure 2. Framework for visualizing the mechanisms that can explain persistent N limitation and 716 
the hypotheses that can explain the latitudinal paradox. The horizontal axis, the N limitation 717 
index, is the difference between instantaneous soil N supply and N demand (in units such as kg 718 
N ha-1 y-1). It represents N limitation to growth for both non-fixers and N-fixers that are not 719 
fixing, which in our model are equal, and therefore to net primary productivity. The vertical axis 720 
is the frequency of habitats (in proportion of area). Shading indicates that the relative population 721 
growth rate of facultative N-fixers exceeds that of non-fixers. The dashed vertical line at 0, the 722 
co-limitation threshold, corresponds to where N supply matches N demand. Habitats to the right 723 
of the dashed line are N rich and those to the left are N limited. Habitats immediately to the left 724 
of the dashed line are only moderately N limited, whereas those further to the left are more 725 
severely N limited. “SNF” indicates symbiotic N fixation. If N fixation is cost-effective 726 
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whenever N-fixers are N limited, the N supply rate at which the benefits of N fixation equal the 727 
costs of N fixation is the same as the co-limitation threshold (a). Alternatively, if N fixation is 728 
only cost-effective when N limitation is sufficiently severe, there is a benefit-cost threshold to 729 
the left of the co-limitation threshold (b). In panel (a), most of the habitat is N limited and N 730 
fixation is cost-effective whenever N is limiting. Panel (b) shows a scenario where most habitats 731 
are N limited but N fixation is only cost-effective when N limitation is sufficiently severe. This 732 
scenario can arise from a number of mechanisms (see text). Panels represent snapshots in time. 733 
Habitats are not defined at a particular spatial scale; they could be different forests across a 734 
continent or different patches across a forest. Lower latitude distributions and benefit-cost 735 
thresholds are shown in red, higher latitude distributions and benefit-cost thresholds are shown in 736 
blue. Panels (c)-(f) show four hypotheses that can account for greater abundance of N-fixers at 737 
lower latitudes. (c) N limitation frequency hypothesis: N limitation is more common at lower 738 
latitudes. (d) N limitation severity hypothesis: More severe N limitation is more common at 739 
lower latitudes, even though some degree of N limitation is more common at higher latitudes. (e) 740 
N fixation benefit-cost hypothesis: The N fixation benefit-cost threshold is at more moderate N 741 
limitation at lower latitudes, so N fixation is cost-effective across a wider range of N limitation at 742 
lower latitudes. In panels (c)-(e) the benefit-cost thresholds are shown for facultative N fixation 743 
only, whereas in panel (f) different thresholds are shown for facultative and obligate N fixation. 744 
(f) Differential regulation hypothesis: Facultative N fixation is more cost-effective than obligate 745 
N fixation (provided there is minimal cost to being facultative), and N-fixers can be somewhat 746 
abundant even in habitats where N fixation is not cost-effective because they turn fixation off 747 
(indicated by pink shading). The facultative and obligate thresholds do not need to correspond to 748 
latitude, so they are written in black. 749 
Figure 3. Trends that would support the N fixation benefit-cost hypothesis. The horizontal axis is 750 
the same as Fig. 2. As in Fig. 2c-f, red and blue indicate lower and higher latitudes, respectively. 751 
“SNF” indicates symbiotic N fixation. Supporting the N fixation benefit-cost hypothesis means 752 
increasing the separation between the co-limitation threshold and the N fixation benefit-cost 753 
threshold at higher latitudes compared to lower latitudes (Fig. 2e). Arrows going from red to blue 754 
indicate this increasing separation with latitude. Either raising the co-limitation threshold 755 
(increasing N demand) or lowering the N fixation benefit-cost threshold (making N fixation less 756 
cost-effective) at higher latitudes support the N fixation benefit-cost hypothesis. The top row (N 757 
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use efficiency) both raises the co-limitation threshold and lowers the N fixation benefit-cost 758 
threshold. The middle row (tradeoffs between N fixation and plant traits) only lowers the N 759 
fixation benefit-cost threshold. The turnover and soil N uptake trends correspond to Fig. 1c, d. 760 
The bottom row only raises the co-limitation threshold. Trends that would support the benefit-761 
cost hypothesis but are unlikely are crossed out. 762 
Figure 4. Conceptual diagram of general hypothesis classes and specific mechanisms to explain 763 
the rarity of N-fixing trees at higher latitudes compared to lower latitudes. Questions are shown 764 
in blue, hypothesis classes in orange, and specific mechanisms for each hypothesis in yellow. 765 
Underlying drivers of specific mechanisms are in parentheses. Crossed out hypotheses are 766 
unlikely. Detailed explanations for each part of this figure can be found in the text.  767 
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B 
D A 
Uptake Turnover 
Organic   Losses 
Inputs 
Nitrogen 
Fixation 
Inorganic   Losses 
Mineralization 
Biomass 
Detritus Available 
(a) (b) 
N fixation 
P
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Soil N uptake 
N use efficiency 
Turnover? 
Max growth rate? 
Competition? 
Turnover? 
Max growth rate? 
Competition? 
(c) 
N fixation 
T
ur
no
ve
r o
r  
su
sc
ep
tib
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ty
 to
 c
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pe
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n Higher Latitude 
Lower Latitude 
(e) 
N fixation 
M
ax
im
um
 g
ro
w
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at
e 
Higher Latitude 
Lower Latitude 
(d) 
N fixation 
S
oi
l N
 u
pt
ak
e 
Higher Latitude 
Lower Latitude 
Previously proposed latitudinal trends 
Previously proposed trait relationships Ecosystem model 
ecy_2034_f1.pdf
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ab
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H
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SNF cost-effective SNF not cost-effective SNF cost-effective
SNF cost-effective SNF cost-effective
N limitation index
Not N limited
N limitation index
N limitation index N limitation index
More moderately 
N limited
Not N limited
Not N limited Not N limited
N limitation index N limitation index
Not N limited Not N limited
Higher-latitude
SNF cost-effective
Obligate
SNF cost-effective
SNF not cost-effective
SNF not cost-effective
Obligate
SNF not cost-effective
Facultative
SNF not cost-effective
Facultative
SNF cost-effective
Higher-latitude
SNF not cost-effective
Lower-latitude
SNF not cost-effective
Lower-latitude
SNF cost-effective
(a) Intuitive scenario (b) N fixation is only cost-effective 
      under severe N limitation
(c) N limitation frequency hypothesis (d) N limitation severity hypothesis
(e) N fixation benefit-cost hypothesis (f) Differential regulation hypothesis
SNF not cost-effective
More severely 
N limited
More moderately 
N limited
More severely 
N limited
More moderately 
N limited
More severely 
N limited
More moderately 
N limited
More severely 
N limited
More moderately 
N limited
More severely 
N limited
More moderately 
N limited
More severely 
N limited
ecy_2034_f2.pdf
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N limitation index 
0 
More severely N limited           More moderately N limited  Not N limited 
SNF cost-effective     SNF not cost-effective 
Susceptibility to 
competition 
Latitude 
Soil N uptake rate 
Latitude 
Max growth rate 
Latitude 
N fixation 
T
ur
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N fixation 
S
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N fixation N
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se
 e
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Higher-latitude Higher-latitude 
N use efficiency 
Latitude 
SNF cost-effective    SNF not cost-effective 
 Lower-latitude Lower-latitude 
Time lags constrain 
facultative N fixation at 
higher latitudes (energy)  
Lower potential N limitation 
at higher latitudes because 
of lower N demand (energy, 
water) 
Stronger N fixation-N uptake 
tradeoff at higher latitudes 
(energy) 
Why are N-fixing trees rare at higher compared with lower latitudes? 
Hypothesis classes 
Evolutionary 
constraints 
hypothesis 
N limitation 
frequency 
hypothesis 
Specific mechanisms 
N limitation 
severity 
hypothesis 
N fixation 
benefit-cost 
hypothesis 
Differential 
regulation 
hypothesis 
Higher soil C:N ratios at 
higher latitudes favor 
obligate N fixation (energy) 
Stronger N fixation-turnover 
tradeoff at higher latitudes 
(herbivory) 
Stronger N fixation-N use 
efficiency tradeoff at higher 
latitudes 
Lower susceptibility to 
competition at higher 
latitudes (energy) 
Lower N uptake rates at 
higher latitudes (energy, 
water) 
Lower disturbance-mediated 
N loss rates at higher 
latitudes 
ecy_2034_f4.pdf
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