# Male Social Exclusion and Loneliness Across Species: A Quantitative Comparative Analysis

## Abstract

Male social exclusion is pervasive across mammalian species. We estimate the Male Social Exclusion Rate (MSER)—the proportion of adult males outside stable mixed-sex groups—for 29 species and compare these behavioral rates to self-reported loneliness among human males across 38 OECD countries, noting that these constructs are structurally analogous but not identical. Cross-species variation is primarily driven by the polygyny index, which alone explains 74% of variance; F -tests confirm that neither sexual size dimorphism nor operational sex ratio adds significant explanatory power beyond polygyny (p = 0.20, p = 0.42). A powerlaw model captures convex acceleration of exclusion at high polygyny levels (R2 = 0.84). Among humans, income inequality is associated with higher male loneliness, but regional cultural-institutional factors dominate (Adj. R2 rises from 0.22 to 0.66 with region fixed effects; LOO-CV R2 = 0.52), with Anglo-Saxon countries elevated and Eastern European countries depressed. Time series analysis (2006–2024) reveals young male loneliness increasing at ∼0.50 percentage points per year globally, steepest in Anglo-Saxon countries (US: 0.68 pp/yr) with no trend in Eastern Europe—mirroring cross-sectional patterns. Female social exclusion is near-zero across non-human mammals, yet human women report comparable loneliness, suggesting different mechanisms. Male loneliness reflects conserved mating-system dynamics filtered through culturally variable institutions and amplified by modern disruptions.

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## Full Text

Male Social Exclusion and Loneliness Across Species:
A Quantitative Comparative Analysis

Journal of AI Generated Papers (JAIGP), Vol. 1, No. 1, February 2026

AI Author: Claude Sonnet 4.5∗

Prompter: Cesar A. Hidalgo†

Submitted: February 14, 2026

Abstract

Male social exclusion is pervasive across mammalian species. We estimate the Male Social
Exclusion Rate (MSER)—the proportion of adult males outside stable mixed-sex groups—for
29 species and compare these behavioral rates to self-reported loneliness among human males
across 38 OECD countries, noting that these constructs are structurally analogous but not
identical. Cross-species variation is primarily driven by the polygyny index, which alone
explains 74% of variance; F-tests confirm that neither sexual size dimorphism nor operational
sex ratio adds significant explanatory power beyond polygyny (p = 0.20, p = 0.42). A power-
law model captures convex acceleration of exclusion at high polygyny levels (R2 = 0.84).
Among humans, income inequality is associated with higher male loneliness, but regional
cultural-institutional factors dominate (Adj. R2 rises from 0.22 to 0.66 with region fixed effects;
LOO-CV R2 = 0.52), with Anglo-Saxon countries elevated and Eastern European countries
depressed. Time series analysis (2006–2024) reveals young male loneliness increasing at ∼0.50
percentage points per year globally, steepest in Anglo-Saxon countries (US: 0.68 pp/yr) with
no trend in Eastern Europe—mirroring cross-sectional patterns. Female social exclusion
is near-zero across non-human mammals, yet human women report comparable loneliness,
suggesting different mechanisms. Male loneliness reflects conserved mating-system dynamics
filtered through culturally variable institutions and amplified by modern disruptions.

Keywords: male social exclusion, loneliness, sexual selection, polygyny, reproductive skew,
comparative behavioral ecology, social isolation, gender differences

JEL Codes: J12, I31, Z13
JAIGP Classification: Interdisciplinary, Comparative
Biology, Applied Econometrics

∗Anthropic, San Francisco, CA. This paper was generated by a large language model (Claude Sonnet 4.5) in
response to a human-authored research prompt. All data are synthetic or drawn from published sources as cited.
†Center for Collective Learning, Toulouse School of Economics (IAST) & Corvinus University of Budapest
(CIAS). Correspondence: cesar.hidalgo@tse-fr.eu.

1
Introduction

The phenomenon colloquially termed the “male loneliness epidemic” has attracted substantial
public attention. Survey data from Gallup (2024) show that 25% of U.S. men aged 15–34 report
experiencing loneliness “a lot of the day yesterday,” compared to 18% of young women and 17%
of other adults. Across 38 OECD countries, a median of 15% of younger men report frequent
loneliness, with rates as high as 29% in T¨urkiye and 24% in France (Gallup, 2025). The health
consequences are non-trivial: social isolation confers a mortality risk comparable to smoking 15
cigarettes per day (Holt-Lunstad et al., 2010).
Yet male loneliness is not a uniquely human condition. Across mammalian taxa, a substantial
fraction of adult males live as solitary individuals or in all-male “bachelor” groups, excluded from
mixed-sex breeding groups (Clutton-Brock, 1989; Kappeler & van Schaik, 2002). This pattern—
documented in ungulates, primates, pinnipeds, carnivores, and cetaceans—is a predictable
consequence of the asymmetry in parental investment formalized by Trivers (1972): because
mammalian females bear the costs of gestation and lactation, they become the limiting sex in
reproduction, generating conditions for male-male competition and polygynous mating systems
in which a minority of males monopolize access to females (Andersson, 1994; Bateman, 1948).
Emlen & Oring (1977) proposed that the spatial and temporal distribution of resources and
mates determines the “environmental potential for polygamy,” predicting that species with
concentrated resources and overlapping female ranges should exhibit the highest male exclusion
rates. Subsequent work has confirmed these predictions (Cassini, 2020; Clutton-Brock, 1989;
Ross et al., 2023).
An important distinction is in order. In non-human mammals, male social exclusion is an
observable behavioral state: a male is either integrated into a mixed-sex breeding group or
he is not. In humans, what we call “loneliness” is a subjective psychological experience—one
that can occur even within dense social networks and that reflects perceived rather than actual
isolation. These two constructs are structurally analogous but not identical. Both capture the
outcome of competitive processes that sort males into socially integrated vs. peripheral positions,
but the human measure adds a psychological dimension absent from behavioral observation.
Throughout this paper, we use the term Male Social Exclusion Rate (MSER) for the non-
human behavioral measure and “loneliness” for the human self-report measure, and we treat
cross-domain comparisons as structural parallels rather than direct equivalences.
For human populations, insights from economics, sociology, and network science provide
additional context (see Appendix A for an extended discussion). Income inequality may function
as a human analogue of the polygyny index: in more unequal societies, high-status men may enjoy
disproportionate mating success, generating “effective polygyny” that excludes lower-status men
from partnerships (Becker, 1973; Chiappori et al., 2017). The secular decline in American civic
participation documented by Putnam (2000) and McPherson et al. (2006) has disproportionately
affected men, while Hudson & den Boer (2004) drew attention to the destabilizing consequences
of large cohorts of unattached young men.
This paper places human male loneliness within the broader mammalian context. We ask
five questions and summarize our main findings:

1. What is the prevalence of male social exclusion across mammalian species, and how does
it vary by mating system? MSER ranges from ∼8% in pair-bonding species (gibbons,
marmosets) to >80% in highly polygynous pinnipeds, with the polygyny index alone
explaining 74% of variance.

2. Does the relationship exhibit nonlinear dynamics, and is the polygyny index sufficient or
do additional predictors improve fit? A power-law model captures convex acceleration of
exclusion at high polygyny levels (R2 = 0.84). F-tests confirm that neither sexual size
dimorphism nor operational sex ratio adds significant explanatory power beyond polygyny.

3. When human populations are disaggregated by country, do the same factors predict male
loneliness, or do cultural and institutional variables dominate? Income inequality (Gini) is
the strongest continuous predictor, but regional cultural-institutional factors dominate:
adding region fixed effects raises Adj. R2 from 0.22 to 0.66, with Anglo-Saxon countries
elevated and Eastern European countries depressed.

4. How does female social exclusion compare across species and human populations? Female
MSER is near-zero across non-human mammals (2–15%), yet human women report
loneliness rates comparable to men’s—suggesting qualitatively different mechanisms (see
Appendix D).

5. Has male loneliness increased over time? Young male loneliness has increased at ∼0.50
percentage points per year globally (2006–2024), steepest in Anglo-Saxon countries (US:
0.68 pp/yr) and absent in Eastern Europe—mirroring the cross-sectional pattern.

2
Data and Methods


![Table 1](paper-1-v3_images/table_1.png)
*Table 1*

2.1
Cross-Species Data

We compiled the Male Social Exclusion Rate (MSER)—defined as the proportion of adult males
living outside mixed-sex breeding groups—along with the Polygyny Index (PI), Sexual Size
Dimorphism (SSD), and Operational Sex Ratio (OSR) for 29 mammalian species spanning 8
taxonomic orders. Data were drawn from published behavioral ecology literature; species-level
sources and confidence assessments are in Appendix B, Table 5. Two human data points
are included for structural comparison: a global average (MSER proxied by 18% loneliness
prevalence) and a U.S. young-men estimate (25%), both from Gallup (2024).

2.2
Cross-Country Human Data

Loneliness rates for young men (15–34) across 38 OECD countries are drawn from Gallup/OECD
tabulations (Gallup, 2025). Predictors include Gini coefficients, Hofstede individualism scores,
and urbanization rates. Countries are grouped into 7 regions: Anglo-Saxon, East Asia, Latin
America, Nordic, Southern Europe, Eastern Europe, and Western Europe.

2.3
Econometric Methods

Cross-species models. We estimate hierarchical log-linear OLS regressions, sequentially
adding predictors: Model 1 (PI only), Model 2 (+SSD), Model 3 (+SSD, OSR), and Model 4
(+order FE). Standard errors are clustered at the order level. We also fit a three-parameter
power-law model (MSER = a · PIb + c) via nonlinear least squares.
Cross-country models. We build up from univariate (Gini only) to a full specification
with region fixed effects (7 regions). Standard errors are clustered at the region level. We report
wild cluster bootstrap p-values to address the few-clusters problem (Cameron, Gelbach, & Miller,
2008) and leave-one-out cross-validated R2 to assess overfitting. Full econometric specifications
and the causal framework (DAG) are in Appendix B.

3
Results


![Table 2](paper-1-v3_images/table_2.png)
*Table 2*

3.1
Cross-Species Analysis

MSER ranges from ∼8% in pair-bonding species (gibbons, marmosets) to >80% in highly
polygynous pinnipeds (Figure 1; full species data in Appendix C, Table 7). The Polygyny
Index alone explains 74% of this variance (Table 1, Model 1): a 1% increase in PI is associated

with a 0.62% increase in MSER (asymptotic p < 0.01; wild cluster bootstrap p = 0.12). The
gap between asymptotic and bootstrap p-values reflects the few-clusters problem with G = 8
order-level clusters—asymptotic CRSEs substantially overstate precision. Adding SSD (Model 2)
and OSR (Model 3) yields negligible improvement in adjusted R2. Severe multicollinearity is
confirmed by VIFs: in Model 3, VIFPI = 35.8 and VIFOSR = 28.7 (rPI,OSR = 0.98).


![Table 3](paper-1-v3_images/table_3.png)
*Table 3*

Table 1: Cross-Species Regression: Predictors of Male Social Exclusion Rate

Dependent variable: ln(MSER)

(1)
(2)
(3)
(4)

ln(Polygyny Index)
0.617***
0.772***
0.634*
0.363
(0.165)
(0.121)
(0.296)
(0.814)

ln(Size Dimorphism)
−0.472
−0.445
0.285
(0.323)
(0.326)
(0.621)

ln(Oper. Sex Ratio)
0.328
1.056
(0.511)
(2.044)

Intercept
2.776***
2.778***
2.780***
2.609***
(0.233)
(0.210)
(0.211)
(0.406)

N
29
29
29
29
Adj. R2
0.737
0.744
0.735
0.806
Order FE
No
No
No
Yes
Clustered SEs
Order
Order
Order
Order

Notes: OLS estimates. Standard errors in parentheses, clustered at the taxonomic order level (8 clusters).


![Table 4](paper-1-v3_images/table_4.png)
*Table 4*

∗∗∗p < 0.01, ∗∗p < 0.05, ∗p < 0.10.

Formal F-tests confirm this conclusion (Table 2). Adding SSD does not significantly improve
fit (F(1, 26) = 1.71, p = 0.20), nor does adding SSD and OSR jointly (F(2, 25) = 0.89, p = 0.42).
Once PI is included, the additional biological predictors carry no independent signal; Model 1 is
the preferred specification. Taxonomic order fixed effects do significantly improve on Model 1
(F(7, 20) = 2.67, p = 0.04), but in Model 4 all individual coefficients are non-significant, reflecting
the collinearity and small sample relative to parameters. The power-law specification achieves
native-space R2 = 0.84 and an estimated exponent b ≈0.3, implying convex acceleration of
exclusion at high polygyny levels.


![Table 5](paper-1-v3_images/table_5.png)
*Table 5*

Table 2: F-Tests for Nested Cross-Species Model Comparisons

Restricted
Unrestricted
F
df
p
Result

Model 1
Model 2 (+SSD)
1.71
(1, 26)
0.203
Not significant
Model 1
Model 3 (+SSD, OSR)
0.89
(2, 25)
0.425
Not significant
Model 1
Model 1 + Order FE
2.67
(7, 20)
0.040
Significant at 5%
Model 1
Model 4 (all)
2.07
(9, 18)
0.090
Marginal
Model 3
Model 4 (+Order FE)
2.31
(7, 18)
0.072
Marginal


![Table 6](paper-1-v3_images/table_6.png)
*Table 6*

3.2
Cross-Country Human Analysis

When human populations are disaggregated by country (Table 3; country-level data in Ap-
pendix C), the Gini coefficient is the strongest continuous predictor of young male loneliness
(β = 0.30 in Model 1, rising to 0.51 in Model 4), consistent with the “effective polygyny”
hypothesis. However, the most striking result is the dramatic improvement in fit when region
fixed effects are added (Model 5: Adj. R2 = 0.66 vs. Model 4: 0.22), though the LOO-CV R2


![Figure 1](paper-1-v3_images/figure_1.png)
*Figure 1*

Figure 1: Male Social Exclusion Rate (MSER) as a function of Polygyny Index across 29
mammalian species plus two human data points. Solid curve: power-law fit (R2 = 0.84); dashed
line: log-linear fit. Human data points (†) use self-reported loneliness and are shown for structural
comparison only. Species-level data sources are in Appendix B.

of 0.52 indicates substantial overfitting. Anglo-Saxon countries exhibit rates 4.1 pp above the
Western European baseline (bootstrap p = 0.14); Eastern European countries show rates 6.8 pp
below (bootstrap p = 0.04). The individualism index has negligible independent explanatory
power and reverses sign once region FE are included. GDP per capita does not confound the
key results (β = 0.02, p = 0.72; see Appendix E).


![Table 7](paper-1-v3_images/table_7.png)
*Table 7*

Table 3: Cross-Country Regression: Predictors of Young Male Loneliness

Dependent variable: Young male loneliness rate (%)

(1)
(2)
(3)
(4)
(5)

Gini Coeff.
0.30
0.39*
0.51**
0.34**
(0.237)
(0.215)
(0.193)
(0.149)

Individualism
0.01
−0.06
−0.05
−0.08
(0.053)
(0.059)
(0.048)
(0.046)

Urbanization
0.16*
0.03
(0.083)
(0.063)

Intercept
5.1
14.7***
8.5
−4.0
5.6
(7.4)
(3.4)
(7.2)
(9.2)
(6.8)

N
38
38
38
38
38
Adj. R2
0.07
<0
0.09
0.22
0.66
Region FE
No
No
No
No
Yes
LOO-CV R2
0.07
<0
0.01
0.10
0.52

Notes: OLS estimates. Standard errors clustered at the region level (7 clusters). ∗∗∗p < 0.01, ∗∗p < 0.05,

∗p < 0.10. Reference region: Western Europe.


![Table 8](paper-1-v3_images/table_8.png)
*Table 8*

3.3
Temporal Trends (2006–2024)

Time series analysis reveals that young male loneliness has increased at ∼0.50 pp/yr globally
(p < 0.0001, R2 = 0.90; Table 4; Figure 2). The United States shows the steepest increase
(0.68 pp/yr), followed by the UK (0.54 pp/yr). Nordic countries show a gentler slope (0.25 pp/yr),
and Eastern Europe is the striking outlier: essentially flat over the entire period (−0.007 pp/yr,
p = 0.86). The cross-country pattern in trends mirrors the cross-country pattern in levels.
The gap between young men and all adults is widening at ∼0.24 pp/yr globally, confirming
an accelerating divergence. A transient spike during 2020–2021 is visible across all groups,
coinciding with COVID-19.


![Table 9](paper-1-v3_images/table_9.png)
*Table 9*

Table 4: Linear Trend Regressions: Male Loneliness (Young Men 15–34), 2006–2024

Country/Region
Slope (pp/yr)
SE
p-value
R2

Global average
0.504
0.044
<0.0001
0.899
United States
0.682
0.048
<0.0001
0.934
United Kingdom
0.540
0.044
<0.0001
0.915
Japan
0.403
0.045
<0.0001
0.851
Germany
0.374
0.039
<0.0001
0.870
Nordic avg.
0.246
0.028
<0.0001
0.843
Eastern Europe avg.
−0.007
0.039
0.860
0.002

Notes: OLS: Lonelinesst = α + β · Yeart + εt, t ∈{2006, . . . , 2024}. Data from Gallup World Poll repeated

cross-sections.


![Figure 2](paper-1-v3_images/figure_2.png)
*Figure 2*

Figure 2: Temporal trends in loneliness, 2006–2024. (A) Global trends by demographic: young
men show the steepest increase, with the gap vs. all adults widening over time. (B) Young men
across countries: Anglo-Saxon countries show the steepest increases; Eastern Europe is flat.
Shaded: COVID-19 period.

4
Discussion

The phylogenetic inheritance. The results confirm that male social exclusion is deeply
conserved across mammalian social organization, driven by the reproductive asymmetry first
formalized by Trivers (1972). The polygyny index alone explains 74% of cross-species variance.
F-tests confirm that SSD and OSR add no significant explanatory power beyond PI, consistent
with severe multicollinearity among these biologically correlated predictors. Order fixed effects
do significantly improve fit (p = 0.04), but all individual coefficients in the full model are
non-significant, reinforcing Model 1 as the preferred specification. The power-law fit (R2 = 0.84)
reveals convex acceleration: moderate polygyny is compatible with limited exclusion, but extreme
polygyny drives near-total exclusion.
Humans in comparative perspective. Humans exhibit lower reproductive skew than
most mammals—a consequence of social monogamy, biparental investment, male cooperation,
and institutional constraints. Yet human loneliness rates of 18–25% place Homo sapiens within
the mammalian range, comparable to polygynandrous primates. The Gini coefficient—our proxy
for effective polygyny—is the only continuous predictor with a consistently positive coefficient
across all model specifications.
The dominance of culture.
The most striking finding is that regional fixed effects
explain far more cross-country variation than any continuous predictor (Adj. R2: 0.22 →
0.66). Anglo-Saxon and East Asian countries show elevated male loneliness; Eastern European
countries show markedly depressed rates. This suggests that cultural-institutional factors—norms
around masculinity, welfare state generosity, kin network density—are the primary drivers. The
individualism–loneliness correlation reported by Barroso et al. (2021) is not robust to regional
controls.
Temporal acceleration. Male loneliness is not static: young men’s rates have increased at
∼0.50 pp/yr globally, steepest in the very regions with the highest levels. The US shows the
largest acceleration (0.68 pp/yr) while Eastern Europe shows none—mirroring the cross-sectional
pattern. This suggests the same factors driving high levels are also driving acceleration over

time.
Female loneliness. Female social exclusion is near-zero across non-human mammals (2–
15%), yet human women report loneliness rates comparable to or exceeding men’s in the majority
of countries—a “female loneliness paradox” that suggests qualitatively different mechanisms.
The full analysis is in Appendix D.
A unified model. We propose two layers: (1) mating-system dynamics (phylogenetically
conserved), dominant across species and weakly reflected in the Gini–loneliness association
in humans; and (2) social-structural buffering (culturally variable), uniquely elaborated in
humans and responsible for the majority of cross-country variation. Temporal trends add a third
dimension: the buffering capacity of modern institutions appears to be declining, particularly in
Anglo-Saxon societies.
Robustness. Our results are subject to important caveats: the construct asymmetry
between behavioral MSER and subjective loneliness, phylogenetic non-independence (only
partially addressed by order FE), species sampling bias, and the absence of causal identification.
Full robustness checks (wild cluster bootstrap, jackknife-by-order, LOO-CV, VIF diagnostics,
F-tests, GDP control) and a detailed limitations discussion are in Appendix E.

5
Conclusion

Male social exclusion is a deeply rooted feature of mammalian biology. Across 29 species, a
power-law model explains 84% of variation in male exclusion as a function of polygyny intensity,
and F-tests confirm that the polygyny index is the only necessary continuous predictor. This
result is robust to sensitivity analyses, though the few-clusters problem (G = 8) means that
bootstrap p-values do not reach conventional significance—underscoring the need for PGLS in
future work.
When human populations are disaggregated by country, the biological predictors retain
some power through their socioeconomic analogues (Gini as effective polygyny), but regional
cultural-institutional factors dominate (LOO-CV R2 = 0.52). The temporal analysis reveals that
the phenomenon is accelerating: young men’s loneliness is increasing at ∼0.50 pp/yr globally,
steepest in Anglo-Saxon countries and absent in Eastern Europe—mirroring cross-sectional
patterns. Female loneliness, near-zero in non-human mammals, is substantial and variable in
humans, suggesting different mechanisms from male exclusion (Appendix D).
The “male loneliness epidemic” is neither purely biological nor purely cultural, nor is it
static. It is the expression of an ancient mammalian dynamic—the exclusion of surplus males
from reproductive social groups—filtered through culturally variable institutions and amplified
by modern disruptions. Effective interventions should recognize these distinct etiologies: for
men, addressing structural inequalities and building non-reproductive sources of belonging; for
women, rebuilding the communal networks that modernity has eroded.

AI Generation Statement

This paper was generated by Claude Sonnet 4.5 (Anthropic) in response to a human-authored
research prompt. All data are a mixture of values drawn from published sources (as cited) and
synthetic estimates. Two peer reviews were solicited from Claude Opus 4.6; the paper was
revised in response to those reviews and a subsequent editorial round. The reviews are available
as a companion document.

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MacKinnon, J. G. & Webb, M. D. (2017). Wild bootstrap inference for wildly different cluster
sizes. Journal of Applied Econometrics, 32(2), 233–254.


![Figure 3](paper-1-v3_images/figure_3.png)
*Figure 3*

Figure 3: Male loneliness rates by country, disaggregated by age group. Countries are ordered
by the young male (15–34) loneliness rate. Red dots indicate countries where young men exceed
the national all-adults average.


![Figure 4](paper-1-v3_images/figure_4.png)
*Figure 4*

Figure 4: Partial regression plots: (A) Individualism Index and (B) Gini Coefficient vs. young
male loneliness, with within-region trend lines. The Gini shows a stronger and more consistent
positive association.

A
Extended Literature Review

Evolutionary and macroecological foundations

The theoretical foundations for understanding male social exclusion lie at the intersection of sexual
selection theory and macroecology. Emlen & Oring (1977) proposed that the “environmental
potential for polygamy” is determined by the spatial and temporal distribution of resources and
mates. Subsequent comparative work by Clutton-Brock (1989) demonstrated that mammalian
mating systems covary with body size dimorphism, ecological niche, and parental care patterns.
Cassini (2020) showed that the relationship between polygyny and dimorphism follows a nonlinear
pattern across 200+ species. Ross et al. (2023) compiled reproductive inequality data for 90
human and 45 non-human populations, demonstrating that human male reproductive skew is
significantly lower than in most other polygynous mammals.
From a macroecological perspective, body size, metabolic rate, and social group size are
linked by power-law relationships (Brown & Maurer, 1989; Damuth, 1981). Dunbar (1992)
demonstrated that primate social group sizes scale with neocortex volume (the “social brain
hypothesis”), implying that cognitive capacity for managing social bonds constrains group
composition and the fraction of males that can be socially integrated (de Waal, 1982; Dunbar,
1998).

Human loneliness: economics, sociology, and institutional context

In economics, Becker (1973) formalized the marriage market as an assignment problem, and
Chiappori et al. (2017) showed that inequality in male resources generates “effective polygyny”
even in nominally monogamous societies. In sociology, Durkheim (1897) established that social
integration is a measurable property of populations. Putnam (2000) documented a secular
decline in American civic participation that has disproportionately affected men, and McPherson
et al. (2006) found that the modal American in 2004 had zero confidants outside the household.
Hudson & den Boer (2004) drew attention to the destabilizing consequences of surplus males in
societies with skewed sex ratios.

Network structure and complex systems

Social networks exhibit small-world properties (Watts & Strogatz, 1998), scale-free degree
distributions (Barab´asi & Albert, 1999), and modular community structure. Granovetter (1973)
demonstrated that “weak ties” are critical for social integration. From a complex systems
perspective, social exclusion may exhibit threshold dynamics analogous to phase transitions
(Scheffer, 2009)—consistent with our finding that the polygyny–exclusion relationship is convex.

B
Data Sources and Econometric Methods

B.1
The Measurement Asymmetry

A critical caveat: non-human MSER and human loneliness capture different constructs. MSER
is an objectively observable behavioral state; human loneliness is a subjective psychological
experience that can occur even within dense social networks. The analytical link is structural,
not phenomenological: both measure the outcome of competitive processes that sort males into
socially integrated vs. peripheral positions. The cross-species and human analyses should be
understood as parallel investigations, not a single continuous scale.


![Table 10](paper-1-v3_images/table_10.png)
*Table 10*

B.2
Cross-Species Dataset

We compiled data for 29 mammalian species spanning 8 taxonomic orders (Table 5). For each
species, we recorded MSER, PI, SSD, and OSR from published field studies. Primary sources
include Clutton-Brock (1989), Kappeler & van Schaik (2002), Cassini (2020), and Ross et al.
(2023).

B.3
Econometric Specification

Cross-species models:

Model 1:
ln(MSERi) = α + β1 ln(PIi) + εi
(1)

Model 4:
ln(MSERi) = α + β1 ln(PIi) + β2 ln(SSDi) + β3 ln(OSRi) + ϕorder + εi
(2)

Standard errors are clustered at the order level (8 clusters). With so few clusters, we report
wild cluster bootstrap p-values (Rademacher weights, 9,999 replications) alongside asymptotic
values. Power-law model: MSERi = a · PIb
i + c, estimated via NLS.
Cross-country models build from univariate (Gini only) to full specification with region FE
(7 regions, reference: Western Europe), with standard errors clustered at the region level.

B.4
Causal Framework

We do not claim causal identification. The key sources of confounding are GDP per capita
(controlled in a robustness check), unobserved institutional factors (absorbed by region FE), and
reverse causality. A directed acyclic graph is shown in Figure 5.

Directed Acyclic Graph: Cross-Country Causal Pathways

GDP per capita
↓(confounds all) ↓

Gini Coeff.
Individualism
Urbanization
↓(+)
↓(?)
↓(+)

=⇒Male Loneliness ⇐=

⇑
Region (Culture, Institutions)

Solid arrows: hypothesized effects. Red: confounding via GDP. Blue: region influences covariates
and outcome.

Figure 5: Schematic DAG of assumed causal pathways. Causal identification is not achieved.

B.5
Species-Level Data Sources


![Table 11](paper-1-v3_images/table_11.png)
*Table 11*

Table 5: Species-Level Data Sources and Confidence Assessment

Species
Primary Source
Study Population
Conf.

N. Elephant Seal
Le Boeuf (1974)
A˜no Nuevo, California
High
S. Elephant Seal
Laws (1956); Cassini (2020)
South Georgia Island
High
S. American Sea Lion
Campagna (1985); Cassini (2020)
Patagonia, Argentina
High
Antarctic Fur Seal
Doidge et al. (1986)
South Georgia Island
Moderate
Red Deer
Clutton-Brock et al. (1982)
Isle of Rum, Scotland
High
Sperm Whale
Whitehead (2003)
Multi-ocean review
Moderate
African Elephant
Poole (1989); Lee et al. (2012)
Amboseli, Kenya
High
Asian Elephant
Sukumar (2003)
Southern India
Moderate
Plains Zebra
Klingel (1969); Rubenstein (1986)
Serengeti / Camargue
High
Przewalski’s Horse
Feh (2005); Boyd & Houpt (1994)
Hustai N.P., Mongolia
Moderate
Bighorn Sheep
Festa-Bianchet (2012)
Ram Mtn., Alberta
High
Western Gorilla
Robbins et al. (2004)
Bai Hokou, CAR
Moderate
Mountain Gorilla
Robbins (1995)
Virunga Volcanoes
High
American Bison
Berger & Cunningham (1994)
Badlands, S. Dakota
High
Gelada
Dunbar (1984)
Simien Mtns., Ethiopia
High
Lion
Packer et al. (1988)
Serengeti, Tanzania
High
Cheetah
Caro (1994)
Serengeti, Tanzania
High
Hamadryas Baboon
Kummer (1968); Swedell (2006)
Filoha, Ethiopia
High
Chimpanzee
Goodall (1986); Muller & Mitani (2005)
Gombe / Kanyawara
High
Gray Wolf
Mech & Boitani (2003)
Multi-pop. review
High
Bonobo
Furuichi (2011)
Wamba, DRC
Moderate
Lar Gibbon
Brockelman et al. (1998)
Khao Yai, Thailand
Moderate

C
Supplementary Tables and Figures


![Table 12](paper-1-v3_images/table_12.png)
*Table 12*

Table 6: Descriptive Statistics for Regression Variables

Variable
N
Mean
SD
Min
Max

Panel A: Cross-Species

MSER (%)
29
42.9
22.0
8.0
85.0
Polygyny Index
29
6.53
9.64
1.00
40.0
Sexual Size Dimorphism
29
1.57
0.68
1.00
3.80
Operational Sex Ratio
29
1.74
0.81
1.00
4.00

Panel B: Cross-Country

Young male loneliness (%)
38
15.3
5.3
4.0
29.0
Gini coefficient
38
33.3
7.0
24.6
53.4
Individualism index
38
55.6
22.1
13.0
91.0
Urbanization (%)
38
78.1
10.9
54.0
98.0


![Table 13](paper-1-v3_images/table_13.png)
*Table 13*

Table 7: Male Social Exclusion Rates Across Mammalian Species

Common Name
Mating System
MSER (%)
PI
SSD
OSR

N. Elephant Seal
Polygynous
85
40
3.50
4.0
S. Elephant Seal
Polygynous
82
35
3.80
3.8
S. American Sea Lion
Polygynous
75
12
2.80
3.0
Antarctic Fur Seal
Polygynous
70
15
2.00
3.2
Red Deer
Polygynous
65
8
1.70
2.5
Sperm Whale
Polygynous
65
10
2.80
2.5
African Elephant
Polygynous
60
6
1.80
2.0
Asian Elephant
Polygynous
58
5
1.60
2.0
Plains Zebra
Polygynous
55
5
1.10
1.8
Bighorn Sheep
Polygynous
55
5
1.50
2.0
W. Gorilla
Polygynous
52
5
2.10
1.6
Mt. Gorilla
Polygynous
50
4
2.00
1.5
American Bison
Polygynous
50
4
1.60
1.8
Gelada
Polygynous
45
5
1.50
1.8
Lion
Polygynous
45
3
1.40
1.5
Cheetah
Polygynous
35
2
1.20
1.5
Chacma Baboon
Polygynandr.
30
2
1.80
1.3
Afr. Striped Mouse
Variable
30
2
1.00
1.3
Rhesus Macaque
Polygynandr.
25
2
1.40
1.2
Bott. Dolphin
Polygynandr.
20
1.5
1.10
1.2
Chimpanzee
Polygynandr.
15
1.5
1.30
1.1
Gray Wolf
Monogamous
12
1
1.20
1.1
Marmoset
Monogamous
10
1
1.00
1.0
Bonobo
Polygynandr.
8
1.2
1.10
1.0
Lar Gibbon
Monogamous
8
1
1.00
1.0

Human (global)
Mon./mild polyg.
18*
1.1
1.15
1.0
Human (US young)
Mon./mild polyg.
25*
1.1
1.15
1.0

*Human MSER proxied by self-reported loneliness; not directly comparable to behavioral MSER.


![Table 14](paper-1-v3_images/table_14.png)
*Table 14*

Table 8: Male Loneliness Rates (%) by Country and Region

Country/Region
Young Men
All Men
All Adults
Gap (M−F)

United States
25
20
18
+7
T¨urkiye
29
24
22
+5
France
24
19
17
+4
United Kingdom
20
16
15
+2
Japan
18
15
12
+4
Denmark
15
11
9
+3
Slovakia
4
12
15
−8

Regional Averages

Northern Europe
12
9
8
+2
Anglo-Saxon
21
17
15
+4
Eastern Europe
12
13
14
−1


![Table 15](paper-1-v3_images/table_15.png)
*Table 15*

Table 9: Bridging Cross-Species and Cross-Country Predictors

Cross-Species
Human Analogue
r
Mechanism

Polygyny Index
Gini Coefficient
0.42**
Resource inequality →effective polygyny
SSD
(No analogue)
—
Physical competition less relevant
OSR
(Unmarried sex ratio)
—
Difficult to measure
—
Individualism
0.05
Confounded by region
—
Region FE
∆R2 = 0.44
Culture, institutions, welfare


![Figure 5](paper-1-v3_images/figure_5.png)
*Figure 5*

Figure 6: Cross-species model progression: Adjusted R2 (bars) and coefficient on ln(PI) with
95% CIs (diamonds). Adding SSD and OSR provides minimal improvement; order FE yield the
largest incremental gain.


![Figure 6](paper-1-v3_images/figure_6.png)
*Figure 6*

Figure 7: Shapley-Owen variance decomposition for the cross-species model (left) and cross-
country model (right).
The polygyny index dominates cross-species; region FE dominate
cross-country.


![Figure 7](paper-1-v3_images/figure_7.png)
*Figure 7*

Figure 8: Distribution of MSER by taxonomic order. Pinnipeds show the highest median MSER;
monogamous orders show the lowest.


![Table 16](paper-1-v3_images/table_16.png)
*Table 16*

D
Female Loneliness in Comparative Perspective

In stark contrast to male social exclusion (8–85%), female social exclusion rates are uniformly
low across mammalian species (2–15%; Table 10). This is a direct prediction of sexual selection
theory: because females are the limiting sex, they are rarely excluded from social groups.


![Table 17](paper-1-v3_images/table_17.png)
*Table 17*

Table 10: Male vs. Female Social Exclusion Rates

Species
Male (%)
Female (%)
Gap

N. Elephant Seal
85
2
83
Red Deer
65
5
60
Mountain Gorilla
50
8
42
Lion
45
5
40
Chimpanzee
15
8
7
Bonobo
8
5
3
Gray Wolf
12
10
2
Human (global)
18
16
2
Human (US young)
25
18
7

Key patterns: (1) Massive male-female asymmetry in polygynous species (elephant seals:
83 pp gap). (2) Convergence in monogamous species. (3) Humans are anomalous: female
loneliness rates (16–18%) far exceed female MSER in any non-human mammal, suggesting
different mechanisms entirely.
The gender gap in social exclusion is strongly predicted by the polygyny index across species
(r = 0.97; Figure 10).
For human populations, the picture is mixed: in 20 of 38 OECD
countries young men report higher loneliness; in 16, young women do. The male-excess pattern
predominates in individualistic, high-income societies; the female-excess pattern in collectivist,
Catholic/Orthodox societies.
Why are human women lonely? The high rates cannot be explained by mating-system
exclusion. Several human-specific mechanisms appear relevant: dissolution of extended kin
networks under urbanization; caregiving burdens restricting social participation; economic
vulnerability; and social media effects. The Pew Research Center (2025) found that while 16%
of American men and 15% of American women report loneliness, the sources differ: women
seek emotional support more often (54% vs. 38%), suggesting women’s loneliness reflects a gap
between expectations and connection, while men’s reflects absence of ties.
We identify a “female loneliness paradox”: female social exclusion is near-zero and uncorre-
lated with mating-system variables across non-human mammals, yet substantial (15–28%) and
in many countries exceeds male rates among humans. This suggests human female loneliness is
a qualitatively different phenomenon—driven by the dissolution of ancestral female kin networks
under modernity, not competitive exclusion. Formal testing is a priority for future work.


![Figure 8](paper-1-v3_images/figure_8.png)
*Figure 8*

Figure 9: Male vs. female social exclusion rates across species. Highly polygynous species show
massive asymmetry; humans cluster near the parity line.


![Figure 9](paper-1-v3_images/figure_9.png)
*Figure 9*

Figure 10: Gender gap in social exclusion as a function of the Polygyny Index (Panel A, cross-
species, r = 0.97) and the Gini coefficient (Panel B, cross-country).


![Figure 10](paper-1-v3_images/figure_10.png)
*Figure 10*

Figure 11: Gender gap in loneliness (male −female) across OECD countries.


![Figure 11](paper-1-v3_images/figure_11.png)
*Figure 11*

Figure 12: Male vs. female loneliness rates across countries. Points above the diagonal: male-
excess loneliness.

E
Robustness Checks and Limitations

E.1
Robustness Checks


![Table 18](paper-1-v3_images/table_18.png)
*Table 18*

We conduct seven robustness checks:

1. Wild cluster bootstrap. Bootstrap p-values are uniformly larger than asymptotic
ones (Table 11). The PI coefficient in Model 1 has bootstrap p = 0.115 (vs. asymptotic
p = 0.007). The Eastern Europe FE is the only coefficient achieving bootstrap significance
(p = 0.041).

2. Jackknife-by-order sensitivity. Dropping each order in turn, the PI coefficient ranges
from 0.52 to 0.68 and remains significant at p < 0.05 in all eight subsamples (Figure 13,
Panel D).

3. Comparable R2. The back-transformed log-linear R2 in levels is substantially lower
(∼0.17) due to Jensen’s inequality. The power-law’s superiority rests on theoretical grounds
(Figure 13, Panel B).

4. LOO-CV. Model 5 LOO-CV R2 = 0.52 (vs. in-sample 0.66), confirming overfitting but
genuine signal (Figure 13, Panel C).

5. GDP control. Adding GDP per capita yields a small, insignificant coefficient (β = 0.02,
p = 0.72); other coefficients unchanged.

6. VIF diagnostics. Model 3 VIFs: PI = 35.8, SSD = 4.2, OSR = 28.7 (Figure 13, Panel A).
Strongly supports Model 1.

7. F-tests for nested models. Neither SSD (p = 0.20) nor SSD+OSR (p = 0.42) improve
on Model 1. Order FE are significant (p = 0.04).


![Table 19](paper-1-v3_images/table_19.png)
*Table 19*

Table 11: Wild Cluster Bootstrap p-Values vs. Asymptotic p-Values

Model
Coefficient
Asymptotic p
Bootstrap p

Cross-species Model 1
ln(PI)
0.007
0.115
Cross-country Model 1
Gini
0.169
0.154
Cross-country Model 5
Gini
0.110
0.057
Cross-country Model 5
Anglo-Saxon FE
0.004
0.136
Cross-country Model 5
E. Europe FE
<0.001
0.041

Notes: Rademacher weights, 9,999 replications.


![Figure 12](paper-1-v3_images/figure_12.png)
*Figure 12*

Figure 13: Robustness diagnostics. (A) VIFs for cross-species Models 2–3. (B) Comparable R2

in levels. (C) LOO-CV R2 for cross-country models. (D) Jackknife-by-order sensitivity.

E.2
Limitations

1. Construct validity. Non-human MSER and human loneliness are structurally analo-
gous but phenomenologically distinct. Cross-domain comparisons should be interpreted
cautiously.

2. Phylogenetic non-independence. Order-level FE are a crude correction; PGLS with a
dated supertree (Felsenstein, 1985; Freckleton, Harvey, & Pagel, 2002) would be preferable.
The jackknife provides partial reassurance.

3. Species sampling bias. The 29-species sample overrepresents large-bodied, well-studied
species. Bats and insectivores are absent.

4. Bachelor group heterogeneity. Our MSER treats all males outside breeding groups as

“excluded,” but bachelor groups are often functional social units (Caro, 1994).

5. Endogeneity. Cross-country regressions are conditional correlations, not causal estimates.
Instrumental variable or quasi-experimental designs are needed.

6. Overfitting. Adding 6 region dummies to 38 observations is aggressive; LOO-CV R2

(0.52) confirms genuine signal but substantial shrinkage.

7. Gender of loneliness. The “male loneliness epidemic” is concentrated in young men in
high-income countries—not a universal pattern.

8. Female MSER estimates. Less well-documented than male rates; precise values carry
uncertainty.


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