How large should academic departments be?

Aaron Clauset; Daniel B. Larremore; Fariba Karimi; Gerardo I\~niguez; Jan Bachmann; Lisette Esp\'in-Noboa

REVIEW 4 major objections 4 minor 40 references

How large should academic departments be?

T0 review · 4 major / 4 minor · reviewed 2026-08-01 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Academic departments across eight fields share one stable size range, 4 to 23 faculty, with smaller departments either growing fast or closing and larger ones shrinking only slightly.

desk verdict A careful, valuable empirical study of department size dynamics whose central organizational-ecology interpretation is undercut by an untested regression-to-the-mean null. read the letter →

arxiv 2607.22189 v1 pith:SUWRPH6O submitted 2026-07-24 physics.soc-ph physics.data-an

Jan Bachmann , Lisette Espín-Noboa , Fariba Karimi , Daniel B. Larremore , Gerardo Iñiguez , Aaron Clauset This is my paper · ORCID

classification physics.soc-phphysics.data-an

keywords departmentsizeorganizationalecologyGibrat'slawcoagulation-fragmentationBecker-Döringmodeluniversitydepartmentsfacultydynamicsdistribution

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that the size of an academic department is not an accident of history or random growth, but the product of size-dependent organizational pressures that pull departments toward a common stable range of about 4 to 23 tenured or tenure-track faculty. Using annual sizes of over 14,000 U.S. departments in eight domains, it shows that the smallest departments face roughly 8% annual closure risk or, if they survive, grow about 30% in a year, while departments in the stable range neither grow nor shrink much and large departments persist with mild attrition. These patterns conflict with Gibrat's law of proportionate growth, which predicts no size dependence. A simple coagulation-fragmentation model, whose rate ratios are derived only from the fitted static size distributions, reproduces the direction of the observed dynamics, supporting an organizational-ecology account of department sizes.

What carries the argument

The Becker-Döring coagulation-fragmentation model, in which departments gain or lose single faculty members at size-dependent rates a_s and b_s. Assuming the fitted size distribution is the model's equilibrium, the ratio a_s/b_{s+1} equals the ratio of consecutive fitted probabilities q_{s+1}/q_s. This ratio, rescaled by the fitted mode, reproduces the empirical pattern: net coagulation below the stable range, net fragmentation within it, and near-balance above it. The shifted log-logistic/shifted log-normal fits and the geometric central range R* are the supporting objects that locate the stable range.

What would settle it

Compile annual closure and growth rates by exact department size (not binned ranges) from an independent longitudinal dataset and test whether the ratio a_s/b_{s+1} from a freshly fitted static distribution predicts the observed direction of change at each size. If the predicted crossover size (the mode) does not align with the empirical tipping point where growth turns to attrition, or if small-department growth disappears once conditioning on survival is varied, the stable-range claim would be undermined. A sharper test: simulate a null model of independent per-faculty attrition plus size-in

Watch

Extended reading notes

Core claim

The central claim is that department sizes are regulated by size-dependent processes of growth and closure: there is a stable size range R* = [4, 23), roughly one geometric standard deviation around the median, where closure risk is low and growth is balanced. Below it, departments are in a grow-or-close regime; above it, large departments are weakly pulled downward but rarely close. This pattern appears in all eight domains, with the stable range widening at the upper boundary in domains with expensive infrastructure. The paper uses fits of shifted log-logistic and shifted log-normal distributions to locate the stable range, then shows that annual size-dependent closure risks and growth rat

Load-bearing premise

The load-bearing assumption is that the measured size-dependence of growth and closure reflects genuine organizational selection, not a statistical artifact of mean reversion or boundary effects; if departments merely fluctuate around fixed sizes, small departments would appear to grow or close even under size-independent dynamics.

Editorial extensions

If this is right

If the stable range is real, then mergers, splits, and closures are not random management events but the tail of a continuous size-regulation process, and the visible extremes are examples of the same forces.
University administrators can expect the highest churn among departments with fewer than about four faculty; such units are not merely small but systematically unstable.
The common rescaled dynamics imply that domain differences are reducible to a scale parameter (the mode) plus the strength of small-size coagulation; policy that shifts the mode would shift the whole distribution.
Large departments, above roughly 23 faculty, do not face a strong ceiling: the paper finds only marginal net attrition and minimal closure risk, so unlimited growth is weakly discouraged rather than prevented.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

A natural extension would track departments' internal faculty turnover rates separately from mergers and renames to test whether the stable range arises from regulation or from selection on which departments survive.
The model identifies only the ratio of coagulation to fragmentation, not the absolute rates; comparing against long-run faculty mobility data would let one estimate both rates and check whether large-department stability stems from low turnover (structural inertia) or from balanced hiring and attrition.
A stationary-fluctuation alternative—departments fluctuating around fixed sizes with mean reversion—is not explicitly tested; the grow-or-close pattern could partly reflect regression toward a stable size rather than organization-level ecology, and a direct test would strengthen the claim.
One could test the model out of sample: predict the size-dependent closure and growth curves from the static distribution of a new domain (or a later decade) and compare with observed dynamics, without refitting the dynamic parameters.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

This paper gives us something genuinely new: a large, 13-year census of 14,000 U.S. academic departments, with careful measurement of size distributions, closure risk, and growth rates across eight domains. The descriptive work is strong—the distribution fitting is rigorous, the standard errors are there, and the code and aggregate data are public. The finding that small departments close or grow quickly, mid-sized ones stagnate, and large ones persist under mild attrition is real and worth knowing.

The problem is the interpretation. The paper claims this pattern supports organizational ecology over Gibrat's law. But it never tests the most obvious alternative: that each department has a stable target size and merely fluctuates around it. Under that null, a department observed at small size is likely a downward fluctuation, so it will regress upward on average—producing exactly the elevated growth rates they see. It will also be closer to the zero boundary, mechanically raising closure risk. The same logic applies in reverse for large departments. Their test of Gibrat's law and the independent-attrition null (Fig. S2) doesn't cover this stationary-fluctuation null, and the paper even defines the "stable range" from the fitted static distribution before using it to bin the dynamics. That makes the match between the static and dynamic ranges partly in-sample.

The Becker–Döring model doesn't rescue the interpretation. Equation 8 derives the rate ratio as/bs+1 directly from the same fitted distribution, so its agreement with empirical growth is a consistency check, not an independent test. The paper itself concedes it compares only direction, not magnitude. That's honest, but it means the model cannot decide between organizational ecology and the regression-to-mean null.

None of this undercuts the descriptive measurements. The dataset and the reported patterns will be useful to anyone studying departmental structure, and the paper is one of the few to take organizational ecology of academia seriously with longitudinal data. But the central conclusion—that departments are pulled toward a common stable range by size-dependent pressures—is not yet established. To claim that, they need to simulate a null model where each department has a fixed latent size with multiplicative noise and show that it cannot reproduce the observed growth/closure patterns. If it can, the "liability of smallness" interpretation collapses. If it can't, the paper becomes much stronger. That's a doable experiment, and the authors have the data and skills to run it.

This paper deserves a serious referee—I would send it out—but the referee should insist on that null test before publication. Applied Sciences also fails the distribution fit, which is minor but should be addressed.

Overall: solid empirical contribution, premature theoretical conclusion. With the null test, it could be an important paper; without it, it's a descriptive report.

Referee Report

4 major / 4 minor

Summary. The paper analyzes annual sizes of 14,418 U.S. academic departments across eight domains, fitting shifted log-logistic or log-normal distributions to the cross-sectional size distribution and defining a 'central range' R* of roughly 4–23 faculty. Using year-to-year transitions, it reports that closure risk declines with size and that growth rates exceed one below R*, are balanced inside R*, and fall below one above R*, concluding that department sizes are governed by size-dependent organizational ecology rather than Gibrat's proportionate growth. A Becker–Döring coagulation–fragmentation model, parameterized from the fitted static distribution, is presented as reproducing the direction of these dynamics. The paper emphasizes commonality across domains and a 'grow-or-close' pattern for small departments.

Significance. If the central claim is correct, the paper provides a large-scale empirical case for size-dependent selection in organizations and identifies a stable size range for academic departments, with direct policy implications for departmental restructuring. The empirical work is careful: the data are extensive, the distribution-fitting procedure includes synthetic refits to assess plausibility, and the paper reports standard errors and provides code and data. The analysis also goes beyond static fits by measuring annual transitions and testing against Gibrat's law and an independent-attrition null. However, the paper's central interpretation rests on ruling out an alternative, untested stationary-fluctuation (regression-to-the-mean) null, and the Becker–Döring 'reproduction' is only an in-sample consistency check in direction, not magnitude. These issues are load-bearing for the paper's main conclusion.

major comments (4)

[Size-dependent closure and growth, Figs. 2 and S2] The central interpretation rejects Gibrat's law and independent per-faculty attrition, but it never tests the natural null in which each department fluctuates around a latent stable size μ_i. Under such a stationary-fluctuation model, a department observed at small s is likely to be a downward fluctuation and will regress upward on average, producing g_s>1 at small sizes; being near zero also increases the chance of hitting the absorbing boundary, producing elevated c_s. This generates the exact Fig. 2 pattern—growth and closure below R*, stagnation inside, mild attrition above—without any size-dependent organizational force. The independent-attrition null of Fig. S2 does not include mean reversion, and the implied per-faculty risk growing with s is also consistent with regression to the mean. I would require a simulation or hierarchical-model test of this stationary-fluctuation null bef
[A coagulation–fragmentation model, Eq. (8), Materials and methods] The Becker–Döring rate ratio is set equal to q_{s+1}/q_s (Eq. 8), which is the detailed-balance condition of the fitted static distribution. Its agreement with the empirical growth rates is therefore guaranteed by construction up to direction, as the paper itself acknowledges in the Materials and methods ('comparisons are limited to the direction of net change, not its magnitude'). Moreover, the mode s* used for normalization and the central range R* used for binning are both obtained from the same fitted q_s, so the claimed coincidence of the geometric and dynamic stable ranges is an in-sample comparison. Claiming the model 'reproduces department dynamics across the full size range' overstates what is shown. An out-of-sample test (e.g., fit on one time period and predict transitions in another) or a magnitude comparison would be needed.
[Table 1 and Figure S1] For Applied Sciences, the optimized SLL/SLN fit is not a plausible draw from the data (Table 1 footnote; Figure S1 gives p≈0.03 for both SLN and SLL). The paper still includes Applied Sciences in the pooled R* and in the cross-domain dynamic comparisons. The claim of a common size distribution and common stable range across all eight domains is therefore not supported for at least one domain. The cross-domain claims should be restricted to the seven domains whose fits pass the goodness-of-fit test, or the failure for Applied Sciences should be explained and analyzed separately.
[Size-dependent closure and growth; Discussion limitations] Closure risk is measured as any transition from s>0 to s=0, which includes renames, mergers, and splits. The Discussion acknowledges this may inflate closure risk, but the size gradient of c_s is central to the grow-or-close claim. If small departments are more likely to be renamed or merged (e.g., as part of restructuring), the measured pattern could arise without a true size-dependent closure process. I would like to see a sensitivity analysis using alternative event definitions, or at least a quantitative assessment of how many size-zero transitions are renames/restructurings versus genuine closures, before the closure-risk result is used as evidence for organizational ecology.

minor comments (4)

[Figure 1c] The whiskers are said to indicate 90%-quantiles, but this is not defined in the text or figure legend. Please clarify what quantity the whiskers represent (e.g., 5th–95th percentiles of the fitted or empirical distribution).
[Table S6] The caption says 'with uncertainty estimates in parentheses,' but the rendered table shows no parentheses or uncertainty values. Please correct the table or the caption.
[Eq. (8) and surrounding text] The step 'setting n_s = q_s/q_1' is not fully explained. As written it appears to fix both the scale and the normalization of the rate ratio; a brief justification would help readers understand how the mode s* enters and why the shape of a_s/b_{s+1} is independent of the absolute normalization.
[Abstract] The abstract says '14,000 U.S.-based departments' but the analyses use 14,418. Consider using the exact number or an explicit approximation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the dynamic measurements are independent of the static distribution fit, and the Becker-Döring comparison is an acknowledged direction-only consistency check.

full rationale

The paper's central dynamical quantities are not fitted inputs. Closure risk c_s = Pr(s_{t+1}=0 | s_t=s) and growth rate g_s = s_{t+1}/(G_t s_t) are computed directly from annual department-size transitions (Materials and methods), while the SLL/SLN parameters (mode s*, central range R*) are fitted to the static median-size distribution. The 'stable range' conclusion is an empirical association between two independently measured objects, not a consequence of the fit. The Becker-Döring rate ratio in Eq. 8 is an analytic consequence of assuming the fitted q_s is the equilibrium: a_s/b_{s+1}=q_{s+1}/q_s. The paper uses it only as a direction-of-change comparison with the measured dynamics and explicitly warns that 'comparisons between the rate ratio and the empirical growth rates are therefore limited to the direction of net change at each size, not its magnitude.' Thus the BD agreement is a weak consistency check, not a fitted parameter disguised as a prediction. The possible regression-to-mean/stationary-fluctuation alternative is a substantive robustness concern, but it does not make the derivation circular: the paper's equations do not reduce to that null, and the dynamic measurements are not defined in terms of the fit. Self-citations (refs 18, 19, 33, 35) supply data categorization, hierarchy context, and fitting methodology; none is a load-bearing uniqueness claim or an answer smuggled in by citation. Overall, the derivation chain is self-contained and the central inference has independent empirical grounding.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central quantitative claims rest on three-parameter distribution fits and on the assumption that the fitted static distribution equals the BD equilibrium. The most important unstated premise is that observed year-to-year changes are not dominated by regression to the mean or boundary effects. No new entities are postulated.

free parameters (3)

SLL/SLN fit parameters (s0, alpha, beta; or mu, sigma) per domain = Table S6
Three parameters per domain fitted to the empirical size distribution; define mode s* and central range R* used throughout.
Central range width (one geometric standard deviation around fitted median) = R* = [s-, s+) with s- ~4, s+ ~23 overall
A modeling choice that sets the boundaries for the small/central/large bins; not a fitted parameter in the dynamic analysis but derived from the static fit.
Normalization a_s = b_{s+1} at mode s* = unit ratio at s*
Sets absolute scale of BD rates; does not affect shape or direction, but is a chosen convention.

assumptions (4)

domain assumption The observed department size distribution is stationary and representative of the equilibrium of the BD process.
Used to convert fitted q_s into rate ratio via detailed balance (Eq. 8). If the system is not stationary, the inferred ratio is not a valid description of dynamics; the paper lists stationarity as a limitation.
domain assumption Department size changes occur only by single-faculty gains/losses; closures/mergers/splits are represented by size-zero transitions.
Becker-Döring model and closure measurement rely on this simplification; the paper acknowledges that closures, mergers, splits, and renames are conflated.
ad hoc to paper Observed annual size s_t is the true organizational size, not a noisy transient; measured size-dependence is not a regression-to-the-mean artifact.
The central interpretation requires this. No stationary-fluctuation null is tested.
domain assumption Domain categorization from ref [19] is valid for these data.
Eight domains are based on a prior categorization by the same research group; errors here propagate to all domain-level claims.

how reviews work

0 comments

Cite this review

Pith. "Pith review of How large should academic departments be?." pith.science (2026). https://pith.science/paper/SUWRPH6O

@misc{pith2026260722189,
  author       = {Pith},
  title        = {Pith review of: How large should academic departments be?},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/SUWRPH6O}},
  note         = {Machine review of arXiv:2607.22189}
}

abstract

Academic departments are the primary unit of scholarship and education at universities, and they vary vastly in their sizes. However, the consequences and natural dynamics of department size are poorly understood. Small departments face disproportionate teaching and administrative overhead per faculty member, while large ones face coordination costs and thematic incoherence. Here, we characterize and model the dynamics of academic department sizes using $14,000$ U.S.-based departments in eight academic domains. Across all domains, similar broad-tailed distributions reveal a common size range from 4 to 23 faculty members, widening across domains at its upper border. Annual size-dependent closure risks and growth rates indicate that stability is greatest in this size range: below it, small departments either close or grow quickly; within it, closure risk is low and sizes stabilize; above it, large departments can persist, with marginal attrition and minimal closure risk. An analytically tractable model of size-dependent coagulation and fragmentation, informed only by the aggregated size distribution, reproduces department dynamics across the full size range. Rescaling each domain by its most stable size reveals a common regression toward the stable range across most domains. Our results establish academic departments as organizations with natural size dynamics defined by a grow-or-close pattern for the smallest departments, and a weak pressure against unlimited growth for the largest.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

40 extracted references

[1]

WVU Board Approves Dramatic Academic Cuts to Address $45M Deficit.Higher Ed Dive.https://www.highereddive.com/news/wvu- board- approves-academic-cuts-45m-deficit/693857/(Sept

Spitalniak, L. WVU Board Approves Dramatic Academic Cuts to Address $45M Deficit.Higher Ed Dive.https://www.highereddive.com/news/wvu- board- approves-academic-cuts-45m-deficit/693857/(Sept. 15, 2023)

2023
[2]

Quinn, R. West Virginia’s Unprecedented Proposed Cuts Become Clear.Inside Higher Ed.https://www.insidehighered.com/news/faculty/tenure/2023/ 08/11/west-virginia-universitys-unprecedented-proposed-cuts-become- clear(Aug. 11, 2023)

2023
[3]

WVU Tech.Academic Transformation Academic Program Portfolio Reviewhttps: //transformation.wvutech.edu/review(2026)

2026
[4]

Merger of UTSA’s Demography and Sociology Programs to In- crease Access to Research Opportunities.UT San Antonio News.https://hcap

Amanda Cerreto. Merger of UTSA’s Demography and Sociology Programs to In- crease Access to Research Opportunities.UT San Antonio News.https://hcap. utsa.edu/news/2023/08/soc-dem-merge.html(Aug. 28, 2023). 16

2023
[5]

Melanie Lefkowitz. New Data Science, Computational Biology Departments Span Colleges.Cornell CALS News.https://cals.cornell.edu/news/2018/10/new- data-science-computational-biology-departments-span-colleges(Oct. 11, 2018)

2018
[6]

Gumport, P. J. & Sporn, B. inHigher Education: Handbook of Theory and Research (eds Smart, J. C. & Tierney, W. G.) 103–145 (Springer Netherlands, Dordrecht, 1999).isbn: 978-94-011-3955-7

1999
[7]

Perkins, J. A. Organization and Functions of the University.The Journal of Higher Education43,679–691.issn: 0022-1546 (1972)

1972
[8]

The Academic Department: How Does It Fit Into The University Reform Agenda?Change: The Magazine of Higher Learning31,16–27.issn: 0009- 1383 (Sept

Edwards, R. The Academic Department: How Does It Fit Into The University Reform Agenda?Change: The Magazine of Higher Learning31,16–27.issn: 0009- 1383 (Sept. 1, 1999)

1999

Show all 40 references

[9]

Walvoord, B. E.et al. Academic Departments: How They Work, How They Change 164 pp.isbn: 978-0-7879-5714-8 (Wiley, 2000)

2000
[10]

& Nielsen, M

Aagaard, K., Kladakis, A. & Nielsen, M. W. Concentration or Dispersal of Research Funding?Quantitative Science Studies1,117–149.issn: 2641-3337 (Feb. 1, 2020)

2020
[11]

A., Maurer, J

Hur, H., Andalib, M. A., Maurer, J. A., Hawley, J. D. & Ghaffarzadegan, N. Recent Trends in the U.S. Behavioral and Social Sciences Research (BSSR) Workforce. PLOS ONE12,e0170887.issn: 1932-6203 (Feb. 6, 2017)

1932
[12]

A., Thompson, H

Smith, B., Arbeit, C. A., Thompson, H. & Yamaner, M. I.Graduate Enrollment and Postdoctoral Appointments in Science, Engineering, and Health Rise, Driven Largely by Increases in the Number of Women and Temporary Visa HoldersNSF 25-316 (National Science Foundation, Jan. 21, 202...

2025
[13]

Gowder, C.Trends in Graduate Students and Postdocs by Field of StudyUseful Stats.https://ssti.org/blog/useful- stats- trends- graduate- students- and-postdocs-field-study(2026)

2026
[14]

26, 2019)

Burke, A.Science and Engineering Indicators 2020: Science and Engineering Labor Force.NSB-2019-8 (National Science Board, National Science Foundation, Sept. 26, 2019)

2020
[15]

Josefy, M., Kuban, S., Ireland, R. D. & Hitt, M. A. All Things Great and Small: Or- ganizational Size, Boundaries of the Firm, and a Changing Environment.Academy of Management Annals9,715–802.issn: 1941-6520 (Jan. 2015)

1941
[16]

& Wagner, K

Leitner, K.-H., Prikoszovits, J., Schaffhauser-Linzatti, M., Stowasser, R. & Wagner, K. The Impact of Size and Specialisation on Universities’ Department Performance: A DEA Analysis Applied to Austrian Universities.Higher Education53,517–538. issn: 1573-174X (Apr. 1, 2007)

2007
[17]

Gibrat, R. P. L. Les Inégalités Économiques (1931)

1931
[18]

& Larremore, D

Clauset, A., Arbesman, S. & Larremore, D. B. Systematic Inequality and Hierarchy in Faculty Hiring Networks.Science Advances1,e1400005 (Feb. 12, 2015). 17

2015
[19]

H., Zhang, S., Clauset, A

Wapman, K. H., Zhang, S., Clauset, A. & Larremore, D. B. Quantifying Hierarchy and Dynamics in US Faculty Hiring and Retention.Nature610,120–127.issn: 1476-4687 (7930 Oct. 2022)

2022
[20]

FitzGerald, C., Huang, Y., Leisman, K. P. & Topaz, C. M. Temporal Dynamics of Faculty Hiring in Mathematics.Humanities and Social Sciences Communications 10,247.issn: 2662-9992 (May 17, 2023)

2023
[21]

Zipf’s Law and the Growth of Cities.American Economic Review89, 129–132.issn: 0002-8282 (May 1999)

Gabaix, X. Zipf’s Law and the Growth of Cities.American Economic Review89, 129–132.issn: 0002-8282 (May 1999)

1999
[22]

Luttmer, E. G. J. Selection, Growth, and the Size Distribution of Firms.The Quar- terly Journal of Economics122,1103–1144.issn: 0033-5533 (Aug. 1, 2007)

2007
[23]

Hannan, M. T. & Freeman, J. Structural Inertia and Organizational Change.Amer- ican Sociological Review49,149–164.issn: 0003-1224 (1984)

1984
[24]

Brinkman, P. T. & Leslie, L. L. Economies of Scale in Higher Education: Sixty Years of Research.The Review of Higher Education10,1–28.issn: 1090-7009. https://muse.jhu.edu/pub/1/article/645243(1986)

1986
[25]

& Groot, W

Tirivayi, N., Maasen van den Brink, H. & Groot, W. N. J.Size and Economies of Scale in Higher Education and the Implications for Mergerspre-published
[26]

Baker, D. D. & Cullen, J. B. Administrative Reorganization and Configurational Context: The Contingent Effects of Age, Size, and Change in Size.The Academy of Management Journal36,1251–1277.issn: 0001-4273 (1993)

1993
[27]

N., West, E

Barron, D. N., West, E. & Hannan, M. T. A Time to Grow and a Time to Die: Growth and Mortality of Credit Unions in New York City, 1914-1990.American Journal of Sociology100,381–421 (Sept. 1994)

1914
[28]

& Auster, E

Aldrich, H. & Auster, E. Even Dwarfs Started Small: Liabilities of Age and Size and Their Strategic Implications.Research in Organizational Behavior8,165–198 (Jan. 1986)

1986
[29]

Blau, P. M. A Formal Theory of Differentiation in Organizations.American Soci- ological Review35,201–218.issn: 0003-1224 (1970)

1970
[30]

& Döring, W

Becker, R. & Döring, W. Kinetische Behandlung Der Keimbildung in Übersättigten Dämpfen.Annalen der Physik416,719–752.issn: 1521-3889 (1935)

1935
[31]

Coagulation-Fragmentation Processes222,1–20.issn: 0167-2789 (Oct

Wattis,J.A.D.AnIntroductiontoMathematicalModelsofCoagulation–Fragmentation Processes: A Discrete Deterministic Mean-Field Approach.Physica D: Nonlin- ear Phenomena. Coagulation-Fragmentation Processes222,1–20.issn: 0167-2789 (Oct. 1, 2006)

2006
[32]

& Hochberg, Y

Benjamini, Y. & Hochberg, Y. Controlling the False Discovery Rate: A Practical andPowerfulApproachtoMultipleTesting.Journal of the Royal Statistical Society. Series B (Methodological)57,289–300.issn: 0035-9246.https://www.jstor.org/ stable/2346101(1995). 18

1995
[33]

& Erwin, D

Clauset, A. & Erwin, D. H. The Evolution and Distribution of Species Body Size. Science321,399–401 (July 18, 2008)

2008
[34]

& Kotz, S.Statistical Size Distributions in Economics and Actuarial Sciences354 pp.isbn: 978-0-471-45716-9 (John Wiley & Sons, Oct

Kleiber, C. & Kotz, S.Statistical Size Distributions in Economics and Actuarial Sciences354 pp.isbn: 978-0-471-45716-9 (John Wiley & Sons, Oct. 10, 2003)

2003
[35]

Clauset, A., Shalizi, C. R. & Newman, M. E. J. Power-Law Distributions in Em- pirical Data.SIAM Review51,661–703.issn: 0036-1445 (Nov. 4, 2009)

2009
[36]

& Singh, S

Diyali, B., Kumar, D. & Singh, S. Discriminating between Log-Normal and Log- Logistic Distributions in the Presence of Type-II Censoring.Computational Statis- tics39,1459–1483.issn: 1613-9658 (May 1, 2024)

2024
[37]

A Brief History of Generative Models for Power Law and Log- normal Distributions.Internet Mathematics1,226–251.issn: 1542-7951 (Jan

Mitzenmacher, M. A Brief History of Generative Models for Power Law and Log- normal Distributions.Internet Mathematics1,226–251.issn: 1542-7951 (Jan. 1, 2004)

2004
[38]

H., Teukolsky, S

Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. Numerical Recipes in C: The Art of Scientific Computing, Second Edition.issn: 0-521-43108- 5 (1992)

1992
[39]

& Price, K

Storn, R. & Price, K. Differential Evolution – A Simple and Efficient Heuristic for Global Optimization over Continuous Spaces.Journal of Global Optimization11, 341–359.issn: 1573-2916 (Dec. 1, 1997)

1997
[40]

Department of Education.College Scorecard DataOffice of Planning, Evalu- ation and Policy Development

U.S. Department of Education.College Scorecard DataOffice of Planning, Evalu- ation and Policy Development. June 2026.https://collegescorecard.ed.gov/ data/. 19 Supplementary Information for How large should academic departments be? 20 Data processing The Academic Analytics Re...

2026

Pith tools

Reviewed August 1, 2026 · model on record in the stance chip above.

[1] [1]

WVU Board Approves Dramatic Academic Cuts to Address $45M Deficit.Higher Ed Dive.https://www.highereddive.com/news/wvu- board- approves-academic-cuts-45m-deficit/693857/(Sept

Spitalniak, L. WVU Board Approves Dramatic Academic Cuts to Address $45M Deficit.Higher Ed Dive.https://www.highereddive.com/news/wvu- board- approves-academic-cuts-45m-deficit/693857/(Sept. 15, 2023)

2023

[2] [2]

Quinn, R. West Virginia’s Unprecedented Proposed Cuts Become Clear.Inside Higher Ed.https://www.insidehighered.com/news/faculty/tenure/2023/ 08/11/west-virginia-universitys-unprecedented-proposed-cuts-become- clear(Aug. 11, 2023)

2023

[3] [3]

WVU Tech.Academic Transformation Academic Program Portfolio Reviewhttps: //transformation.wvutech.edu/review(2026)

2026

[4] [4]

Merger of UTSA’s Demography and Sociology Programs to In- crease Access to Research Opportunities.UT San Antonio News.https://hcap

Amanda Cerreto. Merger of UTSA’s Demography and Sociology Programs to In- crease Access to Research Opportunities.UT San Antonio News.https://hcap. utsa.edu/news/2023/08/soc-dem-merge.html(Aug. 28, 2023). 16

2023

[5] [5]

Melanie Lefkowitz. New Data Science, Computational Biology Departments Span Colleges.Cornell CALS News.https://cals.cornell.edu/news/2018/10/new- data-science-computational-biology-departments-span-colleges(Oct. 11, 2018)

2018

[6] [6]

Gumport, P. J. & Sporn, B. inHigher Education: Handbook of Theory and Research (eds Smart, J. C. & Tierney, W. G.) 103–145 (Springer Netherlands, Dordrecht, 1999).isbn: 978-94-011-3955-7

1999

[7] [7]

Perkins, J. A. Organization and Functions of the University.The Journal of Higher Education43,679–691.issn: 0022-1546 (1972)

1972

[8] [8]

The Academic Department: How Does It Fit Into The University Reform Agenda?Change: The Magazine of Higher Learning31,16–27.issn: 0009- 1383 (Sept

Edwards, R. The Academic Department: How Does It Fit Into The University Reform Agenda?Change: The Magazine of Higher Learning31,16–27.issn: 0009- 1383 (Sept. 1, 1999)

1999