Pith. sign in

REVIEW 2 major objections 3 minor 73 references

Optimum Contribution Selection for Honeybees

T0 review · 2 major / 3 minor · reviewed 2026-08-16 · deepseek-v4-flash

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

Pith's one-line read This paper claims that honeybee breeding decisions can be reduced to an exact optimum-contribution problem: maximize a linear expected-breeding-value expression under a quadratic kinship cap, with explicit formulas for all three…

desk verdict Original honeybee OCS theory with sound algebra buried in 121 pages; the main open risk is the worker-group/replacement-queen identity, not the recurrences. read the letter →

arxiv 2504.12895 v1 pith:W5F4WGM4 submitted 2025-04-17 q-bio.PE

Manuel Du , Richard Bernstein , Andreas Hoppe This is my paper · ORCID
classification q-bio.PE MSC 92D1092D15
keywords honeybeebreedingoptimumcontributionselectionkinshipinbreedingcontrolvaluehaplodiploidgeneticsmatingstationsinstrumentalinsemination
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

The paper aims to carry the classical optimum-contribution selection (OCS) method for diploid livestock over to honeybee breeding, a species whose genetics are haplo-diploid, whose workers are sterile, and whose traits are measured on colonies. It claims that for single-colony instrumental insemination, isolated mating stations, or a mixture of both, the expected breeding value of the next reduced generation is a linear function of per-queen contribution vectors, and the next generation's average kinship is a known quadratic function of the same vectors. Defining honeybee OCS as maximizing that expected breeding value while keeping average kinship at or below a prescribed limit, together with the natural sum-to-one constraints, yields a task that existing quadratic-program solvers can handle. If these formulas are correct, breeders can compute exactly how many daughters, insemination sires, and mating-station uses each queen should contribute, instead of relying on classical selection heuristics.

What carries the argument

The load-bearing construction is the reduced generation $P^*_t=Q_t\sqcup R_t$, in which each colony is represented by its queen and an imaginary replacement queen, while worker groups are kept in the background as kinship proxies. Two identities carry the argument: the estimated breeding value of a worker group equals the expected estimated breeding value of a replacement daughter (Lemma 3.5), and kinship between two new queens equals kinship between the worker groups of their dams (Corollary 3.1). These identities let every future kinship be expressed through the current kinship blocks $K^{QQ}_t$, $K^{WW}_t$, $K^{QR}_t$, and $K^{RR}_t$, with explicit correction terms that account for the one place worker groups and replacement queens differ, namely self-kinship.

What would settle it

Solve Task 4.3 for one generation of a real or realistically simulated population, then compare the observed average kinship and average breeding value of the next reduced generation with the values predicted by Theorem 4.6; systematic underestimation of realized kinship, or a clear discrepancy that tracks the worker-group versus replacement-queen distinction, would refute the central recurrences. A sharper direct check is to regress replacement-queen BLUP values on worker-group BLUP values: Lemma 3.5 predicts the identity relation, so a slope or intercept significantly different from that prediction would break the argument.

Watch

Extended reading notes

Core claim

On its own terms, the central claim is that honeybee OCS is a well-posed optimization problem with explicit, proof-backed recurrence formulas. Modeling generation $P_t$ as queens $Q_t$, worker groups $W_t$, and replacement queens $R_t$, the paper proves that the expected breeding value of the next reduced generation $P^*_{t+1}=Q_{t+1}\sqcup R_{t+1}$ is a linear expression in the dam-path vector $\mathbf{dc}_t$, the 1b-path vector $\mathbf{bc}_t$, and the 4a-path vector $\mathbf{ac}_t$, while the average kinship $k_{P^*_{t+1},P^*_{t+1}}$ is a fixed quadratic form in those vectors plus linear correction terms (Theorem 4.6). Maximizing the first expression subject to the second being at most a chosen kinship ceiling, with $\mathbf{1}^\top\mathbf{dc}_t=1$ and $\mathbf{1}^\top(\mathbf{bc}_t+\mathbf{ac}_t)=1$, is therefore the honeybee OCS task (Task 4.3). The paper shows that using only insemination or only mating stations are special cases of this combined task, and it implements the solver in a small R script that outputs per-queen quotas.

Load-bearing premise

The whole derivation rests on the identity that a worker group's estimated breeding value equals the expected estimated breeding value of a replacement daughter queen, together with the companion identity that kinship between new queens equals kinship between the worker groups of their dams; if real BLUP estimates or pedigree kinship values violate these identities, the predicted breeding values and kinship recurrences are systematically biased.

Editorial extensions

If this is right

  • Breeders can compute per-queen usage quotas for the dam, 1b, and 4a paths in a single optimization step, rather than choosing dams and sires by ad hoc rules.
  • Because the kinship restriction is quadratic and the objective linear, the honeybee task becomes a standard convex quadratic program that existing solvers handle directly.
  • The mixed-mating task contains pure insemination and pure mating-station tasks as special cases, so one implementation covers all three breeding setups.
  • The larger numerical example indicates that OCS can deliver higher expected genetic gain than conventional across- and within-family selection at the same or smaller increase in average kinship.

Reading between the lines

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

  • The same derivation pattern should transfer to other haplo-diploid social insects with colony-level phenotypes, because the formal ingredients—worker groups, drone groups, and drone-producing-queen groups—are not honeybee-specific.
  • The self-kinship correction terms are most consequential in small populations; a direct simulation benchmark could quantify how much kinship prediction degrades if they are dropped, as earlier diploid treatments sometimes did.
  • The theory assumes survival status is known at selection time; a stochastic-survival extension with age classes is the natural next step and would make the recurrence applicable where winter losses are uncertain.
  • An empirical check of Lemma 3.5 on real BLUP data—comparing worker-group and replacement-queen estimates colony by colony—would show whether the identity that feeds the whole recurrence holds in practice.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 3 minor

Summary. This manuscript develops a theory of Optimum Contribution Selection (OCS) for honeybee breeding. It first reviews OCS for diploid monoecious and diecious populations with discrete and overlapping generations, then transfers the theory to honeybees by modeling colonies as triples of a queen, a worker group, and a replacement queen. The core of the paper derives closed-form recurrences for the expected breeding value and the average kinship of the next reduced generation under three mating-control scenarios: single colony insemination, isolated mating stations, and a mixed strategy. These recurrences lead to constrained quadratic optimization tasks whose objective is the expected breeding value and whose main constraint limits the average kinship of the next generation. The paper also provides an R script that solves these tasks using the optiSolve package, and demonstrates it on a small pen-and-paper example and on a larger simulation-derived example comparing OCS with classical selection strategies.

Significance. If the recurrences are accepted, the paper provides the first exact OCS formulation for honeybees and thus fills a genuine gap in the breeding literature. The derivations are unusually careful: the kinship recurrences are built from explicit allele-drawing arguments, self-kinship corrections are handled in Lemma 4.3(viii) rather than ignored, and the mixed-strategy formula (4.71) correctly reduces to the single-path limits (4.34) and (4.57) when ac_t or bc_t vanishes. The work contains no fitted parameters, and the larger example provides concrete, falsifiable quantitative predictions about expected genetic gain and kinship increase. A further strength is the didactic review of diploid OCS with overlapping generations, including the correct finite-population correction in Lemma 2.2, which is often omitted. The accompanying R script and input files support reproducibility, although one input file inconsistency currently undermines that goal.

major comments (2)
  1. [Section 3.2.1, Lemma 3.5] The statement E[\hat u_R] = \hat u_W is not a logical consequence of the unbiasedness property of BLUP; unbiasedness alone gives E[\hat u_R] = E[u_R] = E[u_W] = E[\hat u_W], i.e., equality of unconditional expectations, not an identity between the random variable \hat u_W and the conditional expectation of \hat u_R. What the subsequent recurrences require is the stronger conditional identity E[\hat u_R | data] = \hat u_W (or, equivalently, that the BLUP of a replacement daughter queen equals the BLUP of the worker group). This identity is load-bearing: it enters Lemma 4.2 (Eqs. 4.13 and 4.15) and therefore Theorems 4.1, 4.3, and 4.5, and it underlies Corollary 3.1 and hence the kinship recurrences in Theorem 4.6. The manuscript should replace the one-sentence 'unbiasedness' argument with a derivation from the explicit BLUP animal model of Bienefeld et al. (2007) or Brascamp and Bijma (2014), or alternatively state the vector identity in Remark 4.2(i) explicitly as an assumption about the estimated breeding values. As written, the argument is a gap in an otherwise careful derivation.
  2. [Section 6.1, curr_gen.tsv] The printed input file curr_gen.tsv marks Queen_B as surviving (TRUE) while the surrounding text states that only Queen_A survives to the next generation and queens B and C die. The reported outputs in Example 6.1 correspond to the text, not to the printed file. Because the small example is explicitly presented as reproducible with pen and paper and the input files are part of the contribution, this inconsistency must be resolved by correcting the file (or the text) so that the printed inputs match the described scenario and the reported outputs.
minor comments (3)
  1. [Section 5.2.3] The description of stats.tsv says '31 tab-separated two-elemented columns'; this wording is unclear and should be rephrased, probably to '31 tab-separated columns' or '31 columns, each containing a name and a value'.
  2. [Section 5.1, Remark 5.1(iv)] The remark states that the matrix \tilde K is only positive semi-definite and justifies this by exhibiting a positive semi-definite submatrix. That only proves a lower bound on the inertia; the full matrix must be shown positive semi-definite (or the solver must be shown to handle nonconvex quadratic constraints) to guarantee that the optimization problem is convex and that a global optimum is found.
  3. [Section 3.2.3] The passage introducing the 'imaginary replacement queen' could be clarified: the replacement queen R is not a real individual but a device for encoding the expected breeding value and inbreeding of a future daughter; this helps justify why R has no survival or reproduction path of its own.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the honeybee OCS recurrences are derived algebraically from stated infinitesimal-model assumptions, with no fitted parameters or self-citation chain substituting for proof.

full rationale

The central derivation chain (Section 4, especially Theorems 4.1–4.6 and Tasks 4.1–4.3) is an algebraic construction: expected breeding values and kinships of the next reduced generation are expressed as functions of the current estimated breeding values, kinship blocks, survival vector, eligibility vectors, and the contribution vectors dc_t, bc_t, and ac_t. No parameter is fitted to the quantities the paper reports; the small example supplies all kinship matrices and estimated breeding values as explicit inputs, and the sister kinship of 0.2 is stated as an assumed input, not a fitted output. The larger example explicitly says that the selection strategies were "not explicitly carried out in simulations" and that the values were "merely calculated according to the formulas" (Remark 6.2(ii)), so the comparison is a model computation, not an empirical validation and not a circular fit. The potentially load-bearing Lemma 3.5 / Remark 4.2(i) identity E[\hat u_R] = \hat u_W is a BLUP-model assumption, supported by citations to Bienefeld et al. (2007) and Brascamp and Bijma (2014); it is an input to the derivation rather than a product of it. If that assumption fails, the recurrences would be biased, but that is a correctness or validation concern, not circularity. The self-citations (Du et al. 2021a,b; Bernstein et al. 2018) provide background, simulation motivation, or pedigree-software inputs, but the main theorems are proven in-text from the infinitesimal model and the kinship probability calculus. No circular reduction, renamed fit, or self-citation chain is load-bearing for the claimed OCS results.

Assumptions & free parameters 0 free parameters · 6 assumptions · 1 invented entities

The theory is anchored in standard quantitative genetics assumptions and has no fitted parameters. The only ad hoc modeling choice is the reduced-generation objective weighting (Definition 4.1 and Remark 4.19), which is explicitly discussed rather than hidden.

assumptions (6)
  • domain assumption Additive infinitesimal model with unbiased BLUP breeding values.
    Assumed in Notation 2.2 and Section 3.2.1; all breeding value predictions rely on the expectation of offspring breeding values being the average of parental breeding values.
  • domain assumption Worker group breeding value equals expected breeding value of a daughter queen.
    Lemma 3.5 and Remark 3.5, used to justify that a dam passes the replacement queen's breeding value to new queens (Lemma 4.2).
  • domain assumption Kinship between two non-ancestral sister queens equals kinship between worker groups of their dams.
    Corollary 3.1, used throughout Section 4 to express new-queen kinships in terms of worker-group kinships.
  • domain assumption Mating control assumptions: single colony insemination uses drones from one queen; isolated mating station DPQs are sisters sharing one dam; each queen serves as 4a-queen of at most one station per season; stations are disjoint.
    Stated in Section 4.2, Section 4.3, and Remark 4.13; these structure the contribution paths and the kinship formulas.
  • ad hoc to paper Reduced generation P* with equal weighting of queens and replacement queens in the objective.
    Definition 4.1 and Remark 4.19. The choice is explicitly discussed and the authors note that for mating-station-only schemes one might instead maximize E[u_R].
  • standard math Kinship matrix K_t is symmetric positive definite.
    Remark 2.10(ii), invoked when formulating the quadratic constraint; ensures the kinship quadratics are convex.
invented entities (1)
  • Replacement queen R for each colony
    purpose: Models the expected breeding value of a future daughter queen and provides the correct self-kinship k_{R,R}; each colony is treated as queen plus worker group plus replacement queen in the reduced generation formalism (Section 3.2.3).
    It is a bookkeeping device, not a physical entity. All non-self kinships involving R are set equal to those of the worker group; only the self-kinship differs. It carries no testable prediction outside the model.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Optimum Contribution Selection for Honeybees." pith.science (2026). https://pith.science/paper/W5F4WGM4

@misc{pith2026250412895,
  author       = {Pith},
  title        = {Pith review of: Optimum Contribution Selection for Honeybees},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/W5F4WGM4}},
  note         = {Machine review of arXiv:2504.12895}
}
read the original abstract

In 1997, T. H. E. Meuwissen published a groundbreaking article titled 'Maximizing the response of selection with a predefined rate of inbreeding', in which he provided an optimized solution for the trade-off between genetic response and inbreeding avoidance in animal breeding. Evidently, this issue is highly relevant for the honeybee with its small breeding population sizes. However, the genetic peculiarities of bees have thus far prevented an application of the theory to this species. The present manuscript intends to fill this desideratum. It develops the necessary bee-specific theory and introduces a small R script that implements Optimum Contribution Selection (OCS) for honeybees. While researching for this manuscript, we found it rather cumbersome that even though Meuwissen's theory is 28 years old and has sparked research in many new directions, to our knowledge, there is still no comprehensive textbook on the topic. Instead, all relevant information had to be extracted from several articles, leading to a steep learning curve. We anticipate that many honeybee breeding scientists with a putative interest in OCS for honeybees have little to no experience with classical OCS. Thus, we decided to embed our new derivations into a general introduction to OCS that then specializes more and more to the honeybee case. The result are these 121 pages, of which we hope that at least the first sections can also be of use for breeding theorists concerned with other species than honeybees.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

73 extracted references · 70 canonical work pages

  1. [1]

    Agricola, F

    I. Agricola, F. Pukelsheim, and F. Horst. Niemeyer und das Proportionalverfahren . Math. Semesterber., 64: 0 129--146, 2017. doi:10.1007/s00591-017-0201-8

    work page doi:10.1007/s00591-017-0201-8 2017

  2. [2]

    J. Albuja. electoral: allocating seats methods and party system scores , 2022. URL https://CRAN.R-project.org/package=electoral

    work page 2022

  3. [3]

    Andonov, C

    S. Andonov, C. Costa, A. Uzunov, P. Bergomi, D. Lourenco, and I. Misztal. Modeling honey yield, defensive and swarming behaviors of Italian honey bees (Apis mellifera ligustica) using linear threshold approaches . BMC Genet., 20: 0 78, 2019. doi:10.1186/s12863-019-0776-2

    work page doi:10.1186/s12863-019-0776-2 2019

  4. [4]

    M. L. Balinski and H. P. Young. Fair representation: meeting the ideal of one man, one vote . Yale University Press, New Haven, CT, United States, 1982

    work page 1982

  5. [5]

    Basso, T

    B. Basso, T. Kistler, and F. Phocas. Genetic parameters, trends, and inbreeding in a honeybee breeding program for royal jelly production and behavioral traits . Apidologie, 55 0 (11), 2024. doi:10.1007/s13592-023-01055-3

    work page doi:10.1007/s13592-023-01055-3 2024

  6. [6]

    Bernstein, M

    R. Bernstein, M. Plate, A. Hoppe, and K. Bienefeld. Computing inbreeding coefficients and the inverse numerator relationship matrix in large populations of honey bees . J. Anim. Breed. Genet., 135: 0 323--332, 2018. doi:10.1111/jbg.12347

    work page doi:10.1111/jbg.12347 2018

  7. [7]

    Bernstein, M

    R. Bernstein, M. Du, Z. G. Du, A. S. Strauss, A. Hoppe, and K. Bienefeld. First large-scale genomic prediction in the honey bee . Heredity, 130: 0 320--328, 2023. doi:10.1038/s41437-023-00606-9

    work page doi:10.1038/s41437-023-00606-9 2023

  8. [8]

    Bienefeld and F

    K. Bienefeld and F. Pirchner. Heritabilities for several colony traits in the honeybee (Apis mellifera carnica) . Apidologie, 21: 0 175--183, 1990. doi:10.1051/apido:19900302

    work page doi:10.1051/apido:19900302 1990

Show all 73 references
  1. [9]

    Bienefeld, F

    K. Bienefeld, F. Reinhardt, and F. Pirchner. Inbreeding effects of queen and workers on colony traits in the honey bee . Apidologie, 20: 0 439--450, 1989. doi:10.1051/apido:19890509

    1989 doi

  2. [10]

    Bienefeld, K

    K. Bienefeld, K. Ehrhardt, and F. Reinhardt. Genetic evaluation in the honey bee considering queen and worker effects -- A BLUP-Animal Model approach . Apidologie, 38: 0 77--85, 2007. doi:10.1051/apido:2006050

    2007 doi

  3. [11]

    Bigio, H

    G. Bigio, H. Al Toufailia, W. O. H. Hughes, and F. L. W. Ratnieks. The effect of one generation of controlled mating on the expression of hygienic behaviour in honey bees . J. Apicult. Res., 53: 0 563--8, 2014. doi:10.3896/IBRA.1.53.5.07

    2014 doi

  4. [12]

    E. W. Brascamp and P. Bijma. Methods to estimate breeding values in honey bees . Genet. Sel. Evol., 46: 0 53, 2014. doi:10.1186/s12711-014-0053-9

    2014 doi

  5. [13]

    E. W. Brascamp and P. Bijma. A note on genetic parameters and accuracy of estimated breeding values in honey bees . Genet. Sel. Evol., 51: 0 71, 2019 a . doi:10.1186/s12711-019-0510-6

    2019 doi

  6. [14]

    E. W. Brascamp and P. Bijma. Software to facilitate estimation of genetic parameters and breeding values for honey bees . In: Proceedings of the 46th International Apicultural Congress, Apimondia. Montréal, Canada, 2019 b

    2019

  7. [15]

    E. W. Brascamp, A. Willam, C. Boigenzahn, P. Bijma, and R. F. Veerkamp. Heritabilities and genetic correlations for honey yield, gentleness, calmness and swarming behaviour in Austrian honey bees . Apidologie, 47: 0 739--748, 2016. doi:10.1007/s13592-016-0427-9

    2016 doi

  8. [16]

    E. W. Brascamp, A. Uzunov, P. Bijma, and M. Du. Genetics of selection in honeybees . Wageningen, The Netherlands, 2024. doi:10.18174/677857

    2024 doi

  9. [19]

    Büchler, S

    R. Büchler, S. Andonov, R. Bernstein, K. Bienefeld, C. Costa, M. Du, M. Gabel, K. Given, F. Hatjina, B. A. Harpur, A. Hoppe, N. Kezic, M. Kovačić, P. Kryger, F. Mondet, M. Spivak, A. Uzunov, J. Wegener, and J. Wilde. Standard methods for rearing and selection of Apis mellifera...

    2024

  10. [20]

    Richtlinien für das Zuchtwesen des Deutschen Imkerbundes (ZRL) , 2021

    Deutscher Imkerbund . Richtlinien für das Zuchtwesen des Deutschen Imkerbundes (ZRL) , 2021

    2021

  11. [21]

    Druml, A

    T. Druml, A. Putz, M. Rubinigg, M. H. Kärcher, K. Neubauer, and C. Boigenzahn. Founder gene pool composition and genealogical structure in two populations of Austrian Carniolan honey bees (Apis mellifera carnica) as derived from pedigree analysis . Apidologie, 54: 0 24, 2023. ...

    2023 doi

  12. [22]

    M. Du, R. Bernstein, A. Hoppe, and K. Bienefeld. A theoretical derivation of response to selection with and without controlled mating in honeybees . Genet. Sel. Evol., 53: 0 17, 2021 a . doi:10.1186/s12711-021-00606-5

    2021 doi

  13. [23]

    M. Du, R. Bernstein, A. Hoppe, and K. Bienefeld. Short-term effects of controlled mating and selection on the genetic variance of honeybee populations . Heredity, 162: 0 733--747, 2021 b . doi:10.1038/s41437-021-00411-2

    2021 doi

  14. [24]

    M. Du, R. Bernstein, and A. Hoppe. The potential of instrumental insemination for sustainable honeybee breeding . Genes, 14: 0 1799, 2023. doi:10.3390/genes14091799

    2023 doi

  15. [25]

    M. Du, R. Bernstein, and A. Hoppe. Comparison of pooled semen insemination and single colony insemination as sustainable honeybee breeding strategies . R. Soc. Open Sci., 11: 0 231556, 2024 a . doi:10.1098/rsos.231556

    2024 doi

  16. [26]

    M. Du, R. Bernstein, and A. Hoppe. The number of drones to inseminate a queen with has little potential for optimization of honeybee breeding programs . Hereditas, 161: 0 28, 2024 b . doi:10.1186/s41065-024-00332-0

    2024 doi

  17. [27]

    R. A. Fisher. The correlations between relatives on the supposition of Mendelian inheritance . Trans. Roy. Soc. Edinb., 52 0 (2): 0 321--341, 1918. doi:10.1017/S0080456800012163

    1918 doi

  18. [28]

    Draft guidelines on in vivo conservation of animal genetic resources

    Food and Agriculture Organization of the United Nations (FAO) . Draft guidelines on in vivo conservation of animal genetic resources . Number 14 in FAO Animal Production and Health Guidelines . Rome, Italy, 2013

    2013

  19. [29]

    A. Gallais. Quantitative genetics and breeding methods in autopolyploid plants . INRA Editions, Paris, France, 2003

    2003

  20. [30]

    N. L. Gervan, M. L. Winston, H. A. Higo, and S. E. R. Hoover. The effects of honey bee (Apis mellifera) queen mandibular pheromone on colony defensive behaviour . J. Apicult. Res., 44: 0 175--179, 2005. doi:10.1080/00218839.2005.11101175

    2005

  21. [31]

    A. Gray, N. Adjlane, A. Arab, A. Ballis, V. Brusbardis, A. Bugeja Douglas , L. Cadahía, J.-D. Charrière, R. Chlebo, M. F. Coffey, B. Cornelissen, C. Amaro da Costa , E. Danneels, J. Danihlík, C. Dobrescu, G. Evans, M. Fedoriak, I. Forsythe, A. Gregorc, I. Ilieva Arakelyan , J....

    2019

  22. [32]

    Grimmett

    G. Grimmett. Stochastic apportionment . Am. Math. Monthly, 111: 0 299--307, 2004. doi:10.1080/00029890.2004.11920078

    2004

  23. [33]

    Guichard, M

    M. Guichard, M. Neuditschko, G. Soland, P. Fried, M. Grandjean, S. Gerster, B. Dainat, P. Bijma, and E. W. Brascamp. Estimates of genetic parameters for production, behaviour, and health traits in two Swiss honey bee populations . Apidologie, 51: 0 876--891, 2020. doi:10.1007/...

    2020 doi

  24. [34]

    M. A. Gutiérrez-Reinoso, P. M. Aponte, and M. García-Herreros. A review of inbreeding depression in dairy cattle: current status, emerging control strategies, and future prospects . J. Dairy Res., 89: 0 3--12, 2022. doi:10.1017/S0022029922000188

    2022 doi

  25. [35]

    J. R. Harbo. The value of single-drone inseminations in selective breeding of honey bees . In L. Connor and R. Hoopingarner, editors, Apiculture for the 21st Century , pages 1--5. Wicwas Press, Cheshire, United States, 1999

    1999

  26. [36]

    C. R. Henderson. Best linear unbiased estimation and prediction under a selection model . Biometrics, 31: 0 423--447, 1975. doi:10.2307/2529430

    1975 doi

  27. [37]

    Henryon, T

    M. Henryon, T. Ostersen, B. Ask, A. C. Sørensen, and P. Berg. Most of the long-term genetic gain from optimum-contribution selection can be realised with restrictions imposed during optimisation . Genet. Sel. Evol., 47: 0 21, 2015. doi:10.1186/s12711-015-0107-7

    2015 doi

  28. [38]

    Hoppe, M

    A. Hoppe, M. Du, R. Bernstein, F.-K. Tiesler, M. Kärcher, and K. Bienefeld. Substantial genetic progress in the international Apis mellifera carnica population since the implementation of genetic evaluation. Insects, 11: 0 768, 2020. doi:10.3390/insects11110768

    2020 doi

  29. [39]

    Jiménez-Mena, K

    B. Jiménez-Mena, K. Schad, N. Hanna, and R. C. Lacy. Pedigree analysis for the genetic management of group-living species . Ecol. Evol., 6: 0 3067--3078, 2016. doi:10.1002/ece3.1831

    2016 doi

  30. [40]

    R. J. Kerr, M. E. Goddard, and S. F. Jarvis. Maximising genetic response in tree breeding with constraints on group coancestry . Silv. Genet., 47: 0 165--173, 1998

    1998

  31. [41]

    R. J. Kerr, L. Li, B. Tier, G. W. Dutkowski, and T. A. McRae. Use of the numerator relationship matrix in genetic analysis of autopolyploid species . Theor. Appl. Genet., 124: 0 1271--1282, 2012. doi:10.1007/s00122-012-1785-y

    2012 doi

  32. [42]

    Kistler, B

    T. Kistler, B. Basso, and F. Phocas. A simulation study of a honeybee breeding scheme accounting for polyandry, direct and maternal effects on colony performance . Genet. Sel. Evol., 53 0 (71), 2021. doi:10.1186/s12711-021-00665-8

    2021 doi

  33. [43]

    Kohl and P

    S. Kohl and P. Herold. Problemanalyse zur Implementierung der Selektion nach optimierten Genbeiträgen in kleinen Populationen . Züchtungskunde, 89: 0 345--358, 2017

    2017

  34. [44]

    K. Lange. Mathematical and statistical methods for genetic analysis. Springer, New York, 1997. doi:10.1007/978-1-4757-2739-5

    1997 doi

  35. [45]

    D. Lewis. The evolution of sex in flowering plants . Biol. Rev., 17: 0 46--67, 1942. doi:10.1111/j.1469-185X.1942.tb00431.x

    1942 doi

  36. [46]

    Lijphart

    A. Lijphart. Degrees of proportionality of proportional representation formulas. In B. Grofman and A. Lijphart, editors, Electoral laws and their political consequences, pages 170--179. Algora Publishing, New York, NY, United States, 2003

    2003

  37. [47]

    J. L. Lush. Animal breeding plans. Iowa State Public Press, Ames, 1937

    1937

  38. [48]

    Lynch and B

    M. Lynch and B. Walsh. Genetics and Analysis of Quantitative Traits , volume 1. Sinauer, Sunderland, MA, 1998

    1998

  39. [49]

    Mackensen

    O. Mackensen. Breeding and genetics of bees . In US Agricultural Research Service , editor, Beekeeping in the United States , volume 335 of Agriculture Handbook, pages 68--76. US Government Printing Office, Washington D.C., United States, 1967

    1967

  40. [50]

    G. Malécot. Les mathématiques de l'hérédité . Masson, Paris, France, 1948

    1948

  41. [51]

    H. R. Mattila and T. D. Seeley. Genetic diversity in honey bee colonies enhances productivity and fitness . Science, 317: 0 362--364, 2007. doi:10.1126/science.1143046

    2007 doi

  42. [52]

    T. H. E. Meuwissen. Maximizing the response of selection with a predefined rate of inbreeding . J. Anim. Sci., 75 0 (4): 0 934--940, 1997. doi:10.2527/1997.754934x

    1997

  43. [53]

    T. H. E. Meuwissen and A. K. Sonesson. Maximizing the response of selection with a predefined rate of inbreeding: overlapping generations . J. Anim. Sci., 76: 0 2575--2583, 1998. doi:10.2527/1998.76102575x

    1998

  44. [54]

    Neumann, R

    P. Neumann, R. F. A. Moritz, and J. van Praagh. Queen mating frequency in different types of honey bee mating apiaries . J. Apicult. Res., 38: 0 11--18, 1999. doi:10.1080/00218839.1999.11100990

    1999

  45. [55]

    Panzani, A

    D. Panzani, A. Rota, M. Pacini, I. Vannozzi, and F. Camillo. One year old fillies can be successfully used as embryo donors . Theriogenology, 67: 0 367--371, 2007. doi:10.1016/j.theriogenology.2006.08.004

    2007 doi

  46. [56]

    S. F. Pernal, A. Sewalem, and A. P. Melathopoulos. Breeding for hygienic behaviour in honeybees (Apis mellifera) using free-mated nucleus colonies . Apidologie, 43: 0 403--16, 2012. doi:10.1007/s13592-011-0105-x

    2012 doi

  47. [57]

    Plate, R

    M. Plate, R. Bernstein, A. Hoppe, and K. Bienefeld. Comparison of infinitesimal and finite locus models for long-term breeding simulations with direct and maternal effects at the example of honeybees . PLOS One, 14: 0 e0213270, 2019 a . doi:10.1371/journal.pone.0213270

    2019 doi

  48. [58]

    Plate, R

    M. Plate, R. Bernstein, A. Hoppe, and K. Bienefeld. The importance of controlled mating in honeybee breeding . Genet. Sel. Evol., 51: 0 74, 2019 b . doi:10.1186/s12711-019-0518-y

    2019 doi

  49. [59]

    Plate, R

    M. Plate, R. Bernstein, A. Hoppe, and K. Bienefeld. Long-term evaluation of breeding scheme alternatives for endangered honeybee subspecies . Insects, 11: 0 404, 2020. doi:10.3390/insects11070404

    2020 doi

  50. [60]

    read.table: Data Input

    R Core Team . read.table: Data Input. R Foundation for Statistical Computing, Vienna, Austria, 2019. URL https://www.rdocumentation.org/packages/utils/versions/3.6.2/topics/read.table

    2019

  51. [61]

    J. Tang, C. Ji, W. Shi, S. Su, Y. Xue, J. Xu, X. Chen, Y. Zhao, and C. Chen. Survey results of honey bee colony losses in winter in China (2009–2021) . Insects, 14: 0 554, 2023. doi:10.3390/insects14060554

    2009 doi

  52. [62]

    D. R. Tarpy, D. vanEngelsdorp, and J. S. Pettis. Genetic diversity affects colony survivorship in commercial honey bee colonies . Naturwissenschaften, 100: 0 723--728, 2013. doi:10.1007/s00114-013-1065-y

    2013 doi

  53. [63]

    F. K. Tiesler, K. Bienefeld, and R. Büchler. Selektion bei der Honigbiene . Buschhausen, Herten, Germany, 2016

    2016

  54. [64]

    Uzunov, S

    A. Uzunov, S. Andonov, B. Dahle, M. Kovačić, J. Prešern, G. Aleksovski, F. Jaman, M. Jovanovska, B. Pavlov, Z. Puškadija, J. Wegener, and R. Büchler. Evaluating the potential for mating control in honey bee breeding in three SE European countries (preliminary results) . In: Pr...

    2022

  55. [65]

    Uzunov, E

    A. Uzunov, E. W. Brascamp, M. Du, and R. Büchler. Initiation and implementation of honey bee breeding programs . Bee World, 99: 0 50--55, 2022 b . doi:10.1080/0005772X.2022.2031545

    2022

  56. [66]

    Uzunov, E

    A. Uzunov, E. W. Brascamp, M. Du, and R. Büchler. The relevance of mating control for successful implementation of honey bee breeding programs . Bee World, 99: 0 94--98, 2022 c . doi:10.1080/0005772X.2022.2088166

    2022

  57. [67]

    Uzunov, E

    A. Uzunov, E. W. Brascamp, M. Du, P. Bijma, and R. Büchler. Breeding values in honey bees . Bee World, 100: 0 9--14, 2023. doi:10.1080/0005772X.2023.2166737

    2023

  58. [68]

    Y. Wang, J. Bennewitz, and R. Wellmann. Novel optimum contribution selection methods accounting for conflicting objectives in breeding programs for livestock breeds with historical migration . Genet. Sel. Evol., 49 0 (45), 2017. doi:10.1186/s12711-017-0320-7

    2017 doi

  59. [69]

    Wellmann

    R. Wellmann. Optimum contribution selection for animal breeding and conservation: the R package optiSel . BMC Bioinformatics, 20: 0 25, 2019. doi:10.1186/s12859-018-2450-5

    2019 doi

  60. [70]

    Wellmann

    R. Wellmann. optiSolve: linear, quadratic, and rational optimization , 2021. URL https://CRAN.R-project.org/package=optiSolve

    2021

  61. [71]

    Wellmann and J

    R. Wellmann and J. Bennewitz. Key genetic parameters for population management . Front. Genet., 10: 0 667, 2019. doi:10.3389/fgene.2019.00667

    2019

  62. [72]

    Wellmann and I

    R. Wellmann and I. Pfeiffer. Pedigree analysis for conservation of genetic diversity and purging . Genet. Res., Camb., 91: 0 209--219, 2009. doi:10.1017/S0016672309000202

    2009 doi

  63. [73]

    J. Woyke. Genetic proof of the origin of drones from fertilized eggs of the honeybee . J. Apicult. Res., 4: 0 7--11, 1965. doi:10.1080/00218839.1965.11100095

    1965

  64. [74]

    S. Wright. Coefficients of inbreeding and relationship . Am. Nat., 56: 0 330--338, 1922. doi:10.1086/279872

    1922 doi

  65. [75]

    Zayed and L

    A. Zayed and L. Packer. Complementary sex determination substantially increases extinction proneness of haplodiploid populations . Proc. Natl. Acad. Sci. USA, 102: 0 10742--10746, 2005. doi:10.1073/pnas.0502271102

    2005 doi

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.