Five decades of misunderstanding in the social Hymenoptera: a review and meta-analysis of Michener's paradox

Abstract

In a much-cited 1964 paper entitled "Reproductive efficiency in relation to colony size in hymenopterous societies," Charles Michener investigated the correlation between a colony's size and its reproductive efficiency - the ability of its adult females to produce reproductives, measured as per-capita output. Based on his analysis of published data from destructively sampled colonies in 18 species, he reported that in most of these species efficiency decreased with increasing colony size. His conclusion that efficiency is higher in smaller groups has since gained widespread acceptance. But it created a seeming paradox: how can natural selection maintain social behaviour when a female apparently enjoys her highest per-capita output by working alone? Here we treat Michener's pattern as a hypothesis and perform the first large-scale test of its prediction across the eusocial Hymenoptera. Because data on actual output of reproductives were not available for most species, Michener used various proxies, such as nest size, numbers of brood, or amounts of stored food. We show that for each of Michener's data sets the reported decline in per-capita productivity can be explained by factors other than decreasing efficiency, calling into question his conclusion that declining efficiency is the cause of the pattern. The most prominent cause of bias is the failure of the proxy to capture all forms of output in which the colony invests during the course of its ontogeny. Other biasing factors include seasonal effects and a variety of methodological flaws in the data sets he used. We then summarize the results of 215 data sets drawn from post-1964 studies of 80 species in 33 genera that better control for these factors. Of these, 163 data sets are included in two meta-analyses that statistically synthesize the available data on the relationship between colony size and efficiency, accounting for variable sample sizes and non-independence among the data sets. The overall effect, and those for most taxonomic subgroups, indicates no loss of efficiency with increasing colony size. Two exceptional taxa, the halictid bees and independent-founding paper wasps, show negative trends consistent with the Michener hypothesis in some species. We conclude that in most species, particularly those with large colony sizes, the hypothesis of decreasing efficiency with increasing colony size is not supported. Finally, we explore potential mechanisms through which the level of efficiency can decrease, be maintained, or even increase, as colonies increase in size.

Keywords: Hymenoptera; colony development; colony size; division of labour; ergonomic efficiency; social evolution.

Fig. 1

Colony productivity and the Michener pattern. Outputs (y‐axis) reported by Michener were various measures of brood in the nest. While total colony output increases with colony size (A), per‐capita output decreases with colony size (B). This is the crux of Michener's paradox: it suggests that an individual would do better to reproduce on her own or in a small group than to join a large group.

Fig. 2

Changing allocation of per‐capita investment among major forms of output during the colony cycle. Total investment (100%) is shown by the solid line at the top; it captures all forms of colony output (productivity) and represents the colony's efficiency (E). The three components of output – growth, survival and maintenance, and reproduction – sum to this total 100% at every stage. Michener's commonly used proxy for per‐capita output is represented by the growth line (dashed). Early in development, growth in worker numbers is the major form of output, but as the colony develops it invests increasingly in survival/maintenance (dot‐dashed line), and finally in reproduction (dotted line). These redirections of effort come at the expense of growth. Therefore, growth, the proxy metric for efficiency in most of Michener's analyses (typically measured in terms of numbers of cells or immatures in the nest at collection) gives a good approximation of efficiency early in the colony cycle but becomes increasingly inaccurate as the colony develops. A plot of per‐capita productivity (PCP) based on this proxy will decline with increasing colony size during development, just as in Michener's plots, but that plot will not accurately depict the colony's efficiency across all developmental stages or its ability to produce reproductives.

Fig. 3

The effect of including (O) versus excluding (×) failed colonies on calculations of per‐capita productivity (PCP) as a function of colony size. Sample size = 100 for each colony size. Rate of colony failure decreases with increasing colony size. Numbers indicate number of colonies included in each calculation of PCP; for each colony size the difference between colony numbers included gives the number of failed colonies. The upper plot is a measure of colony efficiency, while the lower plot is a measure of overall relative fitness.

Fig. 4

Per‐capita productivity of Bombus pensylvanicus (= americanorum) colonies, based on total numbers of workers (W) and sexuals produced over the entire season. Seven colonies parasitized by B. (Psithyrus) variabilis (Cresson) are omitted because output of the host species was compromised. The four colonies shown with values of y = 0 did not die, but simply failed to produce males (M) or gynes (Q). Regression equation: (M + Q)/W = −0.092 + 0.0113 W, r ² = 0.52, N = 24. Slope is significantly different from 0 at P < 0.001. Both slope and y‐intercept are significantly affected by year. Data from Webb (, table 26).

Fig. 5

The use of brood counts instead of brood masses creates a Michener pattern bias. (A) In one example, brood count data from Spradbery (1971) show the initial conclusion of a negative effect of colony size on efficiency in Vespula vulgaris (filled circles), with a slope (dashed line) significantly less than 1.0 (black line: neutral effect). However, when plotting pupal biomass data [pupal count data from the same study and biomass data from Archer (2012)], no negative effect is observed (open circles; dotted line). (B) A comparison of brood or cell counts versus brood masses as alternative proxies for measuring productivity. The symbols represent the slopes of the regressions of log(colony output) on log(colony size); lines connect the plot of count with the plot of mass for each of the 28 data sets. A slope of 1.0 indicates no effect of colony size on ergonomic efficiency. A + indicates a slope significantly greater than 1.0, while an × indicates a slope significantly less than 1.0. Filled squares are mean values for the groups. Data sets: a, Exoneura nigrescens (Nov) (Stevens et al., 2007); b, E. nigrescens (Dec) (Stevens et al., 2007); c, Parachartergus fraternus (Bouwma et al., 2006); d, Bombus lucorum (Müller & Schmid‐Hempel, 1992); e, Polybia occidentalis (1982) (Jeanne & Nordheim, 1996); f, Temnothorax crassispinus (Regensburg) (Kramer et al., 2014); g, T. crassispinus (Abensberg) (Kramer et al., 2014); h, Vespula vulgaris (Spradbery, 1971); i, Lasius sakagamii (winter larvae) (Yamauchi et al., 1982); j, Polybia occidentalis (1998) (Bouwma et al., 2005); k, Apis mellifera (brood) (Lee & Winston, 1985); l, T. nylanderi (Sommerhausen West) (Kramer et al., 2014); m, P. occidentalis (1983) (Jeanne & Nordheim, 1996); n, T. nylanderi (Sommerhausen South) (Kramer et al., 2014); o, P. occidentalis (1999) (Bouwma et al., 2005); p, T. americanus (NY) (Kramer et al., 2014); q, T. longispinosus (NY) (Kramer et al., 2014); r, Leptothorax acervorum (Abensberg) (Kramer et al., 2014); s, T. americanus (WV) (Kramer et al., 2014); t, V. germanica (Spradbery, 1971); u, T. longispinosus (WV) (Kramer et al., 2014); v, Myrmica punctiventris (NY) (Kramer et al., 2014); w, Polistes dominula (May) (Turillazzi et al., 1982); x, Leptothorax muscorum (Kramer et al., 2014); y, T. nylanderi (Scharf et al., 2012a); z, Bombus terricola (Owen et al., 1980); aa, E. nigrescens (Sept) (Stevens et al., 2007); bb, Polistes dominula (April) (Turillazzi et al., 1982).

Fig. 6

Patterns of colony growth. Annual (A) and perennial (B) species show different patterns of growth depending on the time of year. In an annual species, the time of year correlates with the colony's stage of development, because all colonies are roughly on the same developmental trajectory (see also Fig. 2). In a perennial species, however, the age of the colony is as important as the time of year. A sample of colonies collected in early summer may include some that had recently been founded (Yr1), some that were investing heavily in growth/maintenance (Yr2) and some that were reproducing (Yr3+). Shading of lines denotes colony developmental stage: light grey = founding; medium grey = ergonomic; dark grey = reproduction; black = winter mortality. Black dotted lines connect surviving colonies from 1 year to the next.

Fig. 7

Lack of congruence of input and output. Growth is depicted of a hypothetical swarm‐founding colony that has established a new nest and begun to produce workers. (A) Colony size decreases due to worker mortality (points i–iii) until workers begin to eclose (iv), and colony size begins to increase (v). (B) The corresponding numbers of eggs, larvae, and pupae, assuming for simplicity constant rates of oviposition and constant development times. Each plateau represents the standing crop due to equal rates of brood entering and leaving that stage. Total brood (in grey), the sum of all forms of output (eggs + larvae + pupae) rises steadily until production plateaus. (C) This hypothetical colony is non‐destructively sampled at times i to v to determine its per‐capita productivity, that is, the number of brood the colony has reared divided by the number of workers in the colony at each point. This shows a negative relationship, like Michener's pattern, but the decline is simply due to the lack of congruence of input and output, and not to a difference in the efficiency of colonies of different sizes.

Fig. 8

Early‐stage growth of a colony of swarm‐founding wasps, with per‐capita output based on eggs, per Michener (1964). Assumptions as in Fig. 6. Mortality of adults during the founding stage is 50% in the ~30 days it takes the colony to produce its first adult offspring (Bouwma et al., 2003a). The number of eggs per adult female (solid line) starts low (few eggs, many females), then rises rapidly as oviposition continues and workers in the founding group (dashed line) die without replacement. As the oldest eggs begin to hatch into larvae (point L), the number of eggs in the nest becomes constant (rate of hatching equals rate of oviposition), but because adult mortality is ongoing (Bouwma et al., 2003a) the number of eggs per‐capita continues to rise, albeit more slowly than before, and reaches a peak when the adult population is at its lowest, just as new workers begin to eclose (point W). After that point the eggs‐per‐adult ratio decreases, because the adult population is now increasing while the number of eggs in the nest remains constant. Thus, the highest value of eggs/adult occurs at the end of the pre‐emergence period, when the colony is smallest (point W). Relaxing the assumption of a constant colony‐wide rate of oviposition by the queens to, say, a sigmoidal or declining function, has no qualitative effect on this ontogenetic pattern.

Fig. 9

Per‐capita output of Apis mellifera colonies. Data from Rangel & Seeley (2012) were analysed to show how the chosen form of worker output leads to results that either support, refute, or are neutral to Michener's pattern. Each colony parameter is measured in cm² of comb area (A–E) or number of workers (F) and is plotted on a per‐capita basis (colony parameter/starting colony size). Starting colony size = number of workers in the swarm. Linear regression was used to determine how each colony parameter responded to colony size. Parameters were measured 18–20 days after the colonies were established, so that new workers had not yet eclosed. Black lines show statistically significant linear regressions (worker comb built: F _1,10 = 15.45, P < 0.005, r ² = 0.57; drone comb built: F _1,10 = 13.80, P < 0.005, r ² = 0.54; sealed worker brood: F _1,10 = 0.92, P > 0.05, NS, r ² = −0.01; sealed drone brood: F _1,10 = 0.01, P > 0.05, NS, r ² = −0.10; food stored: F _1,10 = 3.18, P > 0.05, NS, r ² = 0.17; workers lost: F _1,10 = 0.22, P > 0.05, NS, r ² = −0.08).

Fig. 10

Summary of results by taxonomic group for the continuous colony size meta‐analysis (CMA). Effect sizes and 95% confidence intervals are plotted, with 1.0 indicating no effect of colony size on ergonomic efficiency. In the table, k is the number of data sets within each group, and results of Q‐tests (Q statistics and P values) indicate whether there is significant residual heterogeneity in effect sizes, i.e. heterogeneity not due to sampling variance. I ² values are a measure of the percentage of variance in the estimated slopes that is not due to sampling variance. For a full forest plot of all studies, see Fig. S1. IF Polistinae, independent‐founding Polistinae.

Fig. 11

Summary of results by taxonomic group for the discrete colony size meta‐analysis (DMA). Effect sizes (standardized mean difference, e) and 95% confidence intervals are plotted, with 0 indicating no effect of colony size on per‐capita productivity. In the table, k is the number of data sets within each group, I ² values are a measure of the percentage of variance in the estimated slopes that is not due to sampling variance, and results of Q‐tests (Q statistics and P values) indicate whether there is significant residual heterogeneity in effect sizes, i.e. heterogeneity not due to sampling variance. For a full forest plot of all studies, see Fig. S3. Note that broodless nests were omitted from this analysis. For results including broodless nests, see Fig. S4. IF Polistinae, independent‐founding Polistinae.