Experimental manipulation of natural plant communities

Experimental manipulation of natural plant communities

REVIEWS of natural Experimentalmani plant communities Jessica Gurevitch and Scott L. Collins U correlation among experimental ‘ntil recently, manip...

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REVIEWS

of natural Experimentalmani plant communities Jessica Gurevitch and Scott L. Collins

U

correlation among experimental ‘ntil recently, manipulative Attempts to elucidate the factors units, difficulty in detecting indirect controlling the structure of plant experiments in plant ecolcommunities have relied increasingly on and secondary effects, and results ogy carried out in the field that are highly dependent on the fleld experiments. This is a powerful have largely emphasized the population ecology of plants. approach for testing theoretical predictions scale at which the experiment is that offers important advantages over Questions about communities have conducted. These problems lead more often been approached to numerous constraints, and call observational and comparative studies. However, field experiments suffer from by descriptive and comparative for creative experimental design, methods which might be highly intrinsic difficulties as well as more-easily blocking or some alternative to quantitative but provide limited remediable limitations. Recent progress blocking, adequate replication, the potential for inferring causality. has been made by new approaches use of novel statistical analyses, Attempts to link population-level including the use of multifactor and knowledge of the biology of the events with community patterns experiments, and the development and organisms and systems involved. offer substantive challenges. dissemination of better statistical tools. Doing an ecological experNevertheless, connections between iment is not equivalent to testing population and community-level meaningful ecological hypotheses, Jessica Gurevitch is at the Dept of Ecology and processes using field manipuand results that are statistically Evolution, State University of New York, Stony Brook, lations are being forged on several significant are not necessarily NY 117943245, USA; Scott Collins is at the National fronts because of developments ecologically significant. For inScience Foundation, Division of Environmental in a number of areas. One area stance, an experimental disturb Biology, Washington, DC, USA and the Dept of involves the incorporation of more ante may yield a statistically Botany, University of Oklahoma, Norman, OK, USA. than one factor into the design of significant decrease in similarity ecological experiments, allowing from 85% to 75% between two interactions to be studied so that the true complexity of assemblages of species, but the ecological importance of community properties can be explored. Another is the such a change may be trivial. Secondly, it is possible to deployment of new statistical methods appropriate to the test hypotheses without conducting experiments. Fretwells problems of carrying out and analysing field experiments. credited Robert MacArthur for promoting use of the In this article, the advantages and limitations of field hypothetical-deductive approach in ecology, yet MacArthur experiments in ecology are examined briefly and results was hardly an experimentalist. The use of carefully from several community-level experiments are reviewed. designed sampling schemes and null models provide nonA discussion of some recently developed statistical tools experimental approaches to hypothesis testing. Largethat offer advantages for analysing field experiments follows. scale questions, in particular, may require such approaches, (Experimental manipulation of resource 1evelsiJ and plant but the conclusions may be limited by weak inference. competition in the fields!4are covered elsewhere, and this The experimental approach has other limitations as review will not focus on those topics.) well. It would be foolish to let an ideology of method drive the questions being asked by ecologists. Consider, Why do experiments? for instance, that many field experiments are difficult, or Despite recent attention to field experiments in ecology, impossible, to adequately replicate because the factors the experimental approach is hardly new. Indeed, in 1924, being studied operate at large spatial scales. Large-scale Frederick Clements stated that, ‘.. .actual progress [is] in- analyses of disturbance effects in grasslandssJO are difficult sured only by instrumental and experimental methods.. .‘5. to replicate because the similarity of replicates is reduced Arguments for the use of field experiments are compelling. at the spatial scales necessary for analysis. This should One of the goals of science in general and in particular, of not prevent ecologists from addressing large-scale quesecology, is to make predictions with a given level of probtions, but results from such experiments are constrained by statistical and methodological limitationsii. ability6. Observational and comparative data and the use As an illustration of issues raised by the spatial scale of ‘natural experiments’ can provide only weak inference. Not only are controls and knowledge of initial starting of the phenomena being investigated, Wilson and Shayl* conditions often lacking 637,but it is often impossible to conducted a well-replicated, multifactorial field experiment on fire and nutrient effects on plant community strucdisentangle important driving variables because of strong correlations between factors under investigation. ture in mixed-grass prairie. Treatments were imposed on Field experiments differ from traditional laboratory 5 x 7m plots. Nutrient addition increased productivity experiments in several respects. Ordinarily, the factor of and decreased bare ground, while species composition and diversity were unaffected by fire. Such an experiment interest is varied while all other variables are held constant. In field experiments, however, the community ecologist provides some of the elements needed to understand plant community dynamics in mixed-grass prairie. Other must control the variable of interest, while everything else in the environmental matrix continues to fluctuate. factors controlling this system may be more difficult to Other problems include spatial heterogeneity and autoexamine experimentally. To include the effects of ungulate 94

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REVIEWS herbivores, for example, would require the treatment plots to be many hectares in size to produce realistic grazing effects on the plant community. At that scale, one would expect the spatial variation among replicates to potentially swamp treatment effects. Alternatively, if one set of treatment plots is placed in a grazed area and another set in an ungrazed area, the grazing factor is not replicated and the effect of grazing cannot be readily analysed statistically. Furthermore, fires that encompass many hectares are likely to have different effects on community structure than fires on small plots. Community-level field experiments Effects of single factors on community structure Several recent studies have used field experiments to examine community-level phenomena, rather than responses of individuals or species. For instance, long-term studies on the influences of insect herbivores during secondary succession in Great Britain13J4have detected strong effects on the plant community. Overall cover, species richness and the relative predominance of annual forbs, perennial forbs and perennial grasses were affected by the removal of above-ground herbivorous insect@. Community composition appeared to be determined by a complex interaction between herbivores and the balance of competitive interactions between different plant life forms at different successional stages. In another set of experiments, foliar and root-feeding species were shown to have different effects on plant community structurel4. Soil insecticide had a dramatic effect, more than doubling mean species richness in early successional plots. Species diversity was also increased by the reduction in soil insects. Foliar insecticide had smaller and more variable effects, and in some cases even reduced species richness and diversity. Removal of aboveground insects favored different plant species and life forms more than did the removal of root-feeding species. In a meadow in northern Sweden, experimental enhance ment of larval density of a noctuid moth to outbreak levels, significantly reduced the height and above-ground biomass of grasses, the preferred food of the larvae. The aboveground biomass of forbs actually increased in the presence of high larval densities, apparently in response to reduced competition from the grasses15. Long-term (12-year) removal of kangaroo rats (Dipodomys spp.) in the Chihuahuan desert of southwestern North America altered plant community composition, increasing the predominance of tall grasses and changing the community from desert shrubland to grasslandl6. However, two common short-statured grasses declined in the absence of kangaroo rats, presumably due to the effects of increased competition with taller grasses. The effects of seed-eating rodents on the plant community are apparently a result of both disturbance and grain consumption. In contrast, the effects of small mammal and insect herbivores were apparently limited in mature North American tallgrass prairieu. When above- and below-ground insecticides were applied over a four-year period, few significant effects on the community were found, with the exception that the below-ground insecticide prevented a decline in the number of C, forb species. Similarly, removal of small mammals had few effects on the plant community, and interactions between insect and small-mammal herbivory were unimportant. These results must be interpreted with caution, because the insecticides used in this experiment may not have been effective in reducing the presence of the most important herbivorous insects17J8.

Fire frequency was varied experimentally at Konza Prairie, KS, USA10to test the effects of this disturbance on plant community heterogeneity (measured as mean dissimilarity in species composition among subsamples) and species diversity in a test of disturbance theory. Sites within replicated management units were unburned, burned yearly or burned less frequently. Sites were burned a total of O-18 times over the course of 18 years. The results in general did not conform to theoretical predictions and were dependent on the spatial scale at which data were analysed. Heterogeneity’0 and species diversity (Fig. 1) declined with burning frequency in this prairie community. As sites were burned more frequently, the dominance of the fire-adapted C, grasses, especially Andropogon gerardii and A. scopatius, increased, while the occurrence and cover of other (particularly the non-matrix-forming) species declined. This outcome may be reversed under heavy grazing, however-g. Experimental manipulation of habitat fragmentation in an early successional old-field community in Kansas, USA, revealed subtle but profound effects on the plant community and on small mammals and snakes’g. Small, medium and large patches had similar species diversity, richness and evenness after six years of secondary succession. The actual species composition was substantially different in the three patch types, with certain species occurring uniquely in each one. Greater numbers of unique plant (Fig. 2) and arthropod species were found in the largest patches than in the smaller ones. In particular, clonal plants did not persist in the smallest patches because vegetative spread was likely to move plants out of a patch, but recolonization was difficult’g. Biological and statistical interactions: more complex questions, more complex designs Interspecific competition is generally considered to be an important force structuring plant communities. Curiously, few field experiments on plant competition have explicitly addressed anything about competition other than whether it occurs, and the effects of competition on community-level phenomena have seldom been investigated”. More complex questions about the effects of species interactions on community properties, or about the indirect influences of other factors on the direct effects which two plant species have on one another, have usually not been incorporated into experimental designs. Studies on the effects of more than one factor are often neither appropriately designed nor analysed so that valid comparisons can be made. As an example, experiments in which the effects of competition and predation are both manipulated too often Number of burns alter each factor in a different Fig. 1. Plant species divers@ place or time, making it imposs(Shannon H’) versus number of ex ible to ask anything about their perimental burns in a large flelc interaction or to compare their experiment at Konza Prairie, KS, US/ relative importance. (r2 = 0.48, P= 0.04). Managemen units at Konza are burned at differen Even when factors are approset frequencies (annually. 2years priately manipulated, published 4 years or 20 years) and sites were results may omit statistical tests added into the burning rotation at dli of the interactions, but rather ferent times during the 20year period Each point represents an experlmen test each factor in a separate tal site. (S.L. Collins, unpublished. analysis”. Many of the questions of greatest biological interest 95

REVIEWS plex and more difficult to interpret. Protection from grazing by large mammals over a long period led to a divergence in community composition, particularly in the short- and mid-grass communities.

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Patch size Fig. 2. Cumulative proportion of vascular plant species (open bars) found in each patch type and of unique species found only in that patch type (filled portion of bar) over a period of six years in an experimental successional field community. Drawn from data in Ret 19.

require testing statistical interactions between factors. The methods and perspective of simple factorial designs should be exploited more fully in ecological experimentsx, although elaborate multifactor designs may at times lead to difficulty in interpreting results and in comparing results with those of other studies. Factorial experiments can be powerful tools to address biologically interesting hypotheses. In an early successional system, the responses of rare and common plant species were examined using a complex factorial design (five factors, each at two to four levels)zO.Both mollusc herbivory and competition affected plant performance. Somewhat surprisingly, there were no differences among the species in their responses to herbivory, or to competition; rare species behaved similarly to common ones, with respect to release from both factors. Contrary to some predictions*1J*, moreover, there was no interaction between the effects of herbivory and competition (on a log scale): their effects were simply additive. The removal of competitors had a larger effect on plant size than did the removal of mollusc herbivores. None of these comparisons would have been possible if the more common approach had been taken in which the responses of each species to each factor were examined separately. In East African short-, mid- and tallgrass communities, grazing, physical disturbance, interspecific competition and fire were examined in multifactor manipulative experiments23 (although not all factors were truly replicated). In the shortgrass (driest site), exclusion of large grazing mammals resulted in the replacement of short statured grasses by tall species, an increase in dominance by a few species, a decrease in species diversity and an increase in cover. Similar to the effects of grazing, the removal of dominants, burning and disturbance also apparently resulted in increased diversity, presumably due to decreased competition from the dominant grasses. There were significant interactions between factors. Results were similar in the mid-grass community. The responses of the tallgrass community, in the wettest location, were com96

Old problems, new statistical tools Field experiments are often hampered by failure to use the most appropriate and powerful statistical techniques available. Recently, an edited text*4 and a special section in a major ecological journal25 have attempted to make newer techniques more widely available fo ecologists, and encourage better use of standard techniques. The volume by Scheiner and Gurevitch*J presents, for example: less familiar methods for graphical analysis; suggestions for designing and analysing unreplicated large-scale experiments; a comparison of alternatives for dealing with repeated measures data; and techniques that are far superior to conventional approaches, although little used, such as failure-time analysis for mortality and other ‘time until an event’ data. The special section in Ecology, edited by Matson, Potvin and Travis25, deals with a number of issues including nontraditional regression analysis and a consideration of ANOVAfor unbalanced data - a ubiquitous condition for field experiments. Both the book and the special section devote attention to the problems of designing and analysing experiments when the data exhibit spatial autocorrelation, or when spatial heterogeneity is of concern*k*9. Positive spatial autocorrelation occurs when observations (i.e. plants, plots, etc.) that are close to each other in space resemble one another more closely in their responses than those that are physically far apart. This is almost always the case in field experiments in plant communities. The problem that arises is that ordinary statistics, such as ANOVA,make the assumption that observations are independent, i.e. that there is no spatial autocorrelation. Unlike some other assumptions in ANOVA and related approaches, significance tests are not robust to violation of this major assumption, and can therefore result in faulty hypothesis tests. Use of more accurate and powerful statistics are highly preferable when there is substantial spatial autocorrelation. Another common problem, particularly for large-scale experiments, is that due to small sample sizes and the high degree of natural environmental heterogeneity, it is often difficult to satisfy ANOVAassumptions, such as homogeneity of variances and normality of residuals. Nevertheless, experimentalists may be tempted to use ANOVA or other familiar tests to compare responses in experimental and control groups. An alternative statistical approach, Multiple Response Permutation Procedures (MRPP)30J1,eases many of these assumptions and may be particularly useful for data from large-scale field experiments (Box 1). Because the technique is based on distance measures, it has the additional advantage of being easily applied to multivariate data sets, and to many different kinds of measurements, from soil properties to species abundances. Even experiments that are well designed and well executed yield primarily site-specific data. A good experiment may provide robust tests of hypotheses without necessarily leading to scaling-up or to generalization. For progress to occur in ecology, however, synthetic approaches are essential. Few ecological experiments are ever replicated exactly. One alternative is to conduct experiments simultaneously at different places32, thus expanding the generality of the results and providing a stronger basis TREE uol. 9, no. 3 March

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Box 1. Multiple Response Permutation Procedures @fRPP)~for field experiments MRPP is designed to provide a statistical test for comparing experimental groups (i.e. groups of plots, individual plants, etc. which are subjected to different experimental treatments). The object IS to detect whether individuals within groups are closer in value than individuals in different groups. The technique works by determining all pairwise distances among observations (which might be plots, for example), calculating a weighted average of distances between observations within groups, and comparing this weighted average to a distribution based upon all possible permutations of the original data. The P value is the ranking of the actual weighted average distance compared to the weighted average distance calculated for all possible permutations of the original data. In other words, the P value rep resents the probabrlity of obtaining a weighted average distance that is less than or equal to the average value. If the values of the expenmental outcome for members of a group resemble one another closely (i.e. are ‘concentrated’), then the actual weighted average will be lower than that for most random permutations of the data, and the Pvalue will be small enough to be considered statistically significant. To illustrate this, the following data represent hypothetical results from a fteld experiment on the effects of fire frequency on plant species richness. The experiment has three replicates of three burning treatments, and the data represent number of species per plot: Treatment Replicate 1 2 3 Mean distance:

Annually burned 25 36 25 7.3

4-year burn 51 66 45 14.0

Unburned 47 67 50 13.6

In this case, the number of groups (g)=3, the number of observations within each group (n,)=3, and the total number of observations (N)=9. The MRPP statistic, M, is

where D is the mean distance of group i, and C is a constant. In general, C,=n,/N, which in this example is 3/9. Thus, for these data, M = 7.33(0.333) + 14.0(0.333) + 13.6(0.333) = 11.63. There are Iv!/

ngn,!

I=1

or 1680 permutations of the data. The P value for this example is 0.033; the observed value ranks 55th among all possible permutations of the data and indicates that differences among treatments in species richness are statistically significant.

for ecological theory. Even more broadly, it is becoming increasingly important to be able to quantitatively evaluate the results of ecological experiments carried out in one place at one time, in relation to other similar experiments carried out in different places at different times. Whether one wishes to evaluate the generality of an ecological relationship, or to detect patterns of biotic response in relation to anthropogenic disturbances, there is a compelling need for new statistical tools to combine experimental results.33. These new statistics are collectively called metaanalysis @ox 2). Older methods still commonly in use in the field of ecology have been demonstrated to be inadequate to address the questions of greatest interest, or worse, to give inaccurate and misleading results. More conventional approaches, for example, cannot accurately assess the overall magnitude of an effect across all studies, nor can they test whether one category of experiments demonstrates an effect that

Box 2. What is meta-analysis? Meta-analysis is a set of statistical techniques for synthesizing the outcomes of independent experiments to: (1) calculate the overall magnitude (effect size) of the outcome across all studies; (2) determine whether this effect is significantly greater or less than zero; (3) test whether the results of the different studies are consistent with one another; and (4) compare the magnitude of the effect among different categories of experiments (e.g. aquatic versus terrestrial). There are various ways of calculating an effect size from each study, but one that is commonly used IS:

d=

x-x

z,

s

where d is the effect size, X, is the experimental group mean, X, is the control group mean, and s is the pooled standard deviation of the two groups and J corrects for small sample bias. The dvalues are often combined using a weighted average that depends on sample size. Before meta-analysis became well known, one way in which scientists attempted to quantify the results of a group of studies was to conduct a ‘vote count’: the proportion of statistically significant outcomes was counted up and compared with the proportion of experiments with no statistically significant outcome. It is now understood that this method is biased and mathematically flawed, and leads to incorrect conclusions. This is primarily because vote counting, unlike meta-analysis, is dependent on the power of the individual experiments, and thus on the sample size used in each study. The proportion of significant outcomes does not provide accurate information on the frequency or magnitude of the effect under consideration, and this information should be obtained from a meta-analysis.

is larger, smaller or the same as another (for instance, are the effects of competition greater overall for plants in high-resource environments than for those in infertile soils, if one considers the results of a large set of field experiments?). As meta-analysis becomes increasingly used by, and useful to, ecologists, it will be important to develop meta-analytic statistics better suited to ecological data and ecological problem+. While the increasing use of field experiments is encouraging, all experiments are not going to contribute equally to a better understanding of the structure and function of natural plant communities. We know a great deal about effects on individual plants in the field and something about plant populations, but much less about factors determining the abundance, distribution and coexistence of plant species. Thus, adding to the already large number of studies that simply demonstrate the existence of competitive effects in the field, for instance, will be of limited value. Experiments must be carefully and imaginatively designed to address the more-pressing questions, if they are to make real contributions to our understanding of communities. Field experiments alone cannot resolve all ecological problems, but can only be one important component of an integrated research program. Progress will be made most rapidly by the use of a battery of approaches that includes experimentation, the use of the most appropriate, powerful and robust statistical techniques for design and analysis, intelligent synthesis of experimental results, and reaching sound interpretations resting on a solid understanding of natural history. Acknowledgements The support of the US National Science Foundation grants BSR 8908112 to J. Curevitch, and BSR 9007450 to S.L. Collins and S. Glenn is gratefully acknowledged. The paper benefitted from comments by an anonymous reviewer. This review was written while both authors were visiting scientists at N.S.F.

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REVIEWS References 1 Tilman, D. (1982) Resource Competition and Community Structure,

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Princeton University Press DiTommaso, A. and Aarrssen, L.W. (1989) Vegetatio 84,9-29 Goldberg, D.E. and Barton, A.M. (1992)Am. Nat. 139,771-801 Aarrssen, L.W. and Epp, GA. (1990) J. Veg. Sci. 1,13-30 Clements, F.E. (1924) Experimental Vegetation: the Relation of Chmaxes to Climate, Carnegie Institute of Washington Publication 355 Peters, R.H. (1991)A Critique forEcology, Cambridge University Press Hairston, N. (1989) Ecological Experiments: Purpose, Design and Execution, Cambridge University Press Fretwell, SD. (1975) Annu. Reo. Ecol. Syst. 6, 1-13 Collins, S.L. (1987) Ecology 681243-1250 Collins, S.L. (1992) Ecology 73, 2001-2006 Carpenter, S.R. et al. (1989) Ecology 70, 1142-1152 Wilson, S.D. and Shay, J.M. (1990) Ecology 71,1959-1967 Brown, V.K. (1990) in Pests, Pathogens and Plant Communities (Burden, J.J. and Leather, S.R., eds), pp. 275-288, Blackwell Brown, V.K. and Gange, A.C. (1989) Oikos 54,67-76 Danell, K. and Ericson, L. (1990) Ecology 71,1068-1077 Brown, J.H. and Heske, E.J. (1990) Science 250,1705-1707 Gibson, D.J., Freeman, CC. and Hulbert, L.C. (1990) Oecotogia 84, 169-175 Seastedt, R.R., Todd, T.C. and James, SW. (1987) Pedobiologia 30, 9-l 7 Robinson, G.R. et al. (1992) Science 257,524-526

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Rees, M. and Brown, V.K. (1992) J. Ecol. 80,353-360 Kotler, B.P. and Holt, R.D. (1989) Oihos 54,256-260 Noy-Meir, 1.(1981) Oecotogia 50,277-284 Belsky, A.J. (1992) J. Veg. Sci. 3,187-200 Scheiner, S.M. and Gurevitch, J., eds (1993) Design andAnalysis of Ecologicat Experiments, Chapman & Hall Matson, P., Potvin, C. and Travis, J. (1993) Ecology 74, 1615-1676 ver Hoef, J.M. and Cressie, N. (1993) in Design and Analysis of Ecological Experiments (Scheiner, S.M. and Gurevitch, J., eds), pp. 319341, Chapman &Hall Fortin, M-J. and Gurevitch, J. (1993) in Design and Analysis of Ecological Experiments (Scheiner, S.M. and Gurevitch, J., eds), pp. 342-359, Chapman &Hall Dutilleul, P. (1993) Ecology 74,1646-1658 Legendre, P. (1993) Ecology 74,1659-1673 Zimmerman, G.M.,Goetz, H. and Mielke, P.W., Jr (1985) Eco/ogy 66,606-611 Biondini, M.E., Mielke, P.W., Jr and Redente, E.F. (1988) Coenoses 3.155-174 Willems, J.H., Peet, R.K.and Bik, L. (1993)J. Veg. Sci. 4,203-212 Gurevitch, J., Morrow, L.L.,Wallace, A. and Walsh, J.S. (1992) Am. Nat. 140,539-572 Gurevitch, J. and Hedges, L.V.(1993) in Design and Analysis of Ecological Experiments (Scheiner, SM. and Gurevitch, J., eds), pp. 378-398, Chapman &Hall

Partitioningof r societies

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In

Laurent Keller and H. Kern Reeve

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ocieties where all individuals reproduce equally, versus societies where a single individual completely monopolizes reproduction, only represent end points of a continuum in the variance in the reproductive output among group members. A shorthand term to describe the distribution of direct reproduction among individuals is reproductive skew. In high-skew societies, actual direct reproduction is concentrated in one or a small subset of individuals in the group; in low-skew societies, reproduction is distributed more evenly among group members (see Fig. 1). The first attempt to explain the variation in reproductive skew was made by Sandra Vehrencamp r,z. Here, we discuss recent progress since the develop ment of Vehrencamp’s pioneering skew models.

the subordinate(s)rA. If the dominant benefits from retention of the subordinate, it may pay the dominant to yield some reproduction to subordinates as inducements for these subordinates to remain in the society and cooperate peacefully, rather than to leave or fight for exclusive control of the group’s resources. Reproductive inducements that prevent subordinates from leaving the group are called staying incentives; inducements that prevent subordinates from fighting to the death for complete repro ductive control are called peace incentives4. Laurent Keller is at the Zoologisches Institut, Bern Vehrencamp’s original skew University, Ethologische Station Hasli, Wohlenstrasse models delineated the theoreti50a, 3032 Hinterkappelen, Switzerland, and lnstitut cal circumstances under which de Zoologie et d’Ecologie Animale, Batiment de incentives will be staying Biologie, University of Lausanne, 1015 Lausanne, offered, as well as the magnitude Switzerland; Kern Reeve is at the section of of these incentives. More reNeurobiology and Behavior, Seeley G. Mudd Hall, cently, the skew models4 have Cornell University, Ithaca, NY 14853, USA. been expanded to allow for situTheoretical advances ations in which peace incentives Models of the evolutionarily stable reproductive skew are offered by dominants to subordinates. The rationale have in common the critical assumption that the domifor the expanded theory, which is built on the edifice of nant member(s) of the society control reproduction of kin selection theorys7, is illustrated in Box 1.

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A key feature differentiating cooperative animal societies is the apportionment of reproduction among individuals. Only recently have studies started to focus on intraspecific variability in the distribution of reproduction wlthin animal societies, and the available data suggest that this variability might be greater than previously suspected. How can one account for intraand interspecific variability in partitioning of reproduction? This is one of the most intriguing problems in the study of social behaviour, and understanding the factors underlying this variability is one of the keys to understanding the properties of complex animal societies.

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