Testing Alternative Models of Social Evolution

Vickie L. Backus, Middlebury College

Joan M. Herbers, Ohio State University

Disney View of Social Insects

• Single queen• Workers who are all sisters (r=0.75)• Every individual working for the “good”

of the nest• Workers sacrifice own reproduction in

order to help mother because this increases her own inclusive fitness.

Real world view of social insects

•Number of queens can vary from 0–100’s•Workers may not be related to each other •Queens and workers may disagree on what is “best” for each other and the nest.

Potential conflicts in ant nests

• How many resources to invest in each offspring (packaging decisions)

• Invest in growth (workers) or reproduction (male and female alates)

• Invest in males or female alates (sexual allocation)

Leptothorax longispinosus

• <5 mm in length• Lives in pre–formed

cavities in northern temperate forest

• Nests usually <40 workers

• Multiple queens in nests

• Seasonal polydomy

Location of Studies

• VT site-Mallett’s Bay State Park

• NY site-Edmund Niles Huyck Preserve

Average Female Alate Weight

NY82 NY83 NY87 NY88 NY89 NY90 VT82 VT83 VT86 VT87 VT88 VT89 VT90

Data Set

Mean

fem

ale

weig

ht

(ug

)

How do nests decide how to package new ants?

• Herbers 1990 American Naturalist 136(2):178–208

• Backus 1993 Oecologia 95:283-289

• Both papers used path analysis but each paper took a slightly different approach to constructing the paths

Herbers 1990 Model A

• Path model where alate weight (GF and GM) are determined directly by nest demographics (Q=Queen number; W=Worker number).

Herbers 1990 Model B

• Alate weight (GF and GM) are determined after nests have decided how much energy to allocate to each sex.

• F= total biomass of females

• M=total biomass of males

Methods used by Herbers 1990

• Decompose the paths using the “rules” presented in Li 1975

• Standardize the variables (Q, W, GF, GM, F and M) with mean=0 and s2=1.0

• Calculate multiple-regression coefficients for the standardized variables=path coefficients

Methods of Herbers 1990

• Test internal consistency by comparing observed correlations of internal variables with that expected under the model

Testing internal consistency

• Expected correlation between GF and GM = qq’ + ww’ +qw’RQW + q’wrQW

Results of Herbers 1990 analysis

• Neither model showed consistent strong fit with the data but the fit was in the same direction for model A

Enhanced path model for packaging decisions (Backus

1993)• Nest demographics still

the heart of the model• Addition of maternal

effects (mean queen mass) as an independent variable

• Addition of worker packaging as a dependent variable

One other issue…

• Path analysis produces very large data sets

• E.G. 9 path coefficents for every data set analyzed

• Backus 1993 analyzed 6 data sets; Herbers 1990 another 7

Presentations in print can accommodate large data sets

• Large data table from Backus 1993 showing the path coefficients for the 6 data sets for each of 3 dependent variables.

Graphical presentation of data

• Both magnitude and direction of coefficients shown

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

NY82 NY83 NY87 VT82 VT83 VT86 VT87

Path Coefficients

Queen Number Worker Number

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

NY88 NY89 NY90 VT88 VT89 VT90

Path coefficients

Queen Number Worker Number Mean Q Mass

Packaging for female alatesHerbers 1990; Backus 1993

Data set Effect of Queen # Effect of Worker # Effect of Mean Queen Mass

NY82 + -- NA

NY83 - + NA

NY87 + -- NA

NY88 - - - + + + --

NY89 - + - -

NY90 NA NA NA

VT82 - - - - - NA

VT83 + - - - - NA

VT86 + - NA

VT87 + + + NA

VT88 - - - +

VT89 NA NA NA

VT90 NA NA NA

What did we find out about packaging decisions?

• Able to detect some detailed trends in packaging.

• Example of packaging of males from Backus 1993

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

NY88 NY89 NY90 VT88 VT89 VT90

path coefficients for males

Queen Number Worker Number Mean Q Mass

Two strong conclusions emerged:

• Significant queen worker conflict to packaging occurred.

• The proposed models don’t explain the whole story

Evidence of queen worker conflict in the path analysis

• Data for female alates as an example.

• Direction of coefficients different for queens and workers in 7/10 data sets

-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

NY82 NY83 NY87 VT82 VT83 VT86 VT87

Path Coefficients

Queen Number Worker Number

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

NY88 NY89 NY90 VT88 VT89 VT90

Path coefficients

Queen Number Worker Number Mean Q Mass

Explanatory power of the models was low.

Data Set Female mass

Male mass Worker mass

NY88 40 4.0 11.6

NY89 19.4 30.5 15.1

NY90 NA 9.4 18.3

VT88 8.8 25.0 39.0

VT89 NA 5.1 2.2

VT90 NA 2.2 6.3

Why so little variation explained?

• Many unexplained variables

• Requires a deep understanding of the biology of the system

• Clearest use of the technique is when you have two equally realistic models and want to determine which is correct

Queen–worker conflict in Hymenoptera

• Haplio-diploid sex determination system is critical

• Q-females, sons or workers r=0.5

• W-sisters (females or new workers) r=0.75

• W-brothers r=0.25

Prediction for sexual allocation decisions:

• Queens and workers have different optima for sexual allocation

• Queens prefer equal investment in new female alates and males.

• Workers prefer biased investment with most biased being 1:3 males:females

• Trivers and Hare 1976

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

NY81 NY82 NY83 NY87 VT82 VT83 VT84 VT85 VT86 VT87

Data set

Allo

cati

on

to m

ale

s (0

=all

fem

ale

)

Allocation to Males

• Herbers 1990 Am. Nat. 136(2):178–208.

• Leptothorax longispinosus

• Queen number and worker number as independent variables

• Final dependent variable is proportional allocation to males.

-60

-40

-20

0

20

40

60

80

100

NY81 NY82 NY83 NY87 VT82 VT83 VT84 VT85 VT86 VT87Percent of Variation of R explained

Q W

Major conclusions from Herbers 1990

• Evidence for significant queen-worker conflict

• Variation in the effect of nest demographics is important

• Nest demographics doesn’t explain

everything.

What about growth?

• Reproduction isn’t the only allocation decision that nests need to make.

• Backus (1995 American Naturalist 145(5):775–796)

• Added growth to the model.

• Tested alternative models for how nests may be making allocation decisions.

Comparing the two models

• Model A: proximate level factors important

• Model B: ultimate level (selection) important

Which model fits the data?

• Internal consistency tested.

• Compared the inferred correlation between GB and RB for both models with the observed correlations.

Best fit differed for the two sites.

Data Set Inferred by Proximate

Observed Inferred by Ultimate

NY88 .6037 .3768 .2340

NY89 .0466 -.0595 .0227

NY90 .0491 .0875 .1068

VT88 .0752 .0731 .0320

VT89 .1035 .1512 .0938

VT90 .1326 .0209 .1348

Further conclusions from the analysis of the two models:

• Natural selection is acting differently on the two populations

• Queen-worker conflict does occur over the decision to grow or reproduce.

• Nest demography is important

What has path analysis allowed us to conclude?

• Conflict occurs over all types of allocation decisions made ant nests

• Different populations have different levels of conflict

• Different populations may apply different rules to allocation decisions

• Nest demography is important but not the only factor to consider in allocation decisions.

Acknowledgments

• JMH’s work funded by National Academy of Sciences, E. N. Huyck Preserve, National Science Foundation

• VLB’s work funded by E. N. Huyck Preserve and Sigma Xi. Presentation of this talk funded in part by Middlebury College.

• Samuel Scheiner for inviting me to present this work.

And Especially…