Text and slides from an oral presentation at the meetings of the Society for Conservation Biology in Brasilia, Brazil, 17 July, 2005.




Thomas Olivier, Green Creek Paradigms, LLC, 4632 Green Creek Road, Schuyler, VA, 22969, USA, tolivier@starband.net




This paper analyzes genetic compositions and dynamics of matrilines in simulated monkey populations.  The simulations are built with CRITTRZ, an open-source population modeling library written in the Python computer language.  Structures and processes of simulated social groups resemble those found in some cercopithecine multi-male groups. Each group normally contains immigrant adult males and a natal segment composed of adult females and their immature offspring.   Each natal segment is organized into matrilines, groups of females related by descent through females and their resident immature male offspring.  Simulated groups may fission when large.  In group fissions, natal segments divide matrilineally. This study examines gene distributions in matrilines, matriline numbers and sizes in simulated monkey groups, and matriline influences on group fission processes.  In simulations series, multiple polymorphic loci are present in populations.  Simulation series vary depth of pedigree reckoning of matrilineal relationships and demographic circumstances.  Matrilines also may be defined by descent through females from females present in the founding population of each simulation.   The study also considers evolution over time of the numbers, sizes, distributions and genetic compositions of such matrilines. The implications of these results for conservation are discussed.


In this study I consider the influences of demographic circumstances and  depth of kinship reckoning on matriline numbers and genetic differentiation levels in simulated populations of monkeys.   This report is an exploratory application of CRITTRZ, a simulation system I released in test form in 2004.


CRITTRZ is built to support modeling of demographic, genetic and infectious disease processes in animal populations divided by space or social groupings.  In CRITTRZ applications, individual life histories are simulated in detail.  CRITTRZ is written in Python and currently runs on Windows computers. 


Beginning in the 1960’s,  long-term behavioral studies and molecular genetic surveys showed that many cercopithecine monkey populations were divided into social groups with complex internal behavioral and genetic structures.   In at least some species, matrilineal relationships strongly structured behavioral and genetic relationships within groups.  CRITTRZ has been developed in part to permit detailed modeling of processes sometimes seen in Old World monkey populations, such as those of the rhesus macaque.


In the research I report today, groups in model populations contain immigrant adult males and natal animal segments composed of matrilines.  Matrilines consist of adult females related by maternal descent and immature offspring of both sexes.  Model groups may fission when large, partly along matrilines, and they may fuse with other groups when small.  Males ordinarily leave their natal groups when they reach adulthood.  Males may change groups from time to time when adult.  The present model includes only social subdivision with no spatial distance effects.




In three run series,  age-specific birth and survival rates were set to set to produce expectations of population size stability.  In three series, demographic rates were set to create expected growth of about three percent per simulated time period.  In three series, demographic rates were set to produce a similar rate of decline. 


CRITTRZ maintains detailed information on kinship links among simulated individuals.  In the research I report today, for each demographic circumstance (that is, growing, stable and declining), one run series employs a kin link depth  of 1, another a value of 2 and a third 3.  Kin link depth values control the depth of pedigree links used to identifiy matrilineage members and thus the extent of the kinship network used to collect individuals in groups into matrilines. 


Each series consisted of 25 simulations run for 50 time periods. Model individuals may live a maximum of five time periods.  All simulations reported here used fission size threshold values of 40 and fusion values of 20.  The initial population for all simulations contained 664 individuals divided into 22 social groups.  Five autosomal polymorphic genetic loci were present in the initial population, with alleles randomly distributed among population members.  Unless otherwise specified, statistics presented were calculated every five time periods starting in time period 30.  Fission  analyses were conducted in all time periods greather than or equal to 30. 
























Figure 1.  Group FST Values


In Figure 1, FST genetic differentiation measures among groups are presented.  Mean simulation series values range roughly between 0.03 and 0.045.  Here, as in the report I presented at the 2004 SCB meetings (Olivier, 2004), group level differentiation is highest in the growing population series, intermediate in the stable series and lowest in the declining.  The FST values here also are quite similar to those obtained in last year’s models.  The graphs for each set of demographic circumstances are close to flat as kin link depths are varied, suggesting little influence of kin link depth on among subpopulation genetic differentiation levels.























Figure 2.  Natal Segment FST Values


If we eliminate the immigrant adult males from each group, we are left with natal segments.   These subsets of groups contain animals related by female descent.  As we might expect, Figure 2 shows genetic differentiation levels among group natal segments are higher than for entire groups.  The shapes of the series graphs are quite similar to those for complete groups, but FST values have been raised about  40 % over comparable group values.


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Figure 3.  Matriline Sizes in Groups.


Increasing kinship link depth potentially ties more individuals together into each matriline.   Figure 3 shows the mean numbers of live individuals per matriline in groups in different simulation series.  As we can see, matriline sizes increase from means of about 3 for all series with kin link depths of 1, to 8 for a link depth of 3 in the growing series.  The smaller sizes of matrilines in declining populations may reflect sparser occupancy by live animals in kinship trees assembled at a given kin link depth.























Figure 4.  Matriline Numbers in Groups


In the model, groups fission when large, approximately limiting the maximum sizes of groups and their natal segments.  We would thus expect a drop in matriline numbers as kin link depths and matriline sizes increase.  Figure 4 shows that indeed this is the case.    At a kin link depth of 1, where matriline sizes were small,  six or seven matrilines were present on average in each group.  At a depth of 3,  only 3 or 4 matrilines were found.  Note here that in declining populations, where matrilines were smallest, the highest number of matrilines was found.  In the growing series, where sizes were largest,  the lowest numbers of matrilines were present.






















Figure 5.  Matriline FST Values.


Figure 5 makes clear that a strong decline in differentiation levels among matrilines occurs with kin link depth increases.  Note too that differentiation levels among matrilines within groups are higher than differentiation among groups or group natal segments.  These graphs imply FST values decrease with increasing matriline sizes.   Olivier et al. (1981) presented a model that predicted FST values among matrilines should be inversely proportional to matriline sizes and directly proportional to kinship coefficients in matrilines.   The shapes of these graphs seem broadly consistent with those predictions.






















Figure 6.  Matriline Numbers in Fissioning Groups.


Groups fission when they become large.  Figure 6 shows that groups that are about  to fission contain about a third more matrilines than population averages.  Matriline sizes  were somewhat larger than average – roughly 10 – 20 %.  Within group matriline FST values generally were a few percent lower than previously shown population means.






















Figure 7.  Fission Product Pairs.


We might wonder how kin link depth variations will influence genetic differentiation among fission product groups, particularly with respect to lineal effects. By lineal effect I refer to a tendency of genes identical by descent to join the same fission product group due to group subdivision along kinship lineages, commonly elevating differentiation levels above those expected in simple random allocation processes.  Greater depths of kin reckoning means that larger groups of matrilineally related animals will join the same group.    However,  the degree of genetic similarity among the larger matriline members will be less.  


At the bottom of Figure 7 we see differentiation in fission product group pairs.  Values for all demograhic circumstances and kin link depths are near the value of 0.02.  A simple random allocation of alleles would be expected to produce FST values of about 0.0125 or less.  Observed mean values of 0.02 or higher suggest a ‘lineal effect’ in FST values due to fissioning along matrilineal kinship lines has occurred.   As expected,  values for natal segments higher – generally at or slightly above 0.03.  A study of genetic differentiation is fission product groups in the Cayo Santiago rhesus monkey population ( Buettner-Janusch et al., 1983) found that lineal effects occurred and that differentiation levels between natal segments were higher than for entire groups.  These values for fission product group pairs also are lower than the population means for natal segment FST’s.


I thought I might find an increase in FST values in fission product pairs with kin link depth within each simulation series.  If anything,  a slight peaking occurs at the intermediate depth value of 2.  This relationship is something I hope to examine further.






















Figure 8.  Gro Fission Product Groups


How differentiated  is the set of all fission product groups relative to those in the population at large?  Fission product groups tend to be  small with natal segments necessarily based on  a relatively  small number of matrilines, and might well be more differentiated than average.  I had not intended to look at this when designing the simulations.   However, it was possible to extract from simulations logs the two frequencies at each locus possessed by fission product groups, though not associated with the sizes of groups possessing each frequency.  I calculated FST values ( without group size weighting  ) among all fission product groups in growing series groups.  Values were calculated for time periods >=30 where at least five fissions occurred ( and thus at least 10 fission product groups were created).   I confined this analysis to later time periods in the growing series because fissions per time periods were elevated there.


Figure 8 shows these values are about 20% to 40% higher than comparable average gro series FST mean values.  The consistently higher FST values seen in gro series  simulations may be due to the higher proportion of groups that have recently fissioned.  I aim to investigate this more fully in later simulations.






















Figure 9.  Remaining Female Lineages.


Figure 9  illustrates the decline in numbers of founding female lineages over time in the simulation series.  One can see that the least decline occurred in growing simulated populations and the most in declining populations. 




CRITTRZ has displayed an ability to model interactions between a variety of processes in model populations with complex, dynamic structures.  As so often is the case with simulations, some things in the modeling reported today were as expected, some results were a bit different and some things due further examination were identified.


Conservation often deals with small populations – isolated fragments, threatened declining populations or the beginnings of exotic invasions.  CRITTRZ is designed to deal with populations of these types.   I am about to add GIS support for groups with dynamic home ranges. With an expanding ability portray landscapes occupied by populations in GIS raster files,  the system should lend itself to modeling scenarios in real populations of interest.















Figure 10 – Contact and Further Information


Figure 10 presents my email address and the home page for the CRITTRZ package.    The home page for the CRITTRZ packages is part of the Green Creek Paradigms web site.  The home page provides links to previous studies that use this system and documentation.  CRITTRZ is open source software and can be downloaded for free.  Figure 10 also provides the link to the SourceForge project page with the download site.


Thanks for your attention today.




I thank my wife Wren for her encouragement during the development of CRITTRZ.




Buettner-Janusch, J., T.J. Olivier, C.L. Ober and B.D. Chepko-Sade.  1983.  Models for       Lineal Effects in Rhesus Group Fissions.  Am. J. Phys. Anthropol. 61:347-353.


Olivier, T.J. 2004.  Interactions Between Social, Genetic and Demographic Processes in Simulated Monkey Populations.  Poster presented at the Society for Conservation Biology Meetings, 31 July 2004.  New York, NY.


Olivier, T.J., C. Ober, J. Buettner-Janusch and D.S. Sade.  1981.  Genetic Differentiation Among Matrilines in Social Groups of Rhesus Monkeys.  Behav. Ecol. Sociobiol. 8:279-285.