PMx: software package for demographic and genetic analysis and management of pedigreed populations

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1 Methods in Ecology and Evolution 2012, 3, doi: /j X x APPLICATION PMx: software package for demographic and genetic analysis and management of pedigreed populations Robert C. Lacy 1 *, Jonathan D. Ballou 2 and John P. Pollak 3 1 Chicago Zoological Society, Brookfield, IL 60513, USA; 2 Smithsonian Conservation Biology Institute, Washington, DC 20008, USA; and 3 Cornell University, Ithaca, NY 14853, USA Summary 1. The concepts and algorithms for demographic and genetic analysis of pedigreed populations have been evolving rapidly in recent years. 2. The PMx software brings together into one integrated package a number of tools for pedigree analysis, including methods for dealing with missing, uncertain and probabilistic data not previously available in distributed software. 3. PMx provides tools for optimal demographic and genetic management of populations of wildlife species, rare domestic breeds, and other populations for which the primary goal is to conserve genetic diversity, and it is being implemented as the primary pedigree management tool for the breeding programmes of zoo associations around the world. 4. PMx can be used to characterize the demography and genetics of any captive or wild population for which pedigree and life-history data are available. Key-words: conservation breeding, conservation genetics, demographic analysis, pedigree analysis, population management, population modelling Introduction Breeding programmes aimed at the conservation of wildlife species seek to sustain demographically stable populations that retain as much as possible of the genetic diversity of the source populations (Foose & Ballou 1988; Hedrick & Miller 1992; Lacy 1994, 2009; Frankham, Ballou & Briscoe 2010). Over the past decades, pedigree analysis methods have been developed to provide historical summaries, descriptions of current status, guidance on setting population goals and the selection of breeders, and projections of future trends for both demographic and genetic aspects of managed populations (Ballou & Lacy 1995; Lacy et al. 1995; Fernández & Toro 1999; Ferna ndez & Caballero 2001; Sonesson & Meuwissen 2001; Fernández, Toro & Caballero 2003, 2004; Ballou et al. 2010). Software tools that implement evolving pedigree analysis and management techniques have been widely available and used in the zoo community (Pollak, Lacy & Ballou 2002), and have been used to a lesser extent for management also of breeding programmes for wildlife breeding centres outside of zoos and for intensively managed *Correspondence author. rlacy@ix.netcom.com Correspondence site: wild populations (e.g. Land & Lacy 2000; Leus & Lacy 2009). ThePMxsoftwarepackageforpedigreeanalysisandmanagement was recently released (Ballou, Lacy & Pollak 2011) to update, consolidate, and extend the analyses previously available. PMx accepts data on pedigreed populations ( studbooks ). It was designed to work with pedigree data maintained in the SPARKS studbook software that is distributed by the International Species Information System (ISIS 2011) or in the PopLink studbook software developed by the LincolnParkZoo(Faustet al. 2009). However, PMx can also accept pedigree and life-history data from a variety of database programmes, as long as the data can be transferred in specified formats; specifications for PMx input files are provided in the manual. Components of PMx PMx contains sections for Project Notes, population designation (Selection), Demography, Genetics, determining Goals for population management, and recording Recommendations regarding which animals to breed and to whom. The primary features available within each section are listed here; full descriptions are provided in the manual (Traylor-Holzer 2011). Ó 2011 The Authors. Methods in Ecology and Evolution Ó 2011 British Ecological Society

2 434 R. C. Lacy, J. D. Ballou & J. P. Pollak SELECTION The section provides a listing of all animals in the studbook, with the option to specify which should be included in the analysed population. Tallies of the current population size and age structure will include only the living animals. Genetic analyses of the current population are based on the living animals, but a historical trend of genetic diversity will tally those selected animals alive at the end of each year. Ancestors in the pedigree of selected animals, whether or not the ancestors themselves were selected, will be used as needed in the calculations of kinships and inbreeding of their descendants. DEMOGRAPHY The Demography section provides life-table projections of population growth from birth and death rates (Ebert 1999), the ability to model the effects of changes in rates, tools for exploring the consequences of different management strategies (e.g. harvesting or supplementing the population), and means to determine the numbers of births or deaths needed to achieve demographic goals (Ballou et al. 2010). The sections under demography include the following: Overview (Fig. 1) Presents population level summary information such as number living individual by sex, of reproductive age, of post-reproductive age; summary of the life table (per cent animals surviving to different ages); average reproductive rates; population growth statistics (r, k, R0). After stochastic simulations have been run (under the Projections Tab), this summary will also include 95% confidence intervals for most of these parameters, including probabilities that the population will grow or decline over the next year. Male and Female Life Tables Male and female life tables showing Kaplan Meier (Kaplan & Meier 1958) estimates of survivorship (lx), annual age-specific survival and mortality rates (px and qx), life expectancy (Ex), fecundity (Mx), and the sample sizes used to calculate those rates. Actual and Model life tables are presented for each sex, and the user can modify survival and reproductive rates in the Model life table to explore the effects of changes in reproduction or survival. Age Distribution Shows an age pyramid figure and grid with the number of animals in each age and sex class. An animation function allows the user to see the expected changes in the age distribution over the next several years. The age pyramid can be filtered to show only individuals in defined regions, or with particular characteristics (e.g. founders, successful breeders). Census Shows census data (number, by sex, of births, deaths, imports, exports, captures and releases) over time. Seasonality Presents births or deaths by month in a chart. Two charts are shown so that seasonality for different groups can be compared (e.g. compare birth seasonality in some locations to seasonality in other locations). Data can be filtered by region, country, institution, or sex. Chi-square tests are provided to test differences between seasonality distribution, and if a distribution is significantly different from uniform. Projections Shows a deterministic or stochastic projection of the population. Deterministic projections are derived by applying fecundity and survival rates to the number of individuals in each age-sex class, and iterating across years (Ebert 1999; Ballou et al. 2010). For stochastic projections, an individual-based simulation is run in which each individual survives with the probability determined by its age and sex, and number of offspring produced by each female is sampled from a Poisson distribution with the mean set to the agespecific fecundity, under the constraint that there must be Fig. 1. Demography Overview screen of PMx software for pedigree analysis. Detailed demographic analyses and tools to guide management of breeding programmes are provided in subsequent tabbed sections. Analyses shown in this and subsequent figures are solely for the purpose of illustrating the PMx screens, and the data should not be assumed to be a current and accurate analysis of any real population.

3 PMx software for pedigree analysis 435 sufficient adult males available for the breeding females. Deterministic projections are adequate for large populations (those with 1000s of individuals), but stochastic projections are more realistic for smaller population size, as skewed sex ratio and other chance events will typically depress and cause large variation in population growth (Lacy 2000). The stochastic projection in PMx shows each projected simulation and the mean and 95 percentiles over all simulations. There is an option to project the future trends in the population size without any births (which is useful for modelling populations that are being managed to extinction). Reproductive Planning Here, the user can set a population growth goal (e.g. Grow from 100 to 120 animals over the next 2 years ) and, based on the Model life tables, be provided with the number of breeding pairs and births needed to achieve that goal. Add Remove This allows users to model the impact of removing animals from or supplementing animals to the population. Availability Informs the user how many animals might be available for removal (e.g. for a reintroduction programme) while trying to maintain certain population size or growth goals (e.g. How many males of age 4 6 and females of age 4 8 could be removed while maintaining the population at a given size? ). Graphs Provide the user with a number of standard graphs of life table or census data that can be exported to image files. Settings Options to change a number of parameters, including: the length of an age class (e.g. monthly rather than annually for species with shorter life spans); how the life tables deal with unknown sexed individuals; specifying if the life table is from a birth pulse species, or a birth flow species; the number of iterations run in the stochastic projections. GENETICS The Genetics section provides the genetic diversity retained through the generations, kinships and related metrics (such as inbreeding coefficients), measures of genetic value of individuals, tools for selecting individuals for pairing or culling to maximize retention of genetic diversity, and means to examine the effects on within and between subpopulation diversity of partitioning the population into subpopulations or management units. Most of the genetic results are based on kinship calculations, but some values that cannot be calculated analytically (such as the probability of founder allele retention through the generations) are determined from a simulation of allele transmission. Lacy (1995) and Ballou et al. (2010) provide explanation of the measures of genetic variation calculated by PMx. The primary features included as tabbed sections within Genetics are the following: Summary Statistics (Fig. 2) Basic descriptors of the genetic status of the current population, together with a graph of change over time in gene diversity and population size. Overview A more detailed listing of population genetic values, including also estimates of effective population size and a table of all genetic values over the history of the population. Founders A list of the animals at the top of the pedigree that contributed genetically to the living descendant population. This table includes measures of the contribution of each founder to the living population and the proportion of its alleles surviving in descendants. Individuals A list of all animals in the selected population, with all data available for each. Data include identifiers, basic pedigree data (e.g. parentage, sex, birth date, death date, location), reproductive history (e.g. mates, Fig. 2. Summary screen listing primary genetic statistics calculated by PMx pedigree analysis software. Detailed genetic analyses and tools to guide management of breeding programmes are provided in further screens.

4 436 R. C. Lacy, J. D. Ballou & J. P. Pollak progeny, years of reproduction, current status of being fertile contracepted sterile), and genetic parameters (e.g. inbreeding, per cent ancestry known, mean kinship to the population, and measures of the uniqueness of its alleles in the population). Kinship matrix The pairwise coefficients of kinship (coancestry) for all animals, with options to filter which animals are shown, sort the order of animals, export the matrix, or import kinship values derived in some other way (such as through analysis of DNA markers) to replace, or be averaged with, values calculated from the pedigree. Pairwise information A matrix of values for all possible male by female pairings, reporting measures of the value of that pairing to retention of gene diversity in the population. Values available for display include inbreeding coefficients of progeny, change in population gene diversity if an offspring is produced, and mate suitability indices using the algorithms of the MateRx software (Ballou, Earnhardt & Thompson 2001). Pairing A tool to guide selection of breeding pairs, in order to maximize gene diversity within management constraints. This section provides the option to sort lists of males and females by various measures of genetic value, displays genetic consequences of any proposed pairing, and dynamically updates the genetic measures and the ordered list of priority breeders as pairs are designated and expected reproduction is tallied. It also provides several automated methods for designation of the set of pairs that would maximize gene diversity in the population. Culling A tool for selection of the genetic impact on the population gene diversity of the removal of any animals. This section provides an ordered list of priority animals for removal, dynamic recalculation of the value of each animal to the population gene diversity after prior cullings are com- pleted, and calculation of the optimal set of animals to be culled. Management sets Provides an option to designate subpopulations for genetic analysis. These sets do not have to be exclusive or contain all animals in the full population. Gene diversity and mean inbreeding are calculated for each management set, and statistics provided to summarize each pairwise comparison include Fst measures of the proportion of genetic variance between subpopulations (Wright 1969) and the mean between-subpopulation kinships. Tools are provided to allow testing of the effect on source and recipient subpopulations of moving any animal, and a matrix of all possible moves allow determination of the optimal location for each animal. Graphs Provides line graphs of changes over the history of the population of population genetic statistics (e.g. gene diversity, mean inbreeding, founder genome equivalents), histograms of measures of founder representation and individual characteristics, and two-way scatterplots of any two population variables, founder variables, or individual variables. Genetic Settings Pedigrees often have data gaps individuals with unknown parents or with several possible parents. Kinship calculations and all genetic measures derived from kinships (e.g. population gene diversity, inbreeding) can assume that unknown parents are unique founders, or portions of an animal s pedigree that are unknown can be omitted, or unknown portions of a pedigree can be given reduced weight in genetic calculations. If there are multiple possible parents recorded for an animal, PMx can exclude those uncertain parents (treating them as unknown), can assume that the most likely parent is the correct one, or can probabilistically average across the possible parents to derive weighted mean individual and population statistics. Fig. 3. Goals modeling tool of PMx software for determining demographic and genetic values that will allow a specified level of genetic diversity to be sustained.

5 PMx software for pedigree analysis 437 GOALS The Goals section (Fig. 3) integrates demographic and genetic analyses into a modelling tool for determining the combination of demographic values (population size, growth rate and generation time) and genetic values (effective population size, starting gene diversity) that will achieve a goal of sustaining a desired level of gene diversity over time. It can solve for the necessary value for any specified parameter, including the number and timing of new founders for restoring depleted gene diversity. RECOMMENDATIONS A Recommendations section provides a means to record and report the breeding and transfer recommendations for each individual. Pairings, culls and transfers among managed subpopulations that were specified in the Genetics section will be automatically transferred to the Recommendations section. Technical requirements PMx was developed in the C# programming language, using the Microsoft Visual Studio.NET Ò programming environment. It is compiled to run under both 32-bit and 64-bit versions of Windows Ò, with the Microsoft.NET Framework 4 Client Profile installed. There is no hard-coded limit on the size of the pedigree that can be analysed, although memory and operating system limitations of file size will usually limit the analyses to no more than individuals (requiring 1Æ6 GB RAM just to hold the full matrix of all pairwise kinships); PMx is not intended for analysing large populations of domesticated animals. For populations of 1000 living animals or fewer, as is typical of breeding programmes for wildlife and for rare breeds, PMx requires about 20 MB RAM to store calculations. The use of PMx is described in detail in a user s manual (Traylor-Holzer 2011; included in the PMx installation). PMx is copyrighted, but it is distributed as freeware. Acknowledgements PMx benefited from input and testing by a large number of colleagues, including Rajan Amin, Laurie Bingaman Lackey, Lisa Faust, Jamie Ivy, Kristin Leus, Sarah Long, Colleen Lynch, Jennifer Mickelberg, Kanako Nishimoto, Paul Pearce-Kelly, Kristine Schad and Kathy Traylor-Holzer. PMx was developed with support from the Institute of Museum and Library Services, Association of Zoos and Aquariums (AZA), Chicago Zoological Society and Smithsonian Institution National Zoological Park. References Ballou, J.D., Earnhardt, J. & Thompson, S. (2001) MateRx: Genetic Management Software. Smithsonian National Zoological Park, Washington, DC. Ballou, J.D. & Lacy, R.C. (1995) Identifying genetically important individuals for management of genetic diversity in pedigreed populations. Population Management for Survival & Recovery. Analytical Methods and Strategies in Small Population Conservation (eds J.D. Ballou, M. Gilpin & T.J. Foose), pp Columbia University Press, New York. Ballou, J.D., Lacy, R.C. & Pollak, J.P. (2011) PMx: Software for Demographic and Genetic Analysis and Management of Pedigreed Populations (Version 1.0). Chicago Zoological Society, Brookfield, Illinois. vortex9.org/pmx.html. Ballou, J.D., Lees, C., Faust, L.J., Long, S., Lynch, C., Bingaman Lackey, L. & Foose, T.J. (2010) Demographic and genetic management of captive populations. Wild Mammals in Captivity: Principles and Techniques for Zoo Management, 2nd edn (eds D.G. Kleiman, K.V. Thompson & C.K. Baer), pp University of Chicago Press, Chicago. Ebert, T.A. (1999) Plant and Animal Populations: Methods in Demography. Academic Press, San Diego. Faust, L.J., Bergstrom, Y.M., Thompson, S.D. & Bier, L. (2009) PopLink ver 2.1. Lincoln Park Zoo, Chicago. Fernández, J. & Caballero, A. (2001) A comparison of management strategies for conservation with regard to population fitness. 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(2001) Minimization of rate of inbreeding for small populations with overlapping generations. Genetical Research Cambridge, 77, Traylor-Holzer, K. (ed.) (2011) PMx Users Manual. Version 1.0. IUCNSSC Conservation Breeding Specialist Group, Apple Valley, Minnesota. Wright, S. (1969) Evolution and the Genetics of Populations, vol. 2. The Theory of Gene Frequencies. University of Chicago Press, Chicago. Received 20 May 2011; accepted 27 July 2011 Handling Editor: Emmanuel Paradis Ó 2011 The Authors. Methods in Ecology and Evolution Ó 2011 British Ecological Society, Methods in Ecology and Evolution, 3,