doi: 10.1111/j.2041-210X.2011.00148.x
Methods in Ecology and Evolution
APPLICATION
PMx: software package for demographic and genetic
analysis and management of pedigreed populations
Robert C. Lacy1*, Jonathan D. Ballou2 and John P. Pollak3
1
Chicago Zoological Society, Brookfield, IL 60513, USA; 2Smithsonian Conservation Biology Institute, Washington,
DC 20008, USA; and 3Cornell 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; Fernández & 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. E-mail: [email protected]
Correspondence site: http://www.respond2articles.com/MEE/
wild populations (e.g. Land & Lacy 2000; Leus & Lacy
2009).
The PMx software package for pedigree analysis and management 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
Lincoln Park Zoo (Faust et 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).
2011 The Authors. Methods in Ecology and Evolution 2011 British Ecological Society
2 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.
2011 The Authors. Methods in Ecology and Evolution 2011 British Ecological Society, Methods in Ecology and Evolution
PMx software for pedigree analysis 3
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.
2011 The Authors. Methods in Ecology and Evolution 2011 British Ecological Society, Methods in Ecology and Evolution
4 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.
2011 The Authors. Methods in Ecology and Evolution 2011 British Ecological Society, Methods in Ecology and Evolution
PMx software for pedigree analysis 5
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 programming environment. It is compiled to run under both 32-bit and 64-bit versions of Windows, 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 20 000 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.
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Received 20 May 2011; accepted 27 July 2011
Handling Editor: Emmanuel Paradis
2011 The Authors. Methods in Ecology and Evolution 2011 British Ecological Society, Methods in Ecology and Evolution