### Data

We received pedigree data via ISIC [12] of the population of Icelandic Sheepdogs in the following countries: the Netherlands (725 records), Sweden (1367), Iceland (1654), Germany (153), Norway (774), Denmark (2241) and Finland (113). Pedigree data contained unique ID, father, mother, gender, date of birth, country of birth, and occasionally date of death. Only Iceland had data since 1955. In other countries, breeding started in 1975 or later and most of the data went up to 2002 and some only up to 1998. Except for a few dogs in France, these countries cover the entire Icelandic Sheepdog population. Animals without recorded parents were classified as either (1) 'original founders': animals without any relationship with other founders, documented as such by the kennel clubs, or (2) 'related animals with unknown parents': animals that descend from the 'original founders' or their progeny, but having unknown parentage. Furthermore, some individuals were registered in more than one country. The pedigree data were assembled into a single database table, and animals that were recorded twice were removed based on information on the country of birth. The problem of 'related animals with unknown parents' was solved by assembling all datasets with additional information on parentage from ISIC. After this process, only the original founders had unknown parents. The equivalent complete generations traced for each animal was computed as the sum of the proportion of ancestors known per generation [13]. Until 1998, pedigrees were complete for all countries. A general life expectancy was estimated separately for males and for females from the interval between date of birth of parents and progeny. If date of death was not recorded, it was estimated by life expectancy. All animals born between 1991 and 1998 were considered as the 'current-population'.

### Population diversity measures

Unless otherwise stated, inbreeding and kinship coefficients were calculated using the tabular method. Except for optimal contributions, which were calculated using Fortran, all measures were calculated using Visual Basic. Mean kinship was proposed by Ballou and Lacy [

6] and is the mean of the kinship coefficients between that individual and all candidates, including the individual itself. Candidates are defined as reproductive individuals of the current population. The mean kinship (

*mk*
_{
i
}) for individual

*i* is calculated by Ballou and Lacy [

6] as:

where *N* is the number of candidates and *f*
_{
ij
}is the kinship between individual *i* and individual *j*. The mean kinship of an animal is a measure of the relationship of that individual with a population; animals with a low mean kinship are more valuable for genetic diversity. Mean kinship depends on the population which means that the mean kinship of an animal might change over time when a population changes. In conservation genetics, mean kinship is an important tool to maintain genetic diversity [14].

The following population diversity measures were used:

Average inbreeding (
) is the average of the inbreeding coefficient of all candidates.
indicates the current risk of inbreeding depression in the current population.

Average mean kinship (

) is the average of mean kinships of all candidates within the population under study [

6], and was calculated as:

Average *mean* kinship, which is predominantly used in conservation [2, 6], differs from average *pairwise* kinship because
includes kinship of animals with themselves.

In this work, genetic diversity (*N*
_{
mk
}) is defined as the number of equally contributing founders with no random loss of founder alleles in descendants that would be expected to produce the same average mean kinship (and therefore genetic variation) as in the population under study. *N*
_{
mk
}is
expressed on the scale of founder genome equivalents [15, 16] and is calculated by *N*
_{
mk
}= 1/2
. A lower average mean kinship means a higher genetic diversity and thus a higher capacity to adapt as a population.

In this work, allelic diversity (*N*
_{
AD
}) is defined as half the number of distinct alleles that are still present in the population under study if all founder alleles were unique. The number of unique founder alleles that survive each year was determined by genedrop [17], which was repeated 10.000 times. *N*
_{
AD
}is also expressed in founder genome equivalents and can therefore be compared with *N*
_{
mk
}and *N*
_{
OC
}(see below). For example, if the frequencies of all alleles were equal, *N*
_{
AD
}would be equal to *N*
_{
mk
}. *N*
_{
AD
}monitors the loss of genetic diversity due to extinction of unique (founder-) alleles.

In this work, potential diversity (

*N*
_{
OC
}) is defined as the maximum genetic diversity the population under study can achieve (expressed in founder genome equivalents).

*N*
_{
OC
}is the genetic diversity obtained when average mean kinship is minimised using Optimal Contribution Selection.

*N*
_{
OC
}is calculated as described in Oliehoek

*et al*. [

18]:

where

**F** is a matrix of kinships between all individuals, including kinship of individuals with themselves, and

**c**
_{
OC
}is a column vector of proportional contributions of individuals to the next generation, so that the sum of elements of

**c**
_{
OC
}equals one and minimises

**c**
_{
OC
}
**'Fc**
_{
OC
}[

19].

**c**
_{
OC
}is given by Eding

*et al*. [

20]:

where **1** is a column vector of ones. **c**
_{
OC
}contains contributions of parents to next generations that would minimise
in next generations. However, **c**
_{
OC
}calculated from Equation 4 can contain negative contributions, which is impossible in practice. When negative contributions were obtained, the most negative contribution was set to zero and vector **c**
_{
OC
}was recalculated until all contributions were non-negative. *N*
_{
OC
}is the highest possible *N*
_{
mk
}and measures the diversity that could be obtained in next generations. *N*
_{
OC
}will always be equal or higher than *N*
_{
mk
}and equal or lower than *N*
_{
AD
}. *N*
_{
OC
}is relevant in the case of closed populations, since the population can never reach a diversity higher than *N*
_{
OC
}. Therefore, it monitors the unrestorable loss of genetic diversity.

### Cluster-analysis

Cluster-analysis was performed twice on the current population. (1) The first analysis was based on kinship calculated using the tabular method starting with the founders and then UPGMA was applied for clustering all animals [21]. To determine the most appropriate number of clusters, *R*
^{2}, the cubic clustering criteria and pseudo- *F* statistic were all examined (SAS Institute, release 9.1, Cary, NC, USA). These clusters are displayed in a dendrogram, which is referred to as the all-gen-tree. (2) The second cluster-analysis was performed as described by Ubbink *et al*. [4]. Kinships between all animals were calculated by the path method [22] until seven generations backwards (instead of the tabular method that includes all generations). Note that if the path method included all the generations, results would be equal to the tabular method. Then, all the animals were clustered using UPGMA. Subsequently all the clusters having an average mean kinship greater or equal to 0.0625 were defined as the final clusters and displayed in a dendrogram. This kinship value of 0.0625 that delimits clusters corresponds with kinship between second degree cousins and was used by Ubbink *et al*. [4]. This dendrogram is referred to as the 7-gen-tree.