© Lauri Kahanpää 2007. Updated Jan. 9. 2007
To evaluate international and national action plans for the protection of the Lesser White-fronted Goose (LWfG) Anser erythropus, best possible information about the species, its biology and current status, is of truly vital importance. Today, a wealth of such information is available. Based on this, it is possible to calculate the future of the various European populations of the LWfG in detail in dependence of chosen protection measures. This is done in the computer model "Effects of Protection Measures for Lesser White-fronted Goose in Europe including European Russia" implemented in the document "Effects.xls" (Attachment). The model allows any inputs of fundamental parameters like juvenile, sub-adult and adult mortality and initial numbers of birds - for six interacting populations. Similarly, the model's user may give numerical values describing various protection efforts. Once these data are fed in, the model automatically forecasts the future of six European LWfG populations and displays the results as charts.
The model consists of two interacting halves, the first one just illustrating the input basic facts by a simplified no-action scenario, the second forecasting the effects of restocking.
This background document gives references on underlying numerical data, and explains the calculations. Finally, some conclusions become obvious in the light of the present data and logic. For a general background on LWfG conservation, the reader is referred to [NOF 2005] and [F].
To facilitate the use of the model, the biological background data is concentrated to the following parameters, which the user may feed into the model for four populations separately:
The four populations are labeled "Norway", "Sweden", "Captive Dynamics", and "Russia (European)", respectively. To reveal possible misprints in input and to illustrate the meaning of these inputs, the model generates four introductory diagrams illustrating and comparing independent growth of these populations.
The theoretical populations are intended to represent existing European LWfG. This is expressed as default values for inputs in the model. The given values are by no means arbitrary but are chosen to correspond to the current status of observations. The values are discussed below.
1.1.1. Norway
The default values used for input data labeled "Norway" represent the remaining Norwegian population. Since 1993, this population is carefully monitored by a non-interrupted series of LifeNature- sponsored studies (BirdLife and WWF). Estimates of the parameters were originally published in [NOF 1997]. The most recent summary [WWF 2004] has not changed the overall picture, in particular not the overall trend of about -5 percent for the population. In [NOF 1997], the estimate on nativity was given as 1,2 for each adult pair, the number based on observations of the ratio of juvenile to parent birds at autumn staging. Since not all adults breed, this gives a nativity closer to 0,5 than 0,6. According to [WWF 2004] 225 adult pairs (495 individuals including 45 other (sub)adults) were observed in spring and 334 juveniles were seen in autumn during 1994-2003. This gives a ratio of 0,67. According to [VF 2003], 40 per cent of spring pairs were successful in breeding with an average brood size of 3,0. This gives the ratio 0,6. In [NOF 1997], the mortality in the first calendar year (0,7) was measured by a couple of indicators, and then the average adult mortality (0,165) was calculated from the observed fact that the total Norwegian LWfG population was shrinking 5 per cent a year. The present model's default "Norwegian" mortalities 0,78 and 0,16 are the values in [VF 2003]. The default spring numbers for the "Norwegian" population are simply averages of the monitoring program's Norwegian observations in 2004-2006 [WWF 2004]. There exists strong evidence that essentially all Norwegian LWfG are indeed directly counted: according to [LUU 2005] all (up to one pair) those LWfG who during migration through Estonia and Finland were individually identified by observing their individual dark belly patches were later seen at the known staging ground in Norway!
1.1.2. Sweden
The default values used for the input data labeled "Sweden" represent the Swedish reintroduced population. The default values for mortality, nativity and initial numbers were originally adapted from the mean values for 1995 to 1998 in table 1 in [E 1999] and for 1999 from the annual report of the Swedish project. In particular, the default nativity ratio 0,3 corresponds to the breeding success of year 1999, reported in [E 1999]: a well documented population of 31 Swedish LWfG in fertile age were observed to have produced at least 10 goslings. According to [A], there were about 20 fledglings in 2002 and 2003. This is 20 per cent of the total population, 60 per cent of which can be estimated to be adult or subadult birds. This would give a nativiti index of 0,34. The default values of annual mortality were calculated from [E 1999] for the first four years. This data builds on direct observations of colour ringed birds, both in the breeding area and during spring and autumn migration. The default life span is based on a recent observation reported directly to the author.
There was later corroboration of this original mortality data. At the GOOSE 2001 conference of Wetlands International in Roosta (Estonia) the author published a first prediction on the future of the Swedish population building on this data. The Roosta model was more detailed than the present version. It included a total follow up of all vintages of Swedish reintroduced geese. Later, at the GOOSE 2004 conference in Odessa, a follow up including a comparison with two more years of data and with an advanced stochastic differential equations model was presented. All models give essentially the same predictions and are well in harmony with observations.
Since 2000, there is a temporary interruption in the Swedish restocking program and currently the population is growing with its "natural growth rate". On the other hand, the absence of further colour ringing makes it impossible to monitor young individuals. The default initial values for the Swedish population are taken from reports of the Swedish restocking programme [A] and the, still unfinished, Swedish National Action Plan draft [Nat 2006]. These numbers, with a total population of 100 LWfG, reflect observations in Sweden. The Swedish LWfG migrate to the Netherlands. Dutch observations, carefully documented and analyzed in [KOF 2006] point at a winter population encompassing up to 120 individuals.
1.1.3. Captive Dynamics
The default mortalities, nativity and maximal life span for captive LWfG correspond to the author's 15 years of bookkeeping at the Hämeenkoski LWfG farm in Finland. Under less arctic conditions like in Sweden or Germany, better mortality proportions may prevail. Also, conditions at the Finnish farm may still be improved, if funds are found for this purpose.
The initial number of birds labeled "Captive Dynamics" is essentially arbitrary, and the resulting diagram reflects mainly the effects of the mortality/nativity input.
In the part 2, the "Captive Dynamics" input mortalities, nativity and maximal life will be adapted from part 1, so the model treats them as typical for all captive populations. In contrast, there are special inputs in part 2 for the initial numbers of "Swedish" and "Finnish" captive birds since these numbers are not biological data but subject to human decisions.
1.1.4. Russia (European
The default data on the Russian European population corresponds to the information in [Nat 2006]:
The losses above correspond to annual loss percentages of between 2 and 6 per cent.
1.1.5. Other inputs
The inputs labeled "Max life span" and "Immigration from Norway to Sweden" belong to part 1, since they represent the user's view on biological background facts. To keep things simple for the moment, these parameters have no effect at all on the output in part 1. They will be taken into account in part 2. Their significance is discussed in section 2.2.2.
In part 1, the model's user is supposed to choose input values for the "biological background" parameters listed above in 1.1. The model then generates three introductory diagrams illustrating ten years of independent growth of the populations labeled "Norway", "Sweden", "Captive Dynamics", and "Russia (European)". These first charts mainly intend to illustrate the meaning of the basic input. A fourth diagram illustrates the relatively large uncertainties in the European Russian population data from different sources, by displaying the best and worst scenario together with the scenario corresponding to the chosen input data. In addition, three numbers characterizing the growth of each population are displayed. These are the average annual growth rate, the growth rate in the year 2015, and the population's net growth in the ten years from 2007 to 2016.
The model successively calculates the numbers of 2 cy, 3 cy and adult birds for each year and each population and then displays their sums in the charts. Basically, the number of geese in each following year is calculated by subtracting from the current number the number of those geese that will die according to the mortality assumption. This is done separately for survival in the first and second winters and uniformly for "adult" birds in their later years. Of course, 2 cy in autumn corresponds to 3 cy birds next spring. The number of new juvenile birds introduced to the model is the nativity times the number of adult birds. The formulas for all tables, except the optimal and pessimal Russian scenarios, are:
The outputs in the charts labeled "optimal and pessimal Russian scenario" correspond to simple exponential average growth with no reference to the user's inputs or to any distinction between immature and adult birds. This is motivated by lack of information. In contrast, the main Russian version is calculated by the above more detailed formulas. This is needed for part 2, where catching of juvenile bids is introduced in the model. Goose numbers are not rounded to integers in calculations or charts. Rounding as well as taking into account statistical variations between years have previously been tested on the model. Their effect was negligible so they were left out to speed up calculations.
2.1.1. Description of protection activites
The possible "actions" considered numerically in the model at hand are the following four:
How these are put in, how they are interpreted and what the model calculates from the input data is explained in detail below.
Other possible actions - including public awareness campaigns, formal protection of known staging grounds, further research etc. are not explicitly modelled in part 2. But it is possible to use part 1 together with a zero "action" input in part 2 to generate diagrams displaying scenarios corresponding to modified inputs in the "biological data". In this way, the long time effect of any action can be estimated once the user has an idea on the influence of that particular action on the mortalities or, in some cases, on the nativity. At present, the only known actions with a significant effect on these parameters are the ones listed above: transporting geese from one of the current populations to another. This motivates why part 2 is constructed to represent the effect of this kind of actions.
2.1.2. Six model populations
Part 2 calculates the growth of six interacting populations, labeled "Norway", "Russia (European)", "Sweden", "Captive Sweden", "Finland" and "Captive Finland", respectively. The internal growth for each of these populations follows the logic of part 1 expressed in the four formulas above in 1.2. The initial values for the Swedish and Finnish Captive populations represent reintroduction policies. Therefore, they must be given as inputs in part 2. The default values correspond to an improbable scenario, where all current Finnish captive LWfG are accepted for breedeng and - to demonstrate the contrast - in Sweden only the eight newly imported Russian origin LWfG are accepted. The "biological" parameter values for each population are taken from the input in part 1 in the following way:
2.1.3. Inputs
In addition to the "biology" parameters listed in 1.1. and 2.1.2. the user must give numerical values to twelve "action" parameters. These describe the intended (!) activities in restocking programs.
The user is encouraged to insert her/his favourite numbers for action inputs and to try out what will happen. The "default" numbers given have no actual relevance; they are almost arbitrarily chosen. Anyway, they are feasible and will produce nice and informative"default" output charts.
In part 2, the model's user is supposed to insert values for proposed reintroduction scenarios. One possibility to be tried out is the zero option with no catching in Russia and no releases in Fennoscandia. Current captive LWfG can be eliminated from the model by choosing zero inputs to initial captive population inputs.
2.2.1 Outputs and interpretation of part 2
The output of part 2 consists of seven charts displaying the year by year future of all six populations.
The first two charts give answers to the question "How much will the European Russian donor population be damaged by the planned removal of the goslings or eggs?" The first chart shows the future of the European Russian population with and without the planned catching, based on the full set of input values. A second "Russian" chart compares slightly less exact predictions for a best and worst feasible future scenario.
The following pair of charts answer the question "Will the proposed actions be sufficient to reach the goals of the conservation programs in Sweden and Finland?" The Swedish goal, 500 individuals, corresponds to 200 pairs in 2025, mentioned in the current Swedish national action plan draft [Nat 2006]. The Finnish goal in the diagram is simply half of the Swedish. No official number exists at present, but is feels fair to set a lower goal than in Sweden, since at present there is no initial free LWfG population at all breeding in Finland. The chart for Sweden displays two scenarios, one with no further restocking, the other taking into account the input restocking plans. The latter also respects the maximum life input.
Chart 5 sums up the previous ones by displaying the free living populations in all four countries as piles. Chart 6 does the same for Sweden and Norway in detail.
Finally, chart 7 answers the question: "How many LWfG will be kept in Captivity in each country and how many will/can be released into Nature each year?" This information is of great practical importance for carrying out the plan encoded in the inputs, in particular as keeping large flocks of LWfG in Captivity is a costly business.
There are some numerical outputs as well: the total numbers of caught and released geese is calculated. Here, and throughout, only possible releases are taken into account - only existing goslings can be released from Captivity into nature; there is no such thing as a negative gosling. The total number of individuals caught in Russia has a twofold relevance. On one hand, it is proportional to the damage done for a population already in danger. On the other hand, if no current captive stock is used, at least 150 geese should be caught in Russia since 150 independent individuals is a commonly accepted minimum for a genetically sound founder population.
2.2.2. Parameters and calculations in part 2
Much like in part 1, the model again successively calculates the numbers of 2 cy, 3 cy and adult birds for each year and each population, but now interaction between the populations is introduced into the model. The interactions are the following
Catching fresh LWfG from Russia to Captivity is modelled by adding the number of caught juvenils to the respective Captive populations each year and subtracting them from the Russian population. Mortality of these birds in the first winter is modelled by the mortality in "Captive dynamics". To reflect initial difficulties and final uncertainties of the catching program, the first and last intended catching numbers are halved by the model.
Releases are modelled similarly: each year the planned number of juvenils is subtracted from the captive population, if available (cf. 2.2.1. last section), and added to the free living population in the respective country.
The length of a maximal life span is taken into account by annually subtracting from the number of adult birds the number of remaining adult geese who have reached the maximum age. This can be calculated once we know the inputs for maximal life length L, the number N of 3 cy geese that was living L years before, and the adult mortality M. This logic fails for the initially adult geese whose age distribution is not given by the inputs of the program. In the current version of the model (Jan. 2007), the initial adults' dying of old age of is not included. It may not be worth while to improve the model in this respect. For a a stably growing population, the age distribution could be calculated from the mortalities, but by observation, LWfG can live long and dying of old age is a rare phenomenon both in the wild and in Captivity. Therefore, almost no birds die of old age and their mortality is in practise correctly described without aging. To see this quantitatively, the user may to put in zero releases and then, varying the maximal age of birds in "Sweden", look at the growth chart titled "reaching Swedish goal". The output labeled "SWE+0" ignores aging whereas "SWE+REL" takes it into account. With no release input, the difference between these series is entirely due to aging. The default values for maximal life span are set high and our recommendation is to use this parameter only for testing its theoretical influence. (For conservation of the LWfG, longevity is of fundamental importance. It implies that adult mortality is the key factor for surviving as a population.)
Immigration could be a natural source for increasing an LWfG population. In the model, an immigration number can be put in to reflect growth of the Swedish population by immigration from Norway. The model transports an input-given percentage of 2 cy birds from "Norway" to "Sweden". This input parameter can be used to test the feasibility of actions like improving conditions for the Norwegian birds and looking for positive effects in Sweden. In a sense, the model is overly optimistic here, since in Nature spreading over the political border to Sweden does not mean joining the more viable Swedich population like the model calculates.
No other immigrations are sketched in the model. In Nature, there exists immigration from Russia to Norway; female Norwegian LWfG find Russian mates in winter, and later both breed in Norway. This immigration is compensated by Norwegian males, who follow Russian females to Russian breeding grounds. This exchange is numerically in balance, so there is no need to reflect it in the model. (The resulting gene flow is of independent interest.)
The formulas:
"Norway"
"Russia (European)"
"Russia (Natural)"
"Russia (Optimal)"
"Russia (Optimal / Catch)"
"Russia (Pessimal)"
"Russia (Pessimal / Catch)"
"Sweden+REL"
"Sweden + 0"
"Captive Sweden"
"Finland"
"Captive Finland"
"Releases"
To find out, how many goslings, if any, should be caught or released annually in the ongoing programs for re-introduction of the Lesser White-fronted Goose to Finland and Sweden, we should use models predicting the population growth in dependence of the action. A simple-minded approach to this problem is the following rule: "Transport as many geese as you can to the place/population, where they multipy fastest. Keep them there until they are many enough, then release them to where you finally want to have them."
This rule is correct, and at first glance the place for fastest growth seems to be Captivity. The other place, where the LWfG number may increase, is the Swedish SW-migrating population modelled by "Sweden". At second thought, Captivity cannot be used in this way in practise. trhis is so for several reasond.
Therefore, after an initial increase of the captive population, releases to Nature must begin. The model populations labeled "Sweden" and "Finland" represent South-West migrating LWfG. Only these have positive growth. (Restocking the South-East migrating population was tried out in Finland and failed [M].)
[A] Andersson, Å. 2004. The reintroduction of the esser White-fronted Goose in Swedish Lapland &endash; a summary for 2000-2003. WWF Finland report 20 and Norwegian Ornithological Society, NOF Rapportserie Report no. 1-2004: 51-52.
[E 1999] von Essen, Lambart, Anders Bylin and Bo Fagerström: The Swedish project for re-establishment of the Lesser White-fronted Goose in Swedish Lapland - a summary for 1999. --- WWF Finland Report no. 12 : Fennoscandian Lesser White-fronted Goose conservation project - Annual report 1999.
[F] < http://www.ansererythropus.tk/> Home Page of "Friends of the Lesser White-fronted Goose".
[KOF 2006] Koffijberg K., Cottaar F. & van der Jeugd H. 2005. Pleisterplaatsen van Dwergganzen Anser erythropus in Nederland. SOVON-informatierapport 2005/06. SOVON Vogelonderzoek Nederland, Beek-Ubbergen.
[LUU 2005] Luukkonen A., J. Markkola, P. Tolvanen, M. Ruokonen, S. Timonen, T. Aarvak, A. Arkiomaa, J. Pessa and J. Pynnönen 2005. Kiljuhanhen suojelu 2003-2004. [Conservation of the lesser white-fronted goose 2003-2004]. - Linnut-vuosikirja 2004, BirdLife Finland. 4-13. (In Finnish)
[M] Markkola, J., S. Timonen and P. Nieminen 1999. The Finnish breeding and restocking projet of the Lesser White-fronted goose: results and the current situation in 1998. &endash; WWF Finland Report 10:47-49.
[Nat 2006] Åtgärdsprogram för bevarande af fjällgås. (Draft) Naturvårdsverket, Dec. 2006.
[NOF 1997] Aarvak, Tomas, Ingar Jostein Øien, Eugeny E. Syroechkovski Jr. and Irina Kostadinova: The Lesser White-fronted Goose Monitoring Programme, Annual Report 1997. --- Norwegian Ornithological Society Report No5-1997.
[NOF 2005] <www.piskulka.net > "Portal to the Lesser White-fronted Goose" by the Fennoscandian Lesser White-fronted Goose Conservation Project.
[VF 2003] Øien, Ingar Jostein and Tomas Aarvak. Fjällgås - finns det hopp för Skandinaviens "sjungande gäss"? Vår Fågelvärld 62(3):6-12.
[WWF 1999] Aarvak, Tomas and Ingar Jostein Øien: Monitoring of staging Lesser White-fronted Geese at the Valdak marshes in 1999: -- WWF Finland Report no. 12: Fennoscandian Lesser White-fronted Goose conservation project - Annual report 1999.
[WWF 2004] Aarvak, Tomas and Ingar Jostein Øien: Monitoring of staging Lesser White-fronted Geese at the Valdak Marshes, Norway, in the years 2001-2003: --WWF Finland report 20 and Norwegian Ornithological Society, NOF Rapportserie Report no. 1-2004: