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Keywords:

  • epidemiology;
  • mating systems;
  • Mycobacterium bovis;
  • population density;
  • Trichosurus vulpecula

Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  • 1
    Interactions during mating are thought to be an important mechanism for transmission of tuberculosis (Tb) Mycobacterium bovis in the brushtail possum Trichosurus vulpecula . However, little information is available on the frequency of contacts between males and females in oestrus during the breeding season, and the relationship between mating contacts and population density.
  • 2
    We used radio-telemetry to record contacts between male and oestrous and non-oestrous female possums, and determined paternity of offspring using DNA analysis. This was repeated following the removal of c . 70% of the resident possums to determine the effect of reducing density on the contact rate.
  • 3
    We could not detect any significant differences in the contact rate between oestrous and non-oestrous females and males, either before or after the density reduction, even when paternity was positively identified from DNA analysis. This suggests that actual mating contacts could not be distinguished from other agonistic or affiliative contact behaviours.
  • 4
    Despite this, the relationships between male–female and male–male contact rates and population density were non-linear convex-up, implying that the contact rate during the breeding season did not decrease in proportion to reductions in density. This appeared to be driven by the enlargement of male ranges and a corresponding increase in male overlap of female ranges following the density reduction.
  • 5
    The form of the contact rate function will influence predictions of disease spread in epidemiological models for Tb in wildlife. This has major implications for the development of tactical approaches to disease management based on such models.

Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

Common brushtail possums Trichosurus vulpecula (Kerr) are the major wildlife reservoir for bovine tuberculosis (Mycobacterium bovis, Tb; Karlson & Lessel 1970) in New Zealand. They transmit the disease to livestock (Caley et al. 1999), thwarting attempts to gain official freedom of the disease (O’Neil & Pharo 1995). This situation is similar to that in England, where badgers Meles meles (L.) are the principle wildlife reservoir for Tb, although evidence that they transmit disease to livestock is largely circumstantial (Krebs et al. 1998). The effective control or eradication of bovine Tb from wildlife populations requires that the intraspecific rate of Tb transmission among animals is reduced. In brushtail possums, the overall Tb transmission rate is a function of the relative contributions of the various mechanisms of disease transmission (e.g. behavioural agonistic–affiliative interactions, mating, den-sharing, pseudo-vertical transmission, etc.). These are not well quantified but they are a critical factor in all models of possums and Tb (Barlow 1991a, 1996; Roberts 1996). Similarly, models of Tb in badgers (Smith, Cheeseman & Clifton-Hadley 1997; Swinton et al. 1997; White, Lewis & Harris 1997; Smith et al. 2001) are based on a limited understanding of the mechanisms of disease transmission between badgers, both within and between social groups. Tb infection in possums is transmitted predominantly by aerosols, requiring close contact between individuals (Morris & Pfeiffer 1995). Interactions during mating are thought to be the most important mechanism of Tb transmission (Pfeiffer 1994; Morris & Pfeiffer 1995).

There are little data available on the rate of contact between male and female possums during mating. In a behavioural study of a low density possum population in Australia, Winter (1976) observed male possums forming ‘consort’ relationships with reproductively active females. This involved the pairing of a male with a female in reproductive condition, often for extended periods of time, and is thought to reduce the probability that the female will be mated by other males (Winter 1976). The consort is generally a male whose home range overlaps that of the female (Day, O’Connor & Mathews 2000) and he will usually stay in close proximity to the female (< 5 m) during the consort period, which could last from 30 to 40 days (Winter 1976; Day, O’Connor & Mathews 2000). Consort behaviour usually ceased following mating (Winter 1976), implying that the mating system is temporarily monogamous (Sarre et al. 2000). Short-term pair bonds between males and females around mating were also noted by Jolly (1981) at a site on Banks Peninsula, New Zealand. However, genetic studies of paternity in brushtail possum populations by Taylor et al. (2000) and Sarre et al. (2000) found that approximately half the male population contributed to successful mating, and the distribution of offspring produced per male implied that the mating system ranged between polygyny and promiscuity, suggesting a lack of formal bonding between males and females during mating. Note that these studies can only describe the pattern of successful matings and do not estimate the rate of all sexual contacts, including unsuccessful mating attempts. For example, a radio-telemetry study by Ward (1978) observed interactions in an area of about 10 m2 involving seven possums engaged in mating behaviour over a 3-h period, suggesting that males may compete with each other for mating rights.

The rate of contact among individuals and, hence, the disease transmission rate is usually assumed to have some functional relationship with population density (McCallum, Barlow & Hone 2001). Existing possum Tb models assume that the overall contact rate is either linearly related to population density or takes a convex-up form (Roberts 1996; Barlow 2000). However, Caley et al. (1998) found that the contact rate function of possums simultaneously sharing dens was convex-down. The convex-up form for the contact rate function is assumed to represent contacts between possums due to mating, as it is thought to be relatively independent of population density (Barlow 2000). Another mechanism that may cause contact rates to be non-linearly related to population density is the effect of culling. Culling can disrupt social organization leading to increased contacts between individuals or neighbouring social groups at low density, as has been demonstrated in badgers (Tuyttens et al. 2000). As the form of the contact rate function has direct implications for model predictions of Tb in wildlife, clearly the effect of population density on the rate of contacts needs further elucidation.

As interactions around mating have been proposed as the most important mechanism of Tb transmission in possums, the aim of this study was to determine the effect of reducing population density on the rate of contacts around mating. Initially, we determined the rate of contacts between males and oestrous and non-oestrous females using a combination of DNA paternity analysis (to determine the pattern of successful sexual contacts) and radio-telemetry (to quantify all contacts including both successful and unsuccessful mating attempts). Radio-telemetry was also used to determine the contact rate between males. These data were then used to assess the form of the relationship between the contact rate and population density.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

study site

The study was undertaken in a 13-ha semi-isolated patch of remnant native forest on farmland at Pigeon Flat near Dunedin, New Zealand (45°48′S,170°32′E) (for a description of the study site see Efford, Warburton & Spencer 2000).

possum trapping

Possums were live-trapped in cages (n = 148) set on a 30-m grid throughout the forest, baited with apple coated with aniseed and flour. Since 1993, the population has been trapped regularly every 2 months until October 1998 (Efford, Warburton & Spencer 2000) and then in May and August 1999 and January, April, May and August 2000. Traps were baited and set for four consecutive nights and checked each morning. Each captured animal was given a unique ear-tag and tattoo, weighed to the nearest 50 g and measured. Females were judged to be mature if they had a fully formed pouch and males if the length of a testis exceeded 17 mm.

possum interactions

In 1998, 1999 and 2000, we used radio-telemetry to determine the degree to which male possums associated with both oestrous and non-oestrous females during the breeding season. Observational studies (Winter 1976) were impractical for measuring interactions because the multi-layered structure of the forest in the study area severely hampered visibility. The breeding season occurs over several months (Fletcher & Selwood 2000), hence it is not possible to determine when a particular female will come into oestrus, making it logistically difficult to study naturally occurring oestrus. To overcome this problem, we removed the pouch young from a small number (eight–nine) of female possums each year in the knowledge that these possums would return to oestrus between 9 and 16 days later (Pilton & Sharman 1962). This enabled radio-telemetry to be targeted during the period when ovulation, and hence mating, was most likely. During early June 1998 and again in early May 1999 and 2000, radio-transmitters (Sirtrack 2 stage transmitters, 160 MHz, Havelock North, New Zealand) were attached to the female possums that had had their pouch young removed (RPY treatment), six females that had pouch young and, hence, were not in oestrus during the period of interest (PY females), and at least 15 mature male possums. The larger number of RPY females took into account the likely failure of some females to return to oestrus. Male possums were also radio-collared on the basis that they had access to the maximum number of radio-collared females, as determined from trap-revealed home range overlap.

Radio-telemetry was undertaken over seven nights, starting 8–9 days after the removal of pouch young, using three null-peak aerial systems located at fixed sites surrounding the study area. The locations of each animal were recorded once every hour for 6 h each night starting after dusk during June 1998, and once every 45 min for 6 h each night starting after dusk during May 1999 and 2000. Each operator maintained radio contact to ensure the three bearings were recorded nearly simultaneously. The evening schedule covered the period of greatest nightly activity by possums (Ward 1978). The maximum likelihood estimator (MLE) of Lenth (1981) was used to estimate the location of the transmitter given the three bearings. A function to calculate the MLE of Lenth (1981) and the associated 95% confidence ellipse was programmed in R (Ihaka & Gentleman 1996) adapted from code given in White & Garrott (1990).

Two months after the completion of radio-tracking, we attempted to capture all RPY females to determine whether they had bred, based on the presence–absence of pouch young. Head measurements of pouch young were used to estimate date of birth and, hence, the likely date of oestrus based on a gestation period of 18 days (Pilton & Sharman 1962). A 95% prediction interval for the date of oestrus was assigned based on the 95% confidence interval of the growth rate of pouch young in each year, calculated from trapping records. The exception was in 2000, when there were too few pouch young to estimate the growth rate with any precision, so we used the 1999 estimate, which had a 95% confidence interval that overlapped the 1998 interval.

density reduction

To determine the potential effects of reducing density on mating interactions and contact rates, during April 2000 the study area was trapped and c. 70% of the resident possums were selected at random and humanely killed. The radio-telemetry study outlined above was then repeated after the experimental density manipulation. All experimental procedures in this study were approved by the Landcare Research Animal Ethics Committee (No. 96/11/2).

dna paternity analysis

DNA microsatellite analysis was used to determine whether any of the radio-collared males were the likely fathers of the pouch young born after RPY treatment. Tissue samples, consisting of a 4 × 4-mm piece removed from the distal edge of the ear using a pair of baby pig-ear notchers, were taken from all individual possums during routine trapping. Tissue samples were also taken from all pouch young, including the young produced following the RPY treatment. Seven microsatellite loci, including six used in the study by Taylor et al. (2000), were scored for each sampled individual. The parentage analysis program cervus (Marshall et al. 1998) was used to identify the most likely father of offspring that were born to RPY females following the removal of the first pouch young.

analysis of possum interactions

Two methods were used to determine the extent to which males ‘interacted’ with oestrous and non-oestrous females from the radio-telemetry data. The first method used the Multivariate Ornstein Uhlenbeck (MOU) diffusion model (Dunn & Gipson 1977; Dunn 1979), which is a first-order autoregressive, multivariate Gaussian process and is the only method that accounts for serial correlation in the time series of animal locations. In the absence of serial correlation, the method collapses to the bivariate normal utilization model of Jennrich & Turner (1969). If two or more animals are followed simultaneously, then the MOU model can be generalized to determine the degree of correlation between their simultaneous movements by partitioning the covariance matrix of the equilibrium distribution of the two animals (Dunn & Gipson 1977). Dunn (1979) used this method to develop a hypothesis-testing procedure that formally tests for independence between the simultaneous movements of two animals. The main assumption of this model is that the utilization distributions of the two animals be distributed as bivariate normal (i.e. have a single centre of activity). Although the MOU model estimates the correlation between the simultaneous movements of a pair of animals, this is not dependent on their proximity. To determine the frequency of interaction between a pair of animals that was dependent on their proximity, we used a second method.

The second method of determining the degree of interaction between animals, which also used information on the frequency of proximity, was that proposed by Doncaster (1990). His method of ‘dynamic’ interaction is non-parametric (i.e. there are no distributional assumptions placed on the utilization distribution) and is expressed in terms of the probability that two animals maintain a separation distance greater or less than would be expected from their respective utilization distributions. A significance test of the hypothesis of no dynamic interaction is made by comparing the number of separation distances from the N paired separation distances and from the complete set of N2N unpaired separation distances that fall within some critical distance. For our possum data, a critical separation distance of 10 m was chosen. Ten metres was chosen as the critical distance because we wanted to strike a balance between a distance that included most actual contacts, but also took account of the fact that not all actual contacts would be recorded due to telemetry error. A larger critical distance would be more likely to include all actual contacts but would also include more contacts that were spurious. The frequencies of the paired and unpaired distances in each distance class ( 10 m; > 10 m) were compared using a 2 × 2 contingency table (Doncaster 1990). Functions for calculating the dynamic interaction tests for the MOU model of Dunn (1979) (hereafter MOU test) and the dynamic interaction test of Doncaster (1990) (hereafter DI test) were programmed in R.

simulation of the power to detect interactions incorporating telemetry error

Our ability to detect a significant ‘interaction’ between two possums, given it occurred, was largely dependent on the accuracy of our radio-telemetry system. Estimation of the mean linear distance between estimated and known locations is regarded as the best measurement of telemetry error (Zimmerman & Powell 1995). Because we did not estimate locations at known positions, this method of estimating telemetry error was not possible in this study. Therefore, telemetry error was estimated from the area of the 95% confidence ellipse calculated from the MLE estimator of Lenth (1981). In order for accurate estimation of the 95% ellipse to occur, an estimate of the standard deviation of the angle error is required (White & Garrott 1990). This was calculated using the deviations between the actual bearing and the bearing that would intersect the estimated location, separately for each bearing and location, for each year of the study. Due to the presence of a minority of large errors in one of the tails of the distribution of angle errors, we calculated the median absolute deviation (MAD) of the angle error, which is equivalent to the standard deviation when the median is used as the estimate of central tendency. Separate estimates of the MAD of the angle error in each year were then used to calculate the 95% confidence ellipses for each location. In order to estimate an approximate linear error, which we required for subsequent simulation, we calculated, for each location estimate, the radius of the circle whose area equalled the area of the 95% confidence ellipse. This necessarily assumes that the 95% ellipses were approximately circular. The median and MAD estimate of the radii were then used as our estimate of linear error. This median 95% linear error measurement and associated MAD estimated for the total combined locations was equal to 34·5 ± 9·6 m.

We used simulation modelling to determine the ‘power’ of our parametric (MOU) test and non-parametric (DI) test to distinguish mating interactions or ‘consort’ behaviour, as defined by Winter (1976), given the uncertainty in location estimates estimated above. We first simulated locations for a ‘typical’ female possum from a multivariate normal distribution using average estimates of the variances and covariance of the x and y coordinates from radio-collared females. A similar number of locations was simulated to that collected during a seven-night telemetry period (e.g. seven ‘bursts’ of eight locations per night = 56 total locations). We then simulated locations for a ‘consort’ male who had a mean simultaneous separation distance from the female equivalent to a ‘typical’ consort distance. Using data from Winter (1976, fig. 5.8, p. 160), the mean and standard deviation of the separation distance between two possums during ‘typical’ consort behaviour was 5 ± 5 m. We then simulated uncertainty in the estimates of locations (telemetry error) by displacing the locations of both the male and female a random distance, drawn from a normal distribution with mean 34·5 m and SD 9·6 m. All displacements were orientated in a random direction. The significance of the ‘interaction’ between the male–female pair was then assessed using both the MOU parametric test and the DI non-parametric test. We repeated this simulation procedure 100 times separately for each test. The ‘power’ of each test to determine the presence of ‘consort’ behaviour given the uncertainty in the estimates of locations (telemetry error) was assessed by calculating the percentage of the 100 simulated tests that identified a significant interaction (MOU test, P < 0·05; DI test, P < 0·1).

contact rates

Contact rates were determined between each PY and RPY female and all males that occurred in their respective home ranges using a method similar to Caley (1993). The home ranges of radio-collared individuals over the seven-night period were delineated using the 95% contour of the probability density surface estimated using a bivariate normal kernel, with bandwidth calculated by least-squares cross-validation (Worton 1989) using the RangesV software package (Kenward & Hodder 1996). Initially, the number of contacts between each PY and RPY female and each radio-collared male that occurred within their home range during the radio-telemetry period was determined. Here, a contact was defined when the simultaneous locations of a radio-collared male–female pair were within a 10-m distance. The contact rate between PY and RPY females and radio-collared males was determined by dividing the number of contacts (measured from the simultaneous locations of each PY and RPY female and radio-collared males) by the total number of simultaneous observations that occurred for each radio-telemetry period. However, this underestimates the true contact rate, as contacts would also have occurred with males without radio-collars. To determine the potential number of contacts for each PY/RPY female, we determined the total number of males that overlapped each female's 95% density contour home range using locations derived from trapping data. All males captured within the home range of each PY and RPY female were identified from trapping records during the trapping session that immediately preceded each radio-telemetry period (i.e. within 10 days). To account for the fact that not all males would have been caught during this particular trapping session, we adjusted the number of males by dividing by the capture probability of males estimated for that particular session using the Jolly–Seber mark–recapture model (Pollock et al. 1990). The total number of potential male contacts within a particular home range (radio-collared male possums + trapped male possums) was converted to a density (males ha−1 home range−1).

Assuming that the sample of radio-collared males was representative of the total population of males, and that the contact rate between PY and RPY females and radio-collared males was representative of the contact rate with all males in the home range, we calculated the total contact rate by multiplying the radio-revealed contact rate by the total number of males in the home range and the number of simultaneous observations that occurred during the radio-telemetry period. This contact rate was standardized as contacts h−1.

For comparative purposes, we also repeated the above procedure to calculate the contact rate between radio-collared males and all potential males in their home range. The average contact rates for PY females, RPY female and males were compared between years using the non-parametric Kruskal–Wallis test. Average contact rates for PY and RPY were compared pre- and post-density reduction using the Wilcoxon rank-sum test.

A number of functional forms for the contact rate–density function have been proposed, of which the simplest is a linear model forced through the origin (model 1):

  • c ( N ) = δ N

where δ is the slope of the regression model. Caley et al. (1998) fitted a model to the observed den-sharing contact rate that was convex-down (model 2):

  • image

where λ and κ are shape parameters. Note that values of κ less than 1 will lead to a non-linear convex-up relationship. Finally, Roberts (1996) proposed a model that can take the forms from linear to convex-up (model 3):

  • image

where θ is the shape parameter. We confronted these models with our empirical estimates of male–female and male–male contact rates to determine the appropriate form of the contact rate function. Models were fitted using either non-linear least squares (model's 2 and 3 using the nls() function in R; Ihaka & Gentleman 1996) or linear regression for model 1 (lm() function in R) and were compared using Akaike's information criterion (AIC). AIC values were rescaled as differences between the model and the model with lowest AIC (ΔAIC). The likelihood of the model, given the data, was calculated as exp(−0·5 × ΔAIC). These values were normalized to sum to 1 and expressed as Akaike weights (AICw) (Burnham & Anderson 2001).

The contact rates calculated per individual home range included a measure of pseudo-replication, as some individual male and female possums were radio-collared in more than one year. As contact rates for individuals measured in multiple years are unlikely to be independent, we calculated contact rates averaged over individuals in different years by combining the estimates of male density within home ranges into classes. Six density classes were used with midpoints at 2·5, 7·5, 12·5, 17·5, 22·5 and 27·5 possums ha−1. These averaged contact rates per density class were used to fit the models for the contact rate functions.

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

synchronization of oestrus and density treatments

Overall, the RPY treatment resulted in reasonably good synchronization of oestrus (Fig. 1). During 1998, the RPY treatment was applied fairly late in the breeding season (June) and, as a result, only four of the nine RPY females returned to oestrus. During 1999, all nine RPY females rebred. However, three RPY females were judged to have missed the first opportunity for breeding (first oestrus following RPY) but bred successfully during the following oestrus. As the 95% confidence interval for the date of oestrus was outside the radio-telemetry period, these animals and the 1998 females that did not rebreed were excluded from the RPY treatment group in all subsequent analysis. During 2000, all eight RPY females rebred and were judged to have come into oestrus during the radio-telemetry period.

image

Figure 1. Dates that pouch young were removed from RPY females in each year of the experiment (dark shaded bar), dates of the subsequent radio-telemetry period (light shaded bar) and the 95% prediction interval for the date of oestrus for each RPY female (lines).

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Possum densities in April 2000 were reduced before the 2000 radio-telemetry period by 71% and 67% for males and females, respectively (Fig. 2). The removal of animals predictably led to a reduction in the density of all males in the home ranges of females by 34%, for both PY and RPY females, compared with the 1999 densities, respectively (Table 1). Median home range size of males after the density reduction was more than 30% larger, on average, than in 1999, and 50% larger than in 1998. However, the differences were significant for 1998 (Wilcox test, P= 0·02) and marginal for 1999 (Wilcox test, P= 0·09). The size of female ranges did not change significantly after the density reduction for either PY or RPY females (P > 0·1). Overlap of male ranges on both PY and RPY females was higher following the density reduction in 2000 than in 1999, but was significantly so only for PY females (Wilcox test, PY females, P < 0·01; RPY females, P= 0·27; Table 1).

image

Figure 2. Jolly–Seber mark–recapture estimates of male and female population size (± SE) from 1998 to 2000.

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Table 1.  The median home range (HR) size (95% kernel density isopleth) of males, PY and RPY females during the radio-telemetry period (x̄ HR, ha), the median density of males in the home range of males, PY and RPY females (x̄ldensity, males ha −1 ) and the mean percentage overlap of PY and RPY female home ranges by male ranges (x̄, OL). Values in parentheses are the median absolute deviation
 MalesPY femalesRPY females
Yearx̄ HRx̄ densityx̄ HRx̄ densityx̄ OLx̄ HRx̄ densityx̄ OL
19981·018·50·921·720·40·910·8 8·6
 (0·6)(9·4)(0·6)(5·1) (0·1)(2·4) 
19991·411·80·916·416·40·815·815·6
 (0·8)(5·1)(0·5)(4·2) (0·3)(5·1) 
20002·07·41·410·828·21·210·423·0
 (1·3) (3·7)(0·5) (8·5) (0·3)(4·6) 

possum interactions

Results from the MOU and DI tests revealed little or no differences in the level of interaction between radio-collared males and either PY or RPY females (Tables 2 and 3). For the MOU test, there was no significant difference between the percentage of PY–male and RPY–male pairs, with significant correlation between their simultaneous movements in any year (1998, inline image= 1·46, P= 0·23; 1999, inline image= 0·41, P= 0·52; 2000, inline image= 0·0, P= 1). There were similarly no significant differences in any year for the DI test (1998, inline image= 0·57, P= 0·45; 1999, inline image= 0·22, P= 0·64; 2000, inline image= 0, P= 1). The percentage of PY–male and RPY–male pairs showing significant levels of interaction after the density reduction, was, in most cases, similar to the percentage of significant interactions prior to the density reduction (Tables 2 and 3).

Table 2.  Summary of the number of male–RPY female, male–PY female pairs with overlapping home ranges (no. of pairs) that had evidence of significant correlation between their simultaneous movements (no. of int; P < 0·05) as determined by the multivariate Ornstein–Uhlenbeck diffusion model of Dunn (1979 ). ρ, mean canonical correlation coefficient between simultaneous locations. Chi-squared test comparing the percentage of significant interactions between 1999 and 2000 for male–PY females (χ 2  = 0, d.f. = 1, P = 1) and male–RPY females (χ 2  = 0·99, d.f. = 1, P = 0·32)
YearMale–PY femalesMale–RPY females
No. of pairsNo. of int%ρNo. of pairsNo. of int%ρ
1998742229·70·1831 516·10·17
199940 717·50·12601525·00·10
200053 916·90·10941617·00·15
Table 3.  Summary of the number of male–RPY female, male–PY female pairs with overlapping home ranges (no. of pairs) where the number of simultaneous separation distances that were < 10 m were significantly greater (χ 2 , P  < 0·1) than those expected from the complete set of N2N unpaired separation distances (no. of int), as determined from the dynamic interaction test of Doncaster (1990 ). Chi-squared test comparing the percentage of significant interactions between 1999 and 2000 for male–PY females (χ 2  = 0·052, d.f. = 1, P = 0·82) and male–RPY females (χ 2  = 0·08, d.f. = 1, P = 0·77)
YearMale–PY femalesMale–RPY females
No. of pairsNo. of int%No. of pairsNo. of int%
19987445·43100
19994012·56046·6
20005335·79444·3

dna analysis

Results of the DNA paternity analysis revealed that relatively few successful mating contacts were made by radio-collared males during 1998 and 1999, with two of four and one of six RPY females having offspring fathered by one of the radio-collared males, respectively. Both radio-collared males that fathered offspring with RPY females in 1998 had no overlap in their 95% density contour ranges with these two individuals. However, both male ranges were adjacent to the respective RPY female ranges. Following the density reduction in 2000, four of the eight RPY females had offspring fathered by a different radio-collared male. In spite of these known successful mating contacts, neither the MOU test nor the DI test revealed any significant association between these individuals (Table 4). However, the MOU and DI tests did indicate marginal evidence for association between two RPY females and the respective radio-collared father (P = 0·07 and 0·12, respectively; Table 4). On the other hand, the MOU test indicated a strong significant association between one RPY female and a radio-collared father, despite no recorded home range overlap.

Table 4.  Radio-collared males (male ID) that fathered offspring born to RPY females (RPY ID) as confirmed by DNA microsatellite analysis. For each male ID, the percentage home range overlap (95% kernel isopleth), the significance of the correlation between the simultaneous movements from the MOU model ( P MOU model), the proportion of simultaneous contacts < 10 m, the proportion of expected contacts < 10 m, and the associated chi-squared significance test from the dynamic interaction test of Doncaster (1990 ), are given for each RPY–male pair in each year. *** Chi-squared test due to zero marginals
YearRPY IDMale IDHR overlap (%)P (MOU model) Contacts < 10 mExpected contacts < 10 mP ( inline image )
1998 292373 1·30·0700***
  358375 0< 0·00100***
1999838723417·70·4800·0051·0
2000 31138479·40·690·0360·010·12
  33150545·60·0700·0140·65
  43141712·70·7400·0021·0
  47223444·90·3700·0071·0

simulation of the power to detect interactions incorporating telemetry error

Both the MOU and DI tests identified the majority of the simulated male–female pairs as having significant ‘interaction’, although the parametric MOU test was more powerful than the non-parametric DI test (Table 5). The MOU test identified all 100 simulated consort pairs as having significant dynamic interaction, while only 69% of simulated consort pairs were identified as having significant dynamic interaction based on having significantly more separation distances < 10 m than expected (Table 5).

Table 5.  Summary of the percentage of 100 simulated male–female ‘consort’ pairs that were identified as having significant association according to the MOU test ( P  < 0·05), and the DI test where the number of simultaneous separation distances that were < 10 m (observed percentage) were significantly greater (χ 2 , P < 0·1) than those expected from the complete set of N2N unpaired separation distances (expected percentage). No. of pairs, number of simulated male–female pairs for each test. ρ, mean canonical correlation coefficient between simultaneous locations for the MOU test
MOU testDI test
No. of pairs%ρ%Observed (%)Expected (%)
1001000·86693·80·48

contact rates

Average contact rates did not differ significantly in any year for either PY or RPY females (PY females, Kruskal test, χ2 = 0·64, d.f. = 2, P = 0·73; RPY females, Kruskal test, χ2 = 4·7, d.f. = 2, P = 0·09) (Fig. 3). However, average contact rates for males did differ significantly, being lower post-density reduction than in other years (Kruskal test, χ2 = 7·8, d.f. = 2, P= 0·02). There were no significant differences between the contact rates for PY and RPY females either before or after the density reduction, although results were marginal for 1998 where RPY females had lower contact rates than PY females (Wilcox test, 1998, P = 0·06; 1999, P = 1; 2000, P = 0·66). As there appeared to be no differences between the contact rates for PY or RPY females, the models for the contact rate function were fitted to the combined contact rates for PY and RPY females (Fig. 4a). The contact rate models were also fitted to the contact rates between all males (Fig. 4b). Based on the model with the lowest AIC score, there was clear support for models 2 and 3, indicating a non-linear convex-up relationship between the male–female contact rate and local (male) population density (Table 6 and Fig. 5). A similar, but less well supported, convex-up relationship was also found for the combined male–male contact rates (Table 6 and Fig. 5).

image

Figure 3. The average contact rates between PY females–males, RPY females–males and males–males in each year of the study and plotted against the overall density of males in the study site. Points are the median and lines are the median absolute deviation.

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image

Figure 4. Contact rates for individual possums and the density of males within their home range (local density) for (a) PY and RPY females and (b) males for the periods both prior to and following the density reduction.

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Table 6.  Parameter estimates for three models for the contact rate function c ( N ) fitted to contact rates between radio-collared females vs. the density of males within their home range, and radio-collared males vs. the density of males within their home range, and including the relative support for each model using AIC as the model selection criteria
ModelParameter estimatesSEΔAICAIC weights
Radio-collared females
Model 1δ = 0·0070·00110·10·01
Model 2λ = 0·0460·026 00·71
 κ = 0·3610·197  
Model 3θ = 0·010·002 1·870·28
Radio-collared males
Model 1δ = 0·0090·001 2·880·13
Model 2λ = 0·0270·005 00·54
 κ = 0·5970·057  
Model 3θ = 0·0130·006 1·020·33
image

Figure 5. The relationship between the male–female contact rate (open triangles) and the male–male contact rate (closed circles) and local population density (males ha −1 home range −1 ) aggregated into density classes. Each point is plotted against the mid-point of each class. Fitted lines are the predictions for the convex-up relationship predicted by model 2 (solid line male–males; broken line male–females).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

There was some evidence that the density reduction had an effect on the spacing behaviour and movements of brushtail possums. Male home range size increased, on average, after the density reduction, and there was greater overlap of male ranges with PY and RPY female ranges. Home range increase by males would be expected if they were taking advantage of the decrease in male competitors and seeking increased opportunities for mating by aligning their ranges with those of potential female mates. Increase in range size and a corresponding increase in male overlap with female ranges following a reduction in density have been demonstrated in mammals with territorial social organizations, such as Californian voles Microtis californicus (Ostfeld 1986), and in badgers where there was distinct group territorial boundaries (Tuyttens et al. 2000). In the case of Californian voles, male overlap of female ranges was more pronounced for females who were judged to be in oestrus (Ostfeld 1986). In brushtail possums, induced oestrus in RPY females did not result in an increase in overlap of male ranges with the ranges of RPY females compared with PY females. However, male brushtail possums are not believed to be territorial, based on their high degree of home range overlap with other males (Cowan & Clout 2000), although males do tend to avoid encounters with each other (Day, O’Connor & Mathews 2000). The present data support conclusions about the lack of territoriality in social spacing by brushtail possums.

Complementing the results of reducing density on levels of ‘static interaction’ between male and female possum, were the results of the ‘dynamic interaction’ tests of Dunn (1979) and Doncaster (1990). Neither test indicated an increase in the level of interactions between the simultaneous movements of RPY female–male pairs compared with PY female–male pairs, either before or after the density reduction. Overall, levels of interaction remained relatively constant following the density reduction. There are two possible explanations for this. The first is that induced oestrus in RPY females did not occur during the radio-telemetry period. However, given that the RPY treatment induced synchronous oestrus in all the treated females during 2000, and six of the nine treated females in 1999, it is unlikely that there were no oestrus events in the period from day 9 to 16 after RPY treatment (Pilton & Sharman 1962). DNA paternity analysis also confirms that some radio-collared males were involved in successful mating, especially after the density reduction when 50% of the RPY females were successfully mated by radio-collared males. The second, and probably more likely, explanation is that the extent of male interactions with females around mating could not be detected with the radio-telemetry system used. Simulation modelling confirmed that if male and female possums were engaging in consort behaviour, as defined by Winter (1976), it would have been detected by both the MOU and DI tests, even given the uncertainty in our location estimates. The strength of the level of interaction between a male–female pair can be gauged from the canonical correlation between their coordinates derived from the MOU test. For the simulated consort pair the mean canonical correlation was 0·85, which compares with mean canonical correlations of < 0·2 for RPY female–male and PY female–male pairs. Further, the highest canonical correlation recorded for any male–female pair in any year was 0·53. Thus, we conclude that consort behaviour was not typical male mating behaviour around oestrus females in our study. Winter (1976) also noted mating interactions that were not preceded by consort behaviour, termed casual mating by Cowan (1990). As the duration of actual copulation is around 2–4 min (Winter 1976), it is likely that the majority of casual matings would have gone undetected. In addition, it is unlikely that we were able to distinguish casual mating interactions from other agonistic–affiliative interactions that were unrelated to mating. We conclude that the most likely explanation for our failure to detect an increase in male interactions around RPY (oestrus) females is because most mating interactions on our study site, either successful or unsuccessful, were casual in nature.

Further evidence to support this conclusion was provided by the DNA microsatellite analysis. Despite known paternity by radio-collared males, neither test for dynamic interaction could reliably determine significant correlation between the simultaneous movements of the known parents. This further strengthens our argument that mating interactions were casual in nature. Flexibility in the mating systems of species can reflect adaptation to differences in resource quality and population density (Emlen & Oring 1977; McCarthy & Lindenmayer 1998; Taylor et al. 2000). Thus, differences in population density and habitat characteristics between our study population and populations elsewhere in New Zealand or in Australia where consort behaviour was observed, could explain the lack of consort pairing suggested by the present study. In general, brushtail possum populations can exhibit a high variation in life history characteristics between regions or habitats (Tyndale-Biscoe 1973; Cowan 1990).

A problem with the use of the MOU model of Dunn (1979) concerns the highly significant interaction between the simultaneous movements of RPY female 358 and male 375 (Table 4) despite no area of congruence in their recorded home ranges. This result is obviously spurious and highlights the need to ensure that ranges overlap before inference can be made using this test. Dunn & Brisbin (1985), in a simulation study of the frequency with which the MOU chi-squared test for independence critical values was exceeded, showed that the actual rejection rate was usually 1·5–2 times the specified significance level. Hence, the MOU test for complete independence tended to reject the null hypothesis at a rate higher than expected given the nominal significance level. In the present study, the MOU test for independence in possum movements was only undertaken if there was at least some overlap in the home range of the pair in question. The MOU test statistic on the RPY female–male pair with no home range overlap during 1998 (Table 4) was undertaken only for completeness.

contact rates

Predictions from models of the dynamics of bovine Tb in brushtail possum populations in New Zealand (Barlow 1991a, 1991b, 1996, 2000; Pfeiffer 1994; Roberts 1996) and in badgers in the UK (Smith, Cheeseman & Clifton-Hadley 1997; Swinton et al. 1997; Smith et al. 2001) are all sensitive to the form of the contact rate function c(N) for which there are little data. Of the three forms of the contact rate–density function fitted to contact rates between female–male possums, the models indicating a non-linear convex-up relationship clearly had greater support than the linear model. Although male–male contact rates were also convex-up, the non-linearity was not as pronounced as that for the male–female contact rates. Smith (2001), in a comprehensive review of models of bovine Tb in wildlife, indicated that one of the side-effects of culling a population may be changes to the behaviour of the remaining individuals such that the contact rate may become convex-up or ‘frequency dependent’. This was illustrated in a study showing an increase in group contact rates following the culling of badger populations, driven by an increase in group range size (Tuyttens et al. 2000). A similar explanation for the elevated contact rates post-density reduction might apply to this study, where reductions in population density led to an increase in the size of male ranges and a corresponding increase in range overlap with female ranges. Although we could not detect any increase in the frequency of contacts due to actual mating, it is likely that males were increasing their range size post-density reduction, to maximize their access to females generally. The corresponding decrease in average contact rates among males post-density reduction would suggest that male range expansion was targeting female ranges in particular.

The results of this study are in contrast to those of Caley et al. (1998) who found that the relationship between the simultaneous den-sharing rate and population density was convex-down. This convex-down relationship implied that the probability of a possum sharing a den was easily eliminated by decreasing the relative density. In contrast, this study has shown that the male–female contact rate during the breeding season does not decrease in proportion to decreasing relative density. Thus, this behaviour may make a more important contribution to the overall per capita disease contact rate than simultaneous den-sharing.

The consequences of a convex-up relationship for the contact rate function are a lower threshold density for disease elimination, and at the extreme case where c(N) = 1 the population must be eradicated to eliminate disease (Roberts 1996; Barlow 2000).

The possum–Tb models of Barlow (1991a, 1991b) predicted that possum populations held below 40% of carrying capacity (K) would result in the elimination of disease. This model assumed a linear contact rate function implicit in the mass action transmission term βSI, where β is the transmission coefficient and S and I are the abundance of susceptibles and infecteds, respectively. Cautious support for the predictions of this model were provided by Caley et al. (1999), who maintained an endemically infected possum population at an average of 22% of its pre-control density for 10 years. The prevalence of Tb in the population declined to zero after the sixth year of maintenance control, indicating support for the threshold density predicted by the Barlow (1991a) model. However, this does not necessarily prove a linear form for the contact rate as Tb would still be eliminated from a possum population held to 22% of K if a non-linear contact rate is assumed (Barlow 2000). The results of Caley et al. (1999) do, however, provide an upper limit to the estimate of non-linearity in the contact rate function, all else being equal.

In summary, the relationship between the contact rate of male and female possums and population density during the breeding season was determined to be non-linear convex-up. This non-linearity appears to be driven by changes in male movements following a reduction in relative density, so that they can increase or maintain their access to females. However, the importance of this finding for the dynamics of Tb in possums is dependent on the relative importance that contacts during the breeding season play in the disease transmission process. This is currently unknown. Knowledge of the relative importance of the roles of different behaviours in the disease transmission process, and their relationship to population density, is required to be able to better understand the transmission mechanisms for Tb in brushtail possums.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References

This project was funded by the Foundation for Research Science and Technology (Contract C09801 and C09X009). Lisa McElrea and Richard Heyward ably assisted with night-time radio-telemetry, and the Efford family generously provided accommodation. Phil Cowan and Graham Nugent provided useful feedback on a draft manuscript. This manuscript was greatly improved by the helpful comments of both Dr Graham Smith and Dr Robert Kenward.

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  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
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