# Snowshoe hare and lynx relationship counseling

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exceptional advice on sampling design, statistical analysis, and a review of the thesis. responses of coyotes and lynx to the snowshoe hare cycle. Oikos prey-predator relationship: a cheetah killing a rabbit to eat it. Caracal, The Canadian lynx and its favorite meal, the snowshoe hare. Mohammed Sabti. (Lynx canadensis) and its primary prey, the snowshoe hare (Lepus . I thank John Skinner and Bill Halteman for statistical advice and Erin.

We model the two- on the available long-term hare data, which originate from species system as a first-order vector autoregressive pro- the main drainage of Hudson Bay, Canada Fig. This cess Ives et al.

## Predators and their prey

The Hare 0 influence of current hare abundance on future lynx abun- dance is estimated by considering the distribution of the Lynx lynx time-series conditional on the observed hare series.

In the following, Abundance we assume that the model is stationary, which is validated 8 by the empirical results. However, this assumption is not ln Lynx 6 crucial. Below, we describe how this model can be applied even 12 Hare when the data are not linearly related to actual abundance. Top Original data for the hare, data from onwards are The full model implies an autoregressive-moving aver- from questionnaires; MacLulich This was done to prevent the statistical estimation from being dominated by the occasional deep lows of the hare series, which are believed to result from a nonlinear The data relationship between abundance and trapping when hare abundance is low.

Note that the lynx value for is missing; the grey bar shows a linearly interpolated value. Vertical line shows the divide between The only long fur-trade records of snowshoe hare are from fur returns and questionnaire estimates of hare the main drainage of Hudson Bay, Canada. MacLulich Popul Ecol However, Elton and Nicholson We allowed for this difference in measurement units by centering each log-transformed where g1t and g2t are independent normal distributed error hare series at zero, thus expressing observations relative to terms with expectation 0 and variances r2g1 and r2g2, the geometric mean for each hare series.

The choice to respectively.

As detailed below, adding measurement error center at zero was arbitrary and has no effect on the did not significantly improve the model, so the main parameters of interest, because all parameters except b are emphasis of the paper will be on a model without mea- invariant under a multiplicative change of measurement surement error.

For the lynx, we used the sum of the Lakes and James We estimated parameters by maximum likelihood, Bay regions of Elton and Nicholson The time- finding the values of A, b, R, r2g1 and r2g2 that maximize the series of both hare and lynx exhibit approximately year joint probability density of the observed data i.

Missing observations are easily handled in log-transformation is not sufficient to satisfy the normality such a framework. The model implies that the full data assumption of Eq.

Hare or lynx may not be trapped in series follows a multivariate normal distribution whose proportion to abundance when they are rare e. The marginal distribution of the data that low; see chapter 13 of Turchin for discussion. To are not missing is then also normal with the same element- reduce artifacts caused by this non-normality, at little cost wise expectations, variances and co-variances. The quantiles were the sample quantiles as used in hare? Thus, we need represent a useful supplement to the ecological interaction neither assume that fur returns are proportional to abun- coefficients aij.

All we assume is that the dynamics are linear model Brockwell and Davis to the observed time with constant noise variance for some monotonous series for each species, smoothing the latter using a Parzen transformation of actual abundance, and that fur returns window with the default bandwidth suggested by Chatfield are monotonously related to actual abundance.

We estimated these errors using 1, time- serve areas under the power spectral density curve, we series simulated from the fitted model Eq.

Hence, the parameters both after rank-normalization and without it. Thus, the likelihood of the model was not improved by Because missing values are readily accommodated in our allowing for observation error on lynx. The point estimate maximum likelihood approach, Eq.

Agreement one-sided likelihood ratio testand a joint test for obser- between the three sets of conclusions should be grounds for vation error on both species would thus have P [ 0.

Conversely, inconsistency would suggest favors the model without measurement errors, skepticism. Even for hare, measurement error is only estimated a special case of missing data, as described above.

## What Is the Difference Between a Manx Cat & a Lynx Cat?

The with the maximum likelihood of the unrestricted density-dependence is about equally strong in the two ARMA 2,1 models. This constitutes a test of the hypoth- species, and can be spelled out biologically under the esis that Eq. Coefficients of determination R2 for hare were 0. The R2 for lynx were 0. The measurement error as what hare explains of lynx 0.

The reason for this Popul Ecol This 7 suggests that the independent variation happening at a 8 9 lower level of the trophic system affects the system more -1 -2 -1 0 1 2 strongly than the independent variation higher up in the AR1 coef.: As seen in Fig. Although the point estimates from The label F denotes the full two-species model full model Eq. Label U denotes the unconstrained simultaneous estimation of two ARMA 2,1 processes for the hare and the lynx, where WN denotes white noise.

The corresponding stationary dynamics i. The power spectral density PSD shows the contribution to the variance in each frequency interval.

Top Spectral densities correspond- Solid and dashed lines indicate MA coefficients implied for hare and lynx by the fitted two-species model The full model also has a rather longer period than the 9- to proportion of the variance is due to periodicities shorter year peak of the sample spectral density Fig.

Thus, However, agreement is better for power density with the stochastic processes are somewhat more in accordance respect to period, which for the fitted ARMA 2,1 models with the sample spectral density than what the periodic peaks at Discussion The negative MA term makes the spectral density peak at a shorter period than the corresponding pure AR process The estimates from the full model Eq.

Generally, a large population growth of hares is negatively affected, not only Popul Ecol The former effect describes how the hare pop- are within the variation found in a similar analysis of ulation is affected by the relatively slow process of year-to- mink—muskrat interactions Erb et al.

A Manx may have no tail, a bobbed tails or, rarely, a full tail. Lynx have bobbed tails, hence the name for one of their species, the bobcat.

**Canadian Lynx Hunting Snowshoe Hare - Amazing Animal Species**

Lynx have tufts on their ears; Manx cats do not. The Manx's thick double coat keeps him warm and may be any cat color or markings, including tabby, calico or pointed.

### Science Assignment Mod7 by Cam Brownridge on Prezi

Lynx come in a brown color with black tipping and spots, and black ear tufts. The Lynx's snowshoelike feet help it run through the snow; the Manx does not have snowshoe feet. Personality Cat fanciers call the Manx's personality gregarious and loving -- the Manx is often compared to the dog.

Manx love to swim, play fetch and play with friendly dogs. In comparison, the lynx avoids humans and hunts at night. The shy and solitary nature of the lynx is interrupted only for mating season and when a lynx mother raises her cubs. Lynx swim well and hunt snowshoe hare, mice, squirrels and birds.