BT5751 Methods Not Covered
1. Nearest neighbour methods.
Unlike other methods we have considered, the bias of these methods is strongly
dependent on the model assumption of uniform distribution. Because animals are
seldom uniformly distributed, the methods are usually biased – and can be extremely
biased.
There are two sorts of method: point-to-nearest-animal (example below), and animalto-nearest-neighbour. The former is negatively biased by clustering, the latter
positively biased. They are seldom useful for estimating animal abundance.
WiSP example (see Chapter 8 of book for details):
A clustered population of 250 animals (dots), randomly located points (crosses) and distances
from points to nearest animals (lines to red dots).
Bias of the point-to-nearest-animal estimator. The simulated sampling distribution is shown. Its
mean is at the solid line; true abundance is at the dashed line.
2. Migration counts: a temporal version plot surveys.
Example: Californian gray whales migrating past Monterey.
Migration count surveys involve counting the number of animals passing a fixed
point at a random (or systematic) set of times. Plot surveys as we have seen them
before, involve counting the number of animals at a single time at a random set of
locations. Conceptually the two methods are just versions of the same problem – with
the role of time and space interchanged.
A difference in the way they are usually applied is that migration counts involve
estimating a smooth but non-uniform process model for animal distribution (in time)
– the “migration curve” in the plot above. A non-uniform process model is much
more difficult to estimate with conventional plot sampling because (a) there are two
spatial dimensions (as opposed to one temporal dimension), and (b) the form of the
model in space is usually not known (whereas in migration count surveys it has a very
simple form: increase smoothly then decrease smoothly).
3. Indirect methods
Sometimes the animals you are interested in are difficult to survey because they avoid
you, or because they are unavailable for periods, or for some other reason. If they
produce something that is easy to survey, this can be used to estimate the animal
abundance. Examples are deer & deer dung; mackerel & mackerel eggs; whales &
whale blows; gorillas & gorilla nests; elephants & elephant dung; ...
Plot sampling or line transect (or conceivably another method) surveys are used to
estimate the abundance of the thing the animals produce (the “cue”). Estimates of the
rate at which this thing is produced per time period, per animal allows you to convert
the estimate of cue abundance to an estimate of animal abundance. The conversion
factors are usually estimated from separate surveys and/or laboratory/captive studies.
4. Change-in-ratio methods
The change-in-ratio method is a removal method we have not had time to cover in
this short course. It uses the change in ratio of the numbers of one type of animal to
another (often males to females) detected on consecutive surveys, together with
information about how many of each type have been removed between the surveys, to
draw inferences about abundance. It can be useful when there is a differential kill of
different types of animals between surveys. Example: red deer populations, in which
predominantly stags are killed in the hunting season.
5. Integrated methods
A nice feature of the general likelihood formulation of abundance estimation methods
is that it provides a ready framework for generalising and combining methods. Here
are some examples.
a. Mark recapture and line transects
In some applications, line transect methods would clearly be the best method if only
the crucial assumption that all animals on the transect line are detected, was not
violated. In this case, mark recapture ideas can be combined with line transect ideas
to get the best of both methods.
The method is simple in concept (but often not so simple in application). You have
two independent observers on a line transect survey: neither knows what the other has
seen or is doing but they survey the same area at the same time. You also have some
means of identifying animals that are seen by both observers.
Conceptually, one observer is one “capture occasion” and the other is a second
“capture occasion”. Detection by observer 1 constitutes “capture” on occasion 1;
detection by observer 2 constitutes “capture” on occasion 2; detection by both
constitutes “recapture”.
Line transect methods are used to estimate how detection probability falls off with
distance from the line (as in conventional line transect survey analysis). The mark
recapture data is used to estimate p(0), the probability of detecting an animal on the
transect line. For example, if observer 1 saw 20 animals on the transect line, and of
these, observer 2 saw 15, you estimate p(0) for observer 2 to be 15/20 = 0.75.
Examples: small cetaceans (some dolphins and porpoise), some seals, animals that
spend some time underground and unobservable.
b. Mark recapture and migration counts
Used when not all animals passing in the watch periods are observed. The idea is
much the same as with mark recapture line transect surveys. Two independent
observers and the mark recapture data they generate are used to estimate the
probability of detecting an animal in each watch period. This allows the number
passing in the watch periods to be estimated, and hence the number passing in the
whole survey period to be estimated.
c. Spatial modelling from plot surveys
It is possible to model the spatial distribution of animals from plot surveys, in much
the same way as the temporal distribution of animals is modelled from migration
counts – its just more difficult. Instead of assuming a process model in which
animals are uniformly distributed, a very flexible 2-dimensional (or >2-D) functional
form is assumed for the density surface. The parameters of this process model are
estimated together with the detection probability parameters and abundance
parameters. Because the form of the surface is usually not known, a very flexible
density surface must be used and model selection is an important issue.
Here’s an example of the estimated distribution of mackerel eggs off the west coast
of Britain and France, obtained in this way.
d. Spatial modelling from line transects
It is also possible to model the spatial distribution of animals from line transect
surveys, but this is more difficult than doing the same from plot surveys. The
difficulty comes from the fact that line transect methods sample continuously in
space, not at discrete sets of points.
Here’s an example of the estimated distribution of harbour porpoise in the North Sea,
obtained in this way.
This sort of method can be very useful for understanding why animals are where they are.
Here’s a plot of the depths in the North Sea. Notice that harbour porpoise tend to avoid deep
water.
6. Other Mark recapture methods
Mark recapture methods with individual animal heterogeneity were mentioned very
briefly in this course. There is a vast literature on mark recapture methods (lots of it
dealing with open populations, which we have not covered). Because mark recapture
abundance estimates are so biased by unmodelled animal-level heterogeneity, this is
an important topic for many real-world applications of mark recapture methods. It is a
developing field.
There are kinds of marks other than those we have covered. In particular, animals
might be marked in such a way that you can tell on which occasions they have been
captured in the past (e.g. animals caught on occasion 1 have a “1” attached to them,
those caught on occasion 1 have a “1” attached to them, etc.), or they may be marked
in a way that allows you to identify individuals (each animal has a unique mark). The
additional data provided by these sorts of marking improves estimator properties.
7.
Open population methods
We have dealt only with methods for closed animal populations – those whose members
do not change over the survey period(s). In reality there is no such thing as a closed
population, except over a short period of time. Often the interest in the population relates
mainly or largely to how it is changing in time, whether it is threatened with unhealthy
depletion, extinction, etc. To address this sort of question you need methods for open
populations: methods that allow births and deaths, and possibly animal movement in and
out of the survey region(s).
Often closed population methods are used at a number of points in time, to estimate
abundance at those points. Estimates of population trajectory are then superimposed on
these estimates in some way.
Here’s an example – for the trajectory western gulls off the US West coast, with point
estimates coming from shipboard surveys.
Increasingly, however, population dynamics models are being combined with survey
models to give integrated estimates of current abundance and population trajectory that
takes account of all sources of uncertainty in appropriate ways.
The likelihood methods we have used extend quite naturally to open populations and
provide the necessary theoretical framework. The extension is by way of the process
model. Instead of it modelling only where the are and their characteristics (size, exposure,
etc.), it is expanded to model the temporal processes as well (births, deaths, movement).
The estimation methods are an order of magnitude more complex than those we have
dealt with.
BT5751 Which Method When?
1. Plot Sampling
A crucial assumption is that you detect all in the plot. Plot sampling is widely used in
vegetation studies. The method is cost-effective when the density of plants is high and the
survey area is small, so that the time required to travel from one plot to another is small
and there is no need to survey vast areas.
The method is also useful for animals that occur in high density, providing all in the
covered region are seen. Animals detected outside the covered region can then be
disregarded without much effect on precision. Animals should not move in response to
the observer prior to detection. In high densities, line transect methods, which are usually
more cost-effective, might be infeasible because of the difficulty of estimating distances
to so many individuals
2. Distance Sampling
The method is useful and cost-effective for populations in which animals very close to the
observer are certain to be seen and animals do not respond to the observer prior to being
seen. It is particularly useful for sparsely distributed populations because it allows a large
area to be surveyed with relatively little effort - compared to plot sampling. A large
proportion of the time in the field is spent actively surveying so the method is costeffective.
3. Removal Methods
a. Simple removal method
Has poor precision, is subject to large bias from unmodelled heterogeneity, and can
give silly (negative or infinite) estimates of abundance. The method is really only an
option if a large proportion of the population is being, or has been removed anyway,
or if there are reasons other than abundance estimation to remove a large proportion.
If animals can be marked and returned to the population, mark recapture methods are
preferable. In addition to providing additional data (the recaptures) that results in
improved estimator properties, removing animals runs the risk of “sucking in”
animals from other regions as the animal density in the sampled regions is lowered by
removals.
b. Catch-effort methods
These methods are more flexible than the simple removal method because they allow
capture probability to depend on effort and are therefore more appropriate when
effort varies, and when a suitable measure of effort is available. Aside from this, they
suffer from similar drawbacks to the simple removal method.
Obtaining a suitable measure of effort can be a real difficulty, because in many cases
efficiency increases with time so that with time the same amount of measured effort
(for example fishing boat days spent fishing) tends to have more impact on the animal
population (because of technological improvement in fishing gear, sonar, etc.). This
unfortunate feature has been implicated in the over-harvesting of many a population:
because effort is increasing in its impact on the population, the CPUE can stay
constant while animal abundance is plummeting.
c. Change-in-ratio methods
Suffers from similar drawbacks to the simple removal method, but it can be useful for
a harvested population in which an identifiable subset of animals is targeted in the
harvest. This often occurs in populations subject to trophy hunting (e.g. Scottish red
deer populations, where stags are hunted for trophies). A large proportion (perhaps
25%) of the targeted subset of the population needs to be removed for the method to
work well.
4. Mark Recapture
Mark recapture methods have some advantages over line transect sampling methods.
These include:
a. They can provide detailed information about each captured animal
b. Survival rates can be estimated (in an open population context). Mark recapture
methods are quite good at this. Survival rate estimation is not beset by the problem of
unmodelled heterogeneity in the way that abundance estimation is – because
probability of survival tends to be independent of probability of capture, so the
survival probabilities of very catchable animals tends to be representative of the
survival rates of the population as a whole.
c. Recaptures can provide information on movement.
Their disadvantages with respect to line transect methods include:
a. Field costs are substantially higher than line transect field costs.
b. They are much more sensitive to failures of assumptions than line transect methods.
(Some claim mark recapture methods can’t be used reliably to estimate abundance at
all because of the problem of unmodelled heterogeneity. How serious a problem this
is will depend on the application.)
Mark recapture methods are a viable alternative to line transect sampling when some
assumptions of line transect methods are seriously violated. A population in which line
transect methods will not result in all animals on the transect line being detected is a case
in point. (Examples are marine mammals that spend substantial time underwater and
animals that spend substantial time underground. Animals that avoid, or are attracted to
observers on line transect surveys are also problematic. Many animals can detect and
avoid you before you detect them, and some animals are attracted to surveyors (dolphins
that like “bow-riding”, for example).
Mark recapture methods are also a viable alternative to line transect sampling in the case
of very small closed populations. In the case of small coastal dolphin populations, for
example, it might be possible to mark and/or individually identify 80%-90% of such the
population, and in this case mark recapture methods would work well. Line transect
methods are inefficient on such small populations because it might be necessary to cover
the survey region several times and perhaps detect every animal more than once before
getting sufficient sample size to estimate abundance with acceptable precision.
5. Indirect Methods
This approach can be effective for animals that produce some sign of their presence, but
are too scarce to yield sufficient detections for a distance sampling survey (e.g. apes,
elephant and large cats), or animals that avoid detecting by hiding or moving away from
the observer before detection (e.g. deer in closed habitats, foxes, pelagic fish), The sign
most often used is dung, but nests and eggs are also useful in some contexts. The methods
require the mean production rate of the signs and the mean “decay” rate of the signs to be
estimated. Both rates can be difficult to estimate reliably, but these difficulties must be
weighed against the problems associated with surveying the population directly.
6. Mark Recapture Line Transect
When line transect survey would be a good method, but for the fact that not all animals on
the line are detected, and there are concerns about the feasibility of mark recapture on its
own (as there often are), this method can be effective. It takes advantage of the ability of
mark recapture methods to estimate detection probability without it being known
anywhere (on the line in particular), and the pooling robustness of line transect methods.
This method is fairly new and is seeing increasing use. It has been successfully applied to
harbour porpoise and dolphins, small whales, pack ice seals, and polar bears (the last two
are missed because they are white on a white background).
7. Migration Counts
a. Ordinary Migration Counts
To date the method has only been used for large whale populations that migrate past shore
based watch points, within visible distance.
b. Mark Recapture Migration Counts
When some animals may be missed in watch periods on a migration count survey, two
independent observer stations can be used in much the same way as two independent
observers can be used on line transect surveys.
8. Spatial Modelling
This is not so much a method in itself as an extension of other methods that incorporates
estimation of more realistic spatial process models than a uniform distribution.
The extension can be very useful both in reducing variance (because some of the spatial
variation in counts is “explained” by the shape of the spatial process model), and in
understanding why animals are where they, predicting the sorts of environments they
prefer, and (potentially) in predicting the effects of environmental change.
These methods are new and developing.
9. Nearest Neighbour
These methods have attracted some interest for populations of plants, but they are of
limited practical use – estimates of abundance are too dependent on unrealistic
assumptions about animal distribution. Much time can be wasted in establishing which
animal or plant is closest and detections of other objects that turn out not to be closest are
not used.