# Landscape – how to deal with it in science

## Introduction

The title of this blog-post sounds like I want to solve all problems that exist when dealing with “Landscape” in scientific works. In fact this is in some way or the other even the overall or major aim of scientific work. Since I want to answer at least some of the questions that arise when one asks about which role “landscape” plays in understanding ecosystems and since my first scientific work is a meta-analysis about how small mammals depend on landscape composition and fragmentation, I at least want to try to give an overall answer or, more realistically, give hints on how we can find such an answer in this field. Some say that a meta-analyses wants to summarize the current status of a scientific field, but more realistically it will summarize the knowledge of one aspect only, due to the restrictions when calculating the meta-analysis. Thus, this meta-analysis tries to evaluate if it is possible to develop a general model for small mammals and the dependence of their density on landscape parameters.

With this blog-post I want to:

1. give some definitions to clarify how I see and work with landscape and
2. to show the techniques used to calculate the landscape parameters for the meta-analysis.

Some of the information might change, if we have to adapt something or add or remove some parameters, since they seem to be of importance. A big difference of this meta-analysis to other meta-analyses is, that we calculate a big part of the material we want to evaluate on our own and don’t rely on the reported statistics only. This is mainly due to all the nice fellow researchers which were generous enough to hand over their raw data and will in return participate as co-authors in this work! All landscape parameters are calculated from the corine land cover and the Global Forest Change (GFC) dataset. The corine dataset is provided by the European Environmental Agency and freely available to everybody. The Global Forest Change dataset has been published by Hansen, Potapov, Moore, Hancher et. al (2013) under a CC BY 4.0-license.

As I am convinced that knowledge must be free to everybody and that this starts with software which is available for and usable by everybody, I also tried to and so far succeed to use only open source software and data for my scientific work, those awesome datasets support me in this aim and I think a general “Thank you!” to all the participants of such work is the least anyone of us can do!
Not only do I want to give and overview of how to calculate landscape parameters, but also show that the time has come where you can achieve those things easily and without much trouble with open software. I am using Q-GIS and the R-Package for those reasons.

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## Some definitions

#### Habitat

The term habitat is used in correspondence with the classical understanding of it in German literature. Habitat has an autoceological meaning and needs to be distinguished from “biotope” which is a homogeneous part of the landscape and can be a combination of several habitats for several different species and thus has a synecological meaning (orchard, forest or even stream). Especially for small mammals it is important to make this distinction, since some small mammal species live in several “parts” of a landscape (complementary habitat) or share one biotope (e.g. forest), depending on the scale we look at biotopes. (Forest-Interior (A. flavicollis) vs. Forest-Edge (A. sylvaticus) or Forest (A. flavicollis and A. sylvaticus) vs. Field (A. agrarius and A. sylvaticus)).

#### Habitat fragmentation and habitat loss

Habitat fragmentation is a process where a habitat is fragmented into smaller pieces (and should probably be called – or at least be distinguished from – biotope fragmentation if we consider the above written, since there is often a synecological connotation to the term of habitat fragmentation). This can be due to road construction or any other process which makes it harder or impossible for a species to reach from one fragment to the other. We need to distinguish between the fragmentation of a habitat and the loss of a habitat. Habitat loss can happen without fragmentation (burning of an edge-area) and fragmentation can happen with no or very little habitat loss (fence/wall). The degree of fragmentation determines the isolation of a (fragmented) population or community. The degree of habitat loss determines how much habitat is left for a species.

Habitat loss will presumably lead to the decline of population size, but not necessarily to a decline of population density. Habitat fragmentation might or might not lead to decline in population size and decline or increase (crowding) of population density. To find out about the drivers of a declining population we need to look at both, habitat loss and habitat fragmentation.

#### “Patch” and Patch Quality

Patch can be defined as a biotope which remains in a landscape, often embedded into a matrix of other patches which isolate the biotope more or less. The patch is than an island. Examples would be a small forest in an agricultural landscape, a field or windfall/clearcut in a closed forest (gap) but also a group of lime trees in an otherwise oak-dominated stand. Succession and the mosaic cycle of forests can also be described as providing several different patches with different functions.
Each patch can have a quality which depends on the scope the quality is being looked at. The quality a forest has for small mammals might depend on the cover of those plants providing food and shelter for the small mammals. Especially herbivorous small mammals seem to depend on hard seed bearing trees, as Marsh & Harris (2000) and others showed. But also other animals need to find food and shelter in a landscape in order to survive.

For small mammals not all papers give data on the vegetation composition and thus we will focus on the protocol for landscape-data extraction described below.

#### Landscape metrics vs. landscape indices

For an overview of how landscape has been characterised over the years see Uuemaa et al. (2009), where they analysed 337 articles dealing with landscape metrics and 141 articles dealing with landscape indexes or -indices, combined with several other terms from the realm of diversity and landscape and which have been published in the Web of Science. They found that the term “landscape metrics” is used more frequently and give lists of landscape metrics and in which context they have been used.

#### Other

Many other definitions can for examples be found on the website of the Convention on Biological Diversity.

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## Metrics…

Landscape metrics are calculated on circles spanning a 1000 m (3,14 km²) and a 1784 m (10 km²) radius. We chose the 1 km radius since landscape metrics within this range seemed to have greatest influence on population densities compared to 200 m and 500 m (Glatthaar et al., unpublished). The 1,784 km radius represents the maximum home range of the most mobile predator for small mammals, the red fox (Vulpes vulpes). Several studies are undertaken on a rather small research area and we have to expect a high spatial autocorrelation in those studies. For larger scale studies or such studies where the sample points are in different landscape types, we use a 10 km radius to quantify the landscape and can use those values as moderators in a the meta-analysis.

#### Patch Number and Richness

The Patch Number is basically the amount of patches and Patch Richness tells us how many different classes (patch types) can be found.

#### Descriptive Statistics

Descriptive statistics of patches are the mean and median size of a set of patches (within one landscape that is being looked at). The deviation the mean has from the median tells us about the distribution of those patch sizes and the range or quartiles give information about the width of this distribution.

#### Shannon-Index

The Shannon-Index is of the form
$H' = -\displaystyle \sum_{i=1}^R p_i \ln p_i$.
If we want to describe animal or plant communities and calculate a Shannon-Index, we usually relate it to species counts for animals and cover for plants. Relative amount of each species i (pi) is used as abundance index and R is the overall number of individuals of all species. If we are interested in a diversity on landscape level we could also use this approach and just substitute “species” by “patch” in our thought-model. However, we can and should use the area of each patch or each patch type as abundance instead of only the count of those patches, as we would also do it with plants. Both plants and patches are both immobile and have a certain surface they cover, while animals are mobile. (It is a funny thought to take the surface animals would cover with their body and calculate the Shannon-index based on this information.) After all, the “count of patches” does not account as accurately for “how much of each patch” is available in our landscape as the “area covered by each patch type” does. Thus we used R as the count of patch types and pi is the proportion of the area each patch type covers. We have to be aware thought, that any diversity information about the count of patches is not included in this version of the Shannon-Index and we thus have to look at other metrics to get information on patch counts. Patch counts are insofar important, as two landscapes can have the same or very similar values of Shannon-Index but still a configuration which is significantly different when we see it through the eye of an animal or with a different process in the background.

#### Pielou’s Evenness

To deal with the problem of different landscape configuration while having same values for the Shannon-Index we can use Pielou’s Evenness
$J' = \frac{H'}{H'_{max}}$
with
$H' = Shannon\text{-}Index$
$H'_{max} = \displaystyle \sum_{i=1}^S{1 \over S} \ln{1 \over S} = \ln S$.
Each theoretical landscape with a certain amount of patches of certain sizes can have a maximum diversity H’max. Shannon-Diversity tends towards the maximum when patches are equally distributed and thus have the same sizes. After all we still have to bear in mind that we do not have any information about the real manifestation of landscape configuration as it would be important to small mammals.

#### Edge density

The edge density is the amount of edges per hectare [m/ha]. This includes total length of edges if the respective area is known (3.14 km² and 10 km² in this case). Edge density in combination with patch number is a very good proxy when it comes to estimating fragmentation of a landscape. A landscape with a high patch number either has:

• a complex spatial structure with a high edge density (Fig. 1 A),
• a simple spatial structure with a low edge density (Fig. 1 B).

A landscape with a low patch number either has:

• a complex spatial structure with a high edge density (Fig. 1 C),
• a simple spatial structure with a low edge density (Fig. 1 D).

Descriptive statistics can additionally be used to estimate complexity of a landscape. A landscape which has a big difference of mean size-values between patch types is always more heterogeneous than a landscape with similar means of size between patch-types and as mentioned above, the deviation between mean and median can be used to characterize the within patch-type variability.

Fig. 1: Different landscape compositions have different edge-densities, depending on their complexity at a given patch number. A: high patch-number (26) and high heterogeneity (ED = 12.56 m/ha), B: high patch-number (27) and low heterogeneity (ED = 8.52 m/ha), C: low patch-number (11) and heigh heterogeneity (ED = 7.50 m/ha), D: low patch-number (11) and low heterogeneity (ED = 4.48 m/ha)

Other landscape metrics could also be taken into account, but we think that this set of values is enough to characterise the spatial configuration of a landscape. When we think about metrics concerning the shape of a patch, this is hard to quantify and work with and of little relevance to processes in nature. Perimeter-Area-Ratio would be easy to calculate but does not give us information other than on complexity classes, which we also get from Edge Density in combination with Patch Richness already. Furthermore the amount of edges is of vital meaning to small mammal populations, since small mammals either depend on resources they mainly find in edges or are inhabiting the patch (or matrix) interior and thus have in relative means less (or more) habitat with more edge in a landscape.

#### Crown cover

Crown cover was shown to have an effect on small mammal abundance.
We can use the Landsat Global Forest Change (GFC) dataset to calculate crown or canopy-cover for all of the sites. Crown cover was calculated by a weighted mean of the percentage crown-cover weighted by the cover of each of those percentage-classes. Unfortunately this dataset only gives those crown-cover-values for the year 2000. However, we can also extract more accurate values for general forest-cover and edge-density (per year, with a certain limitation discussed below). The GFC dataset has a resolution of ca. 30m and shows each of those 30m pixels which have tree-height of > 5m as forest with the respective crown-cover in 1% steps with a range of 0-100%.

The website where the dataset can be downloaded provides several layers which can deliver already or can serve for calculation of several interesting values. There is a layer which shows crown- and general forest-cover of the year 2000, a layer which shows the loss of forest between 2000 and 2012 as well as a layer which shows the gain of forest between 2000 and 2012. Additionally there is a layer which shows the loss-year but unfortunately no layer which shows the gain-year. However from the supplementary material (Hansen et. al 2013, SM) we can see, that gain is recorded when non-forest pixels (pixels without trees > 5m in 2000) have a crown-cover of > 50% in 2012, but also when pixels with forest suffered a loss between 2000 and 2012 but recovered to > 50% until 2012. Forest gain took always place after forest loss and thus we can calculate an “earliest date” of forest gain for those pixels that show forest loss and forest gain. For all other pixels showing forest gain we can assume that they were in a development from 0% to > 50% crown-cover and < 5m to > 5m tree-height from 2000 to 2012.

To maximise the quality of those values we will subtract all forest loss which occurred until the date of the sampling per study from the “treecover2000”-layer and add all forest gain. We can add all forest gain since it is the more likely to gain a crown-cover of > 50% by 2012, the earlier the loss occurred. The inaccuracy lays in the “gain”-layer and will be quantified by giving a percentage of gained forest per sampling point. The closer a study is to 2012, the more likely it is, that forest gain actually took place to the full extend already and is thus not spuriously in the sum of cover.

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