## Wildlife Ecology: Animal Population Sampling & Estimation: Brief Introduction

Wildlife Ecology: Animal Population Sampling & Estimation: Brief Introduction

Mohammed Ashraf

Ecology is not the kind of science that takes people by storm hence I am not expecting that it is just what the doctor ordered. But we at Species Ecology are pretty ‘gung ho’ about the motion and rolled up our sleeves and buckled down to do our part to ensure science bound ecological sustainability find its niche in the face of anthropogenic development across the chessboard. I am not going to beat around the bush hence one of the main purposes of reaching out to people neatly rooted into the fact that collaborative and collective actions are fundamental to reinforce the conservation pillars in which wildlife science and ecology are basic ingredients. Therefore, I am at the crossroad reaching out potential academic scholars so that collectively we could go back to the drawing board and crank out rudiments of common language (mathematics) to preserve mosaic of heterogeneous pristine ecological units from Baluchistan in Pakistan to Yosemite in California and anything in between. I like to keep the ball rolling and I am twisting arms to get scholars on board depending on what variety of fresh food (ecology) and ingredients (mathematical tools) they can bring on the table.

Lot of ecological inquires can be modeled into finding priority action measures and to predict scenarios hence for example looking into fish population (denoted with $P$) which can be modeled into quadratic equation to predict future population size. Here I have modeled the fish population $P$ below and solved the equation to determine the time (in days) when fish population will reach 500. This is just an example of some of the works I am pretty ‘gung ho’ about.

$\left( 3t + 10 \sqrt{t} + 140 \right) = P$

$\left( 3(\sqrt{t})^{2} + 10 \sqrt{t} + 140 \right) = 500$

$\left( 3(\sqrt{t})^{2} + 10 \sqrt{t} - 360 \right) = 0$

$\left( ax^{2} + bx + (-360) \right) = 0$

$t = \left( \frac{-10 \pm \sqrt{(10)^{2} - 4 \cdot{3} \cdot{-360}}}{2 \cdot {3}} \right)$

$t = \left( \frac{-10 \pm \sqrt{(10)^{2} - 4 \cdot{3} \cdot{-360}}}{2 \cdot {3}} \right)$

$t = \left( \frac{ -10 \pm \sqrt{100 + 4320}} {6} \right)$

$t = \left( \frac{-10 \pm \sqrt{4420}}{6} \right)$

$t = \left( \frac{-10 \pm 66.48}{6} \right)$

$t = \left( \frac{56.48}{6} \right)$

$t = 9.41$

$\sqrt{t} = 9.41$

$(\sqrt{t})^{2} = (9.41)^{2}$

$t = 88.5$

Fish population Model

Therefore for fish population to reach 500 it would require 88.5 days or roughly 12 weeks. Refer to the $3t + 10\sqrt{t} + 140 = P$ population model curve.

Its critically important to develop an algorithm so that we can generalize quadratic model and in this example I have used Python programming language to model the equation $(3t + 10 \sqrt{t} + 140) = P$ into square-root function for the purpose of fish population prediction.

Once critically endangered Florida Panther: Subspecies of Mountain Lion recovered from population decline : Thanks to dedicated science bound conservation measure…

The other example I would like to draw attention to is sampling size and the determination of sampling size based on simple (or stratified) random sampling. Animal population estimation is function of two critical parameters. 1. Occupancy 2. Detectability. Here the probability of animal occupancy is one of the statistical factors that need to be taken into account before carrying out animal population survey. In other words, statistically valid survey design is at paramount importance. Generally speaking, at one given time, our chance to detect any animal depends on whether our sampling units are true representation of the population size. For example, If I ought to find out the Florida panther (subspecies of mountain lion) population in any given area of 100 sq km, my primary objective is design a survey unit based on proportional and true representation of all the units. It simply means, if we conduct animal detection survey of roughly 2 sq km that I can cover in a day on foot, then I need to ensure that each 2 sq km I choose is a true representation or have the equal probability of selection among my fifty 2-sq-km panther survey unit (50 times 2 equates our total 100 sq km). Surely 100 sq km is a relatively big area for me to survey on my own but I still need to conduct the survey hence I could survey 40 sq km out of my total 100 sq km potential survey area to estimate the Florida panther population. Since my survey units are all 2 sq km each, hence 40 sq km translates to total 20 blocks which I would need to randomly select out of total 50 blocks or 100 sq km. Here I have used R programming language to write up a function that will allow me to randomly select 20 blocks out of 100 or any numbers of blocks depending on how many blocks you wish to include into your survey as random sample. I have provided below the block matrix of 100 in which twenty 2-sq-km block are randomly selected. Blocks are highlighted for the purpose of clarity. Also note, this is not an algebraic matrix that you may often utilize to solve problems in linear algebra. This is just a block sample that some folks may simply present in a grid block as oppose to block matrix.

Sampling blocks under conceptually unified statistically valid random sampling procedure undertaken through R programming language

These 20 blocks are true representation of my sampling survey area and if survey is carried out in these blocks, even if I can detect only few panther from my survey unit, the sampling size would still be true representation of the population size hence it would allow me to estimate the detection probability of panther population from the entire 100 sq.km. ecological unit. As an example, if I manage to detect only 3 panther out of my 40 sq km survey unit and my detection probability stands out 0.1, it then translates to undetected panther population size of 30 which in turn give me the total population size of 33 in that particular Everglade mangrove habitat.

This is just a short article providing some very brief understanding with regards to ecological study focusing animal population survey design and estimation techniques. The article deduced hard core mathematical rigor and modeling techniques to produce succinct easy-to-understand ecological piece without compromising the statistical rigor. The primary objective of this short essay is to publicize these rather mathematically challenging models in simplistic coherent format so that average people from non scientific background yet avid conservationist can able to digest the rudiment of population ecology and its conservation implications.

This draft is prepared in $\LaTeX$ – the brainchild of Donald Knuth, developed by American Mathematical Society (AMS) and created by George Gratzar from University of Manitoba Department of Mathematics. I have also utilized both Python and R Programming Language to develop quadratic population model and for designing random sampling matrix. No commercial software under capitalistic market share is used in preparation of this draft. UNIX variant GNU-Debian Linux is used throughout as core to run all software packages.

## Wetland ecosystems, its benefits and science based conservation management practice

World Wetland Day: Wetland ecosystems, its benefits and
science based conservation management practice

Mohammed Ashraf

Waterfowl in wetland

February 02 is World Wetland Day. It may or may not mean much to people who are either too busy focusing on ‘earning money’ hence to use money as their standard yardstick of development when it comes to their personal and career growth or simply not interested on this topic. For many years, wetlands are considered as wastelands and still in many developing nations, wetlands are rapidly transforming into agricultural paddy field or cash farm of shrimp aquaculture in the expense of large scale degradation or complete decimation of this biologically most productive ecosystems on earth. So what is wetlands, how do we distinguish wetlands from other water bodies, what are the benefits of conserving wetlands, what are their international conservation status or designation, who is responsible for maintaining the global database of wetlands, how to access these database, what is the biological and or ecological potential of wetlands comparing to other ecosystems like rain forest or shrub land and what species serve as an ecological indicator and how do we go about measuring these species in order to ensure ecological integrity, functions and the processes of the wetlands are maintained so that we human can continue to receive the vested unconditional ecosystem services e.g. fresh water supply either directly or from ground water, nutrients in the form of fish and other aquatic fauna, shoreline stability, retention of silts hence avoiding coastal erosion and so forth.

In this short essay, I am going to provide some brief background information about wetlands of different types, the importance of wetland conservation to human, and the species that wetland ecologist or limnologist may consider measuring and monitoring as part of implementing the wise use and conservation management of wetland ecosystems.

Let me start by finding out what is not a wetland? A fraction of land that is covered with rain water hence formed a small rainwater pool, is not a wetland. It is not a wetland because the water is not a permanent one and the soil may not be the one that is adapted to water based plant species to grow and thrive on it. Water base species of plants means a selective group of botanically important species that can only grow in soil that are either permanently or seasonally wet but wet, nevertheless, throughout the year. These kind of plants are also know as Hydrophytes or aquatic plants and the soil they grow on is classed as hydric soil. Now that we have some crude idea what is not a wetland, lets just move on finding out what is actually a wetland. Wetland is an ecosystem comprise with hydric soil and hydrophytes. This is possibly the simplest definition to appreciate. Wetlands sometimes are also known as ecotone which refers to a transition inter phase between dry soil and wet soil. For example, mangrove ecosystem is essentially an unique ecotone due to the fact that the wetland within the mangroves is in the transition zone between dry or semi-dry land surface that are regularly and periodically inundated by tidal waves. Dry or semi dry wetland based ecosystems are also known as terrestrial ecosystem although the diversity and the characteristic of floral species may set it apart from other terrestrial ecosystems and the botanical species that would inhabit in this particular kind of wet-terrestrial ecosystem would be predominantly hydrophytes. Strictly speaking, there are four major kinds of wetlands-marsh lands, swamp forest, however not all swamp forests are mangroves, but all mangroves are swamp forest, bog lands and fen lands.

Although, bogs and fens are often collectively known as mires. Below is the list of different types of wetlands that are under various degree of anthropogenic threats.

1.Lakes including oxbow lakes (both man made and natural), 2. Rivers 3. Swamps, 4. Marshes, 5. Peat lands, 6. Bogs 7. Fends 8. tidal flats or also known as mud flats, 9. Estuaries, 10. Oases, 11. Deltas, 12. Wet grasslands, 13. Near shore marine areas, 14. Freshwater Corridors or River Corridors that are often found meandering through path of forest and finally 15. Man made sites such as fish ponds, rice paddies, reservoirs and salt pans.

So how we go about making sure we are doing the right thing to conserve and manage wetlands. In other words how do we ensure that our current management practice is as such that we can confidently say that our wetlands are healthy, productive ecological unit. One critically important management practice deeply rooted in to the science of ecology-lending mathematically sophisticated tools and integrating them with further powerful tool of geographical information science. Here we will briefly provide the fundamentals of mathematical estimator that if appropriately employed by wetland ecologist for collecting data can serve as baseline index to measure and monitor the health of wetland ecosystems. Wetlands are dominated by hydrophytes. Although there are relatively good number of vascular aquatic plants inhabiting the terrestrial wetlands. However, these woody species need to compete very hard with each other resulting in the local dominance of single or few species through the process of competition. Therefore these species are not necessarily a good indicator of understanding or measuring the health of the wetlands considering their low diversity and richness. Therefore, wetland ecologists often relies on rooted submerged aquatic plants known as macrophytes. Some of these macrophytes are halophytes- a group of submerge aquatic species that grow in high salinity in the water}. Macrophytes in general serve as an ecologically valid indicator species to statistically appraise the health of the wetland ecosystem. In other words, high diversity (number of different species of macrophytes, their proportional abundance, and evenness of the different species) of macrophytes means grater production of algal species, high biomass and lower loss of phosphorus, all signs of a healthy wetlands. The implication from management perspective is, estimating and monitoring the aquatic macrophytes diversity can at least provide us the lower bound of the index measure to detect the overall health of the wetlands. Ecologically speaking, management practice that maintain macrophyte diversity and monitor the diversity index both in spatial and temporal scales, can potentially enhance the ecological functioning and associated services of wetland ecosystems. So how we go about establishing a diversity index focusing macrophyte species. Here I have introduced a diversity estimator and mathematically illustrated it through algebraic simplifications.

Diversity Index
Diversity index is a mathematically valid numeric representation of a value that not only reflects how many different species are there but also simultaneously take into account the evenness that is how equally or (unequally) the types of different species are distributed across the data sample. Here I start with general estimator and algebraically work my way down to come up with suitable diversity estimator that we can employ in our macrophyte diversity estimation in wetlands. Please note this is a very brief mathematical treatment of figuring out the diversity index hence the estimator. For full treatment, please refer to standard ecological literature that are at your disposal.

$q_{D}=\frac{1}{\sqrt[q-1]{\sum_{i=1}^{R} p_{i} p_{i}^{q-1}}}$

Here, D is our Diversity Index, q is diversity order, in other words, the value of q can help us to model the estimator in terms of understanding how sensitive our diversity index is that is rare versus abundance species across the species’ proportional abundance in our sample data, $p_{i}$ is our proportional abundance of $i$th type of species and R is our total number of species. Notice R is actually Species Richness that simply reflects how many total number of different types of species we have found. We now simplify the above equation below:

$q_{\textbf{D}}=\left(\sqrt[q-1]{\sum_{i=1}^{R} p_{i} p_{i}^{q-1}}\right)^{-1}$

$q_{\textbf{D}}=\left(\left[\sum_{i=1}^{R} p_{i} p_{i}^{q-1}\right]^{\frac{1}{q-1}}\right)^{-1}$

We continue further algebraic simplification

$q_{\textbf{D}}=\left(\left[\sum_{i=1}^{R} p_{i} p_{i}^{q-1}\right]^{\frac{1}{-(1-q)}}\right)^{-1}$

$q_{\textbf{D}}=\left(\sum_{i=1}^{R} p_{i} p_{i}^{q-1}\right)^{\frac{1}{1-q}}$

If we take radical of $(1-q)$ in both side of the equation, things will start to make more sense:

$\sqrt[1-q]{q_{D}}=\left(\sqrt[1-q]{\sum_{i=1}^{R} p_{i} p_{i}^{q-1}}\right)^{\frac{1}{1-q}}$

$\sqrt[1-q]{q_{D}}=\sum_{i=1}^{R} p_{i} p_{i}^{q-1}$

Now this is simply a raw version of Shannon-Weaver Index, also commonly known as Shannon entropy. Lets trim the equation to make more sense out of it.

$\left[q_{\textbf{D}}\right]^{\frac{1}{-(q-1)}}=\sum_{i=1}^{R} p_{i} p_{i}^{q-1}$

$\left[q_{D}\right]^{\frac{1}{-(q-1)}}= \sum_{i=1}^{R} p_{i} p_{i}^{q-1}$

$\left(\sqrt[q-1]{q_{\textbf{D}}}\right)^{-1} = \left(\sum_{i=1}^{R} p_{i} p_{i}^{q-1}\right)$

We are going to take natural logarithm $ln$ in both side of our equation in order to bring down our exponents.

$ln \left(\sqrt[q-1]{q_{\textbf{D}}}\right)^{-1} = ln \left(\sum_{i=1}^{R} p_{i} p_{i}^{q-1}\right)$

$-ln \sqrt[q-1]{{q_{\textbf{D}}}} = \sum_{i=1}^{R} p_{i} (q-1) ln p_{i}$

We multiply both side of our equation with negative (-) resulting simply a Shannon entropy.

$ln \sqrt[q-1]{q_{\textbf{D}}}= -\sum_{i=1}^{R} (q-1) p_{i} ln p_{i}$

The left hand side of our equation is simply a value of Shannon Diversity Index and can be written as $H$, however, the value of $q$ as mentioned earlier can take up any magnitude although, considering to the fact that $p_{i}$ is our proportional number of species and we are interested to find out the weighted distribution and the richness ($R$) in order to enumerate the value of species diversity index that takes both the distribution and evenness into account, therefore, a general rule of thumb in this case would be to consider the value of $q=1$ that would give us a weighted geometric mean across our proportional number of individual type of species in our sample data set. Hence plugging in the value of $q=1$ in our equation results a Shannon Diversity Index Estimator:

$\textbf{H}= - \sum_{i=1}^{R} p_{i} ln p_{i}$

Please note the above equation. Shannon index is grounded to the weighted geometric mean of the proportional abundances of the types of species viz-a-viz the species richness $R$, and it equals the logarithm of true diversity as calculated with $q = 1$. We can carry out further simplification of our $H$ as shown below:

$\textbf{H} = -\sum_{i=1}^{R} ln p_{i}^{p_{i}}$

This can also be written as

$\textbf{H} = - \left(ln p_{1}^{p_{1}} + ln p_{2}^{p_{2}} + ln p_{3}^{p_{3}} + ln p_{4}^{p_{4}} + \dots + ln p_{R}^{p_{R}} \right)$

Which equals

$\textbf{H} = - ln p_{1}^{p_{1}} ln p_{2}^{p_{2}} ln p_{3}^{p_{3}} ln p_{4}^{p_{4}} \dots ln p_{R}^{p_{R}}$

$\textbf{H} = ln \left(\frac{1}{p_{1}^{p_{1}} p_{2}^{p_{2}} p_{3}^{p_{3}} p_{4}^{p_{4}} \dots p_{r}^{p_{R}}} \right)$

The final algebraic simplification of the above equation can be written in a succinct form as shown below:

$\textbf{H} = ln \left(\frac{1}{\prod_{i=1}^{R} p_{i}^{p_{i}}} \right)$

Algebraic simplifications of our original general estimator lead us to workable succinct Shannon-Weaver Diversity Index which if utilized in a conceptually unified and statistically valid sampling framework can produce ecologically correct diversity index of macrophyte species in wetland ecosystems. Therefore conservation management plan, particularly in the developing nations where tropical wetlands are facing grim future, must focus on integrating scientifically valid statistical sampling design- lending necessary mathematical estimator to better appraise the species diversity index. With adequate baseline data on macrophytes both in spatial and temporal scales, conservation managers will be armed with accurate limnological knowledge to detect any changes in the overall functionality of the wetland health hence to adopt sound management prescription that can help maintain macrophyte diversity viz-a-viz enhancing the functioning and associated ecological services of the wetland ecosystems both in tropical and semi tropical belt.

## The Power of Linux-Resources for Wildlife Ecologists

The Power of Linux and its Utilization: Free and Open Source Software (FOSS) Resources for Wildlife Ecologists & Conservation Biologists

Mohammed Ashraf

I want to tell you a story. No, not the story of how, in 1991, a guy from Finland called Linus Torvalds wrote the first version of the Linux kernel. You can read that story in lots of Linux books. Nor are we going to tell you the story of how, some years earlier, Richard Stallman began the GNU (GNU is not Unix) Project to create a free Unix-like operating system. That’s an important story too, but most other Linux books have that one, as well. No, we want to tell you the story of how you can take back control of your computer. When we began working with computers as a school student in the mid 1980s, there was a revolution going on. The invention of the microprocessor had made it possible for ordinary people like you and us to actually own a computer. It’s hard for many people today to imagine what the world was like when only big business (American Telegraph and Telephone-AT&T) and big government (Pentagon or FBI) ran all the computers. Let’s just say you couldn’t get much done. Today, the world is very different. Computers are everywhere, from iPhone to giant data centers to everything in between. In addition to ubiquitous computers, we also have a ubiquitous network connecting them together. This has created a wondrous new age of personal empowerment and creative freedom, but over the last couple of decades something else has been happening. A single giant corporation (guess who?) has been imposing its control over most of the world’s computers and deciding what you can and cannot do with them. Fortunately, people from all over the world are doing something about it. They are fighting to maintain control of their computers by writing their own software. They are building Linux. Many people speak of “freedom” with regard to Linux, but I don’t think most people know what this freedom really means. Freedom is the power to decide what your computer does, and the only way to have this freedom is to know what your computer is doing. Freedom is a computer that is without secrets, one where everything can be known if you care enough to find out.

Why Use the Command Line?

Have you ever noticed in the movies when the “super hacker”—you know, the guy who can break into the ultra-secure military computer in under 30 seconds—sits down at the computer, he never touches a mouse? It’s because movie makers realize that we, as human beings, instinctively know the only way to really get anything done on a computer is by typing on a keyboard. Most computer users today are familiar with only the graphical user interface (GUI) and have been taught by vendors and pundits that the command line interface (CLI) is a terrifying thing of the past. This is unfortunate, because a good command line interface is a marvelously expressive way of communicating with a computer in much the same way the written word is for human beings. It’s been said that “graphical user interfaces make easy tasks easy, while command line interfaces make difficult tasks possible,” and this is still very true today. Since Linux is modeled after the Unix family of operating systems, it shares the same rich heritage of command line tools as Unix. Unix came into prominence during the early 1980s (although it was first developed a decade earlier), before the widespread adoption of the graphical user interface and, as a result, developed an extensive command line interface instead.

Linux on Conservation Science