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2\chapter{Behind the scene}
3There are several challenges specific to \CFA when implementing concurrency. These challenges are a direct result of \gls{bulk-acq} and loose object-definitions. These two constraints are the root cause of most design decisions in the implementation. Furthermore, to avoid contention from dynamically allocating memory in a concurrent environment, the internal-scheduling design is (almost) entirely free of mallocs. This is to avoid the chicken and egg problem \cite{Chicken} of having a memory allocator that relies on the threading system and a threading system that relies on the runtime. This extra goal, means that memory management is a constant concern in the design of the system.
4
5The main memory concern for concurrency is queues. All blocking operations are made by parking threads onto queues. The queue design needs to be intrusive\cite{IntrusiveData} to avoid the need for memory allocation, which entails that all the nodes need specific fields to keep track of all needed information. Since many concurrency operations can use an unbound amount of memory (depending on \gls{bulk-acq}), statically defining information in the intrusive fields of threads is insufficient. The only variable sized container that does not require memory allocation is the callstack, which is heavily used in the implementation of internal scheduling. Particularly variable length arrays, which are used extensively.
6
7Since stack allocation is based around scope, the first step of the implementation is to identify the scopes that are available to store the information, and which of these can have a variable length. The threads and the condition both allow a fixed amount of memory to be stored, while mutex-routines and the actual blocking call allow for an unbound amount (though the later is preferable in terms of performance).
8
9Note that since the major contributions of this thesis are extending monitor semantics to \gls{bulk-acq} and loose object definitions, any challenges that are not resulting of these characteristiques of \CFA are considered as solved problems and therefore not discussed further.
10
11% ======================================================================
12% ======================================================================
13\section{Mutex routines}
14% ======================================================================
15% ======================================================================
16
17The first step towards the monitor implementation is simple mutex-routines using monitors. In the single monitor case, this is done using the entry/exit procedure highlighted in listing \ref{lst:entry1}. This entry/exit procedure does not actually have to be extended to support multiple monitors, indeed it is sufficient to enter/leave monitors one-by-one as long as the order is correct to prevent deadlocks\cite{Havender68}. In \CFA, ordering of monitor relies on memory ordering, this is sufficient because all objects are guaranteed to have distinct non-overlaping memory layouts and mutual-exclusion for a monitor is only defined for its lifetime, meaning that destroying a monitor while it is acquired is undefined behavior. When a mutex call is made, the concerned monitors are agregated into a variable-length pointer array and sorted based on pointer values. This array presists for the entire duration of the mutual-exclusion and its ordering reused extensively.
18\begin{figure}
19\begin{multicols}{2}
20Entry
21\begin{pseudo}
22if monitor is free
23        enter
25        continue
26else
27        block
28increment recursions
29\end{pseudo}
30\columnbreak
31Exit
32\begin{pseudo}
33decrement recursion
34if recursion == 0
35        if entry queue not empty
37\end{pseudo}
38\end{multicols}
39\caption{Initial entry and exit routine for monitors}
40\label{lst:entry1}
41\end{figure}
42
43\subsection{ Details: Interaction with polymorphism}
44Depending on the choice of semantics for when monitor locks are acquired, interaction between monitors and \CFA's concept of polymorphism can be more complex to support. However, it is shown that entry-point locking solves most of the issues.
45
46First of all, interaction between \code{otype} polymorphism and monitors is impossible since monitors do not support copying. Therefore, the main question is how to support \code{dtype} polymorphism. It is important to present the difference between the two acquiring options : callsite and entry-point locking, i.e. acquiring the monitors before making a mutex routine call or as the first operation of the mutex routine-call. For example:
47\begin{figure}[H]
48\begin{center}
49\begin{tabular}{|c|c|c|}
50Mutex & \gls{callsite-locking} & \gls{entry-point-locking} \\
51call & pseudo-code & pseudo-code \\
52\hline
53\begin{cfacode}[tabsize=3]
54void foo(monitor& mutex a){
55
56        //Do Work
57        //...
58
59}
60
61void main() {
62        monitor a;
63
64        foo(a);
65
66}
67\end{cfacode} & \begin{pseudo}[tabsize=3]
68foo(& a) {
69
70        //Do Work
71        //...
72
73}
74
75main() {
76        monitor a;
77        acquire(a);
78        foo(a);
79        release(a);
80}
81\end{pseudo} & \begin{pseudo}[tabsize=3]
82foo(& a) {
83        acquire(a);
84        //Do Work
85        //...
86        release(a);
87}
88
89main() {
90        monitor a;
91
92        foo(a);
93
94}
95\end{pseudo}
96\end{tabular}
97\end{center}
98\caption{Call-site vs entry-point locking for mutex calls}
99\label{fig:locking-site}
100\end{figure}
101
102Note the \code{mutex} keyword relies on the type system, which means that in cases where a generic monitor routine is desired, writing the mutex routine is possible with the proper trait, for example:
103\begin{cfacode}
104//Incorrect: T may not be monitor
105forall(dtype T)
106void foo(T * mutex t);
107
108//Correct: this function only works on monitors (any monitor)
109forall(dtype T | is_monitor(T))
110void bar(T * mutex t));
111\end{cfacode}
112
113Both entry-point and callsite locking are feasible implementations. The current \CFA implementations uses entry-point locking because it requires less work when using \gls{raii}, effectively transferring the burden of implementation to object construction/destruction. The same could be said of callsite locking, the difference being that the later does not necessarily have an existing scope that matches exactly the scope of the mutual exclusion, i.e.: the function body. Furthermore, entry-point locking requires less code generation since any useful routine is called at least as often as it is define, there can be only one entry-point but many callsites.
114
115% ======================================================================
116% ======================================================================
118% ======================================================================
119% ======================================================================
120
121Figure \ref{fig:system1} shows a high-level picture if the \CFA runtime system in regards to concurrency. Each component of the picture is explained in details in the fllowing sections.
122
123\begin{figure}
124\begin{center}
125{\resizebox{\textwidth}{!}{\input{system.pstex_t}}}
126\end{center}
127\caption{Overview of the entire system}
128\label{fig:system1}
129\end{figure}
130
131\subsection{Context Switching}
132As mentionned in section \ref{coroutine}, coroutines are a stepping stone for implementing threading. This is because they share the same mechanism for context-switching between different stacks. To improve performance and simplicity, context-switching is implemented using the following assumption: all context-switches happen inside a specific function call. This assumption means that the context-switch only has to copy the callee-saved registers onto the stack and then switch the stack registers with the ones of the target coroutine/thread. Note that the instruction pointer can be left untouched since the context-switch is always inside the same function. Threads however do not context-switch between each other directly. They context-switch to the scheduler. This method is called a 2-step context-switch and has the advantage of having a clear distinction between user code and the kernel where scheduling and other system operation happen. Obiously, this has the cost of doubling the context-switch cost because threads must context-switch to an intermediate stack. However, the performance of the 2-step context-switch is still superior to a \code{pthread_yield}(see section \ref{results}). additionally, for users in need for optimal performance, it is important to note that having a 2-step context-switch as the default does not prevent \CFA from offering a 1-step context-switch to use manually (or as part of monitors). This option is not currently present in \CFA but the changes required to add it are strictly additive.
133
134\subsection{Processors}
135Parallelism in \CFA is built around using processors to specify how much parallelism is desired. \CFA processors are object wrappers around kernel threads, specifically pthreads in the current implementation of \CFA. Indeed, any parallelism must go through operating-system librairies. However, \glspl{uthread} are still the main source of concurrency, processors are simply the underlying source of parallelism. Indeed, processor \glspl{kthread} simply fetch a \glspl{uthread} from the scheduler and run, they are effectively executers for user-threads. The main benefit of this approach is that it offers a well defined boundary between kernel code and user code, for example, kernel thread quiescing, scheduling and interrupt handling. Processors internally use coroutines to take advantage of the existing context-switching semantics.
136
137\subsection{Stack management}
138One of the challenges of this system is to reduce the footprint as much as possible. Specifically, all pthreads created also have a stack created with them, which should be used as much as possible. Normally, coroutines also create there own stack to run on, however, in the case of the coroutines used for processors, these coroutines run directly on the kernel thread stack, effectively stealing the processor stack. The exception to this rule is the Main Processor, i.e. the initial kernel thread that is given to any program. In order to respect user expectations, the stack of the initial kernel thread, the main stack of the program, is used by the main user thread rather than the main processor.
139
140\subsection{Preemption} \label{preemption}
141Finally, an important aspect for any complete threading system is preemption. As mentionned in chapter \ref{basics}, preemption introduces an extra degree of uncertainty, which enables users to have multiple threads interleave transparently, rather than having to cooperate among threads for proper scheduling and CPU distribution. Indeed, preemption is desireable because it adds a degree of isolation among threads. In a fully cooperative system, any thread that runs into a long loop can starve other threads, while in a preemptive system starvation can still occur but it does not rely on every thread having to yield or block on a regular basis, which reduces significantly a programmer burden. Obviously, preemption is not optimal for every workload, however any preemptive system can become a cooperative system by making the time-slices extremely large. Which is why \CFA uses a preemptive threading system.
142
143Preemption in \CFA is based on kernel timers, which are used to run a discrete-event simulation. Every processor keeps track of the current time and registers an expiration time with the preemption system. When the preemption system receives a change in preemption, it sorts these expiration times in a list and sets a kernel timer for the closest one, effectively stepping between preemption events on each signals sent by the timer. These timers use the linux signal {\tt SIGALRM}, which is delivered to the process rather than the kernel-thread. This results in an implementation problem,because when delivering signals to a process, the kernel documentation states that the signal can be delivered to any kernel thread for which the signal is not blocked i.e. :
144\begin{quote}
145A process-directed signal may be delivered to any one of the threads that does not currently have the signal blocked. If more than one of the threads has the signal unblocked, then the kernel chooses an arbitrary thread to which to deliver the signal.
146SIGNAL(7) - Linux Programmer's Manual
147\end{quote}
148For the sake of simplicity and in order to prevent the case of having two threads receiving alarms simultaneously, \CFA programs block the {\tt SIGALRM} signal on every thread except one. Now because of how involontary context-switches are handled, the kernel thread handling {\tt SIGALRM} cannot also be a processor thread.
149
150Involuntary context-switching is done by sending signal {\tt SIGUSER1} to the corresponding processor and having the thread yield from inside the signal handler. Effectively context-switching away from the signal-handler back to the kernel and the signal-handler frame is eventually unwound when the thread is scheduled again. This approach means that a signal-handler can start on one kernel thread and terminate on a second kernel thread (but the same user thread). It is important to note that signal-handlers save and restore signal masks because user-thread migration can cause signal mask to migrate from one kernel thread to another. This behaviour is only a problem if all kernel threads among which a user thread can migrate differ in terms of signal masks\footnote{Sadly, official POSIX documentation is silent on what distiguishes async-signal-safe'' functions from other functions}. However, since the kernel thread hanlding preemption requires a different signal mask, executing user threads on the kernel alarm thread can cause deadlocks. For this reason, the alarm thread is on a tight loop around a system call to \code{sigwaitinfo}, requiring very little CPU time for preemption. One final detail about the alarm thread is how to wake it when additional communication is required (e.g., on thread termination). This unblocking is also done using {\tt SIGALRM}, but sent throught the \code{pthread_sigqueue}. Indeed, \code{sigwait} can differentiate signals sent from \code{pthread_sigqueue} from signals sent from alarms or the kernel.
151
152\subsection{Scheduler}
153Finally, an aspect that was not mentionned yet is the scheduling algorithm. Currently, the \CFA scheduler uses a single ready queue for all processors, which is the simplest approach to scheduling. Further discussion on scheduling is present in section \label{futur:sched}.
154
155% ======================================================================
156% ======================================================================
157\section{Internal scheduling} \label{impl:intsched}
158% ======================================================================
159% ======================================================================
160The following figure is the traditional illustration of a monitor (repeated from page~\pageref{fig:monitor} for convenience) :
161
162\begin{figure}[H]
163\begin{center}
164{\resizebox{0.4\textwidth}{!}{\input{monitor}}}
165\end{center}
167\label{fig:monitor}
168\end{figure}
169
170This picture has several components, the two most important being the entry-queue and the AS-stack. The entry-queue is an (almost) FIFO list where threads waiting to enter are parked, while the acceptor-signalor (AS) stack is a FILO list used for threads that have been signalled or otherwise marked as running next.
171
172For \CFA, this picture does not have support for blocking multiple monitors on a single condition. To support \gls{bulk-acq} two changes to this picture are required. First, it is non longer helpful to attach the condition to a single monitor. Secondly, the thread waiting on the conditions has to be seperated multiple monitors, which yields :
173
174\begin{figure}[H]
175\begin{center}
176{\resizebox{0.8\textwidth}{!}{\input{int_monitor}}}
177\end{center}
178\caption{Illustration of \CFA monitor}
179\label{fig:monitor_cfa}
180\end{figure}
181
182This picture and the proper entry and leave algorithms is the fundamental implementation of internal scheduling (see listing \ref{lst:entry2}). Note that when threads are moved from the condition to the AS-stack, it splits the thread into to pieces. The thread is woken up when all the pieces have moved from the AS-stacks to the active thread seat. In this picture, the threads are split into halves but this is only because there are two monitors in this picture. For a specific signaling operation every monitor needs a piece of thread on its AS-stack.
183
184\begin{figure}[b]
185\begin{multicols}{2}
186Entry
187\begin{pseudo}
188if monitor is free
189        enter
191        continue
192else
193        block
194increment recursion
195
196\end{pseudo}
197\columnbreak
198Exit
199\begin{pseudo}
200decrement recursion
201if recursion == 0
202        if signal_stack not empty
206
207        if entry queue not empty
209\end{pseudo}
210\end{multicols}
211\caption{Entry and exit routine for monitors with internal scheduling}
212\label{lst:entry2}
213\end{figure}
214
215Some important things to notice about the exit routine. The solution discussed in \ref{intsched} can be seen in the exit routine of listing \ref{lst:entry2}. Basically, the solution boils down to having a seperate data structure for the condition queue and the AS-stack, and unconditionally transferring ownership of the monitors but only unblocking the thread when the last monitor has transferred ownership. This solution is deadlock safe as well as preventing any potential barging. The data structure used for the AS-stack are reused extensively for external scheduling, but in the case of internal scheduling, the data is allocated using variable-length arrays on the callstack of the \code{wait} and \code{signal_block} routines.
216
217\begin{figure}[H]
218\begin{center}
219{\resizebox{0.8\textwidth}{!}{\input{monitor_structs.pstex_t}}}
220\end{center}
221\caption{Data structures involved in internal/external scheduling}
222\label{fig:structs}
223\end{figure}
224
225Figure \ref{fig:structs} shows a high level representation of these data-structures. The main idea behind them is that, while figure \ref{fig:monitor_cfa} is a nice illustration in theory, in practice breaking a threads into multiple pieces to put unto intrusive stacks does not make sense. The \code{condition node} is the data structure that is queued into a condition variable and, when signaled, the condition queue is popped and each \code{condition criterion} are moved to the AS-stack. Once all the criterion have be popped from their respective AS-stacks, the thread is woken-up, which is what is shown in listing \ref{lst:entry2}.
226
227% ======================================================================
228% ======================================================================
229\section{External scheduling}
230% ======================================================================
231% ======================================================================
232Similarly to internal scheduling, external scheduling for multiple monitors relies on the idea that waiting-thread queues are no longer specific to a single monitor, as mentionned in section \ref{extsched}. For internal scheduling, these queues are part of condition variables which are still unique for a given scheduling operation (e.g., no single statment uses multiple conditions). However, in the case of external scheduling, there is no equivalent object which is associated with \code{waitfor} statements. This absence means the queues holding the waiting threads must be stored inside at least one of the monitors that is acquired. The monitors being the only objects that have sufficient lifetime and are available on both sides of the \code{waitfor} statment. This requires an algorithm to choose which monitor holds the relevant queue. It is also important that said algorithm be independent of the order in which users list parameters. The proposed algorithm is to fall back on monitor lock ordering and specify that the monitor that is acquired first is the one with the relevant wainting queue. This assumes that the lock acquiring order is static for the lifetime of all concerned objects but that is a reasonable constraint.
233
234This algorithm choice has two consequences :
235\begin{itemize}
236        \item The queue of the highest priority monitor is no longer a true FIFO queue because threads can be moved to the front of the queue. These queues need to contain a set of monitors for each of the waiting threads. Therefore, another thread whose set contains the same highest priority monitor but different lower priority monitors may arrive first but enter the critical section after a thread with the correct pairing.
237        \item The queue of the lowest priority monitor is both required and potentially unused. Indeed, since it is not known at compile time which monitor will be the lowest priority monitor, every monitor needs to have the correct queues even though it is possible that some queues will go unused for the entire duration of the program, for example if a monitor is only used in a specific pair.
238\end{itemize}
239
240Therefore, the following modifications need to be made to support external scheduling :
241\begin{itemize}
242        \item The threads waiting on the entry-queue need to keep track of which routine is trying to enter, and using which set of monitors. The \code{mutex} routine already has all the required information on its stack so the thread only needs to keep a pointer to that information.
243        \item The monitors need to keep a mask of acceptable routines. This mask contains for each acceptable routine, a routine pointer and an array of monitors to go with it. It also needs storage to keep track of which routine was accepted. Since this information is not specific to any monitor, the monitors actually contain a pointer to an integer on the stack of the waiting thread. Note that the complete mask can be pushed to any owned monitors, regardless of \code{when} statements, the \code{waitfor} statement is used in a context where the thread already has full ownership of (at least) every concerned monitor and therefore monitors will refuse all calls no matter what.
244        \item The entry/exit routine need to be updated as shown in listing \ref{lst:entry3}.
245\end{itemize}
246
247\subsection{External scheduling - destructors}
248Finally, to support the ordering inversion of destructors, the code generation needs to be modified to use a special entry routine. This routine is needed because of the storage requirements of the call order inversion. Indeed, when waiting for the destructors, storage is need for the waiting context and the lifetime of said storage needs to outlive the waiting operation it is needed for. For regular \code{waitfor} statements, the callstack of the routine itself matches this requirement but it is no longer the case when waiting for the destructor since it is pushed on to the AS-stack for later. The waitfor semantics can then be adjusted correspondingly, as seen in listing \ref{lst:entry-dtor}
249
250\begin{figure}
251\begin{multicols}{2}
252Entry
253\begin{pseudo}
254if monitor is free
255        enter
257        continue
259        push criterions to AS-stack
260        continue
261else
262        block
263increment recursion
264\end{pseudo}
265\columnbreak
266Exit
267\begin{pseudo}
268decrement recursion
269if recursion == 0
270        if signal_stack not empty
274                endif
275        endif
276
277        if entry queue not empty
279        endif
280\end{pseudo}
281\end{multicols}
282\caption{Entry and exit routine for monitors with internal scheduling and external scheduling}
283\label{lst:entry3}
284\end{figure}
285
286\begin{figure}
287\begin{multicols}{2}
288Destructor Entry
289\begin{pseudo}
290if monitor is free
291        enter
293        increment recursion
294        return
295create wait context
298        push self to AS-stack
299        baton pass
300else
301        wait
302increment recursion
303\end{pseudo}
304\columnbreak
305Waitfor
306\begin{pseudo}
308        if found destructor
309                push destructor to AS-stack
310                unlock all monitors
311        else
312                push self to AS-stack
313                baton pass
314        endif
315        return
316endif
317if non-blocking
318        Unlock all monitors
319        Return
320endif
321
322push self to AS-stack


text:
Chapter 98. Burns

• A burn patient is a trauma patient; therefore, other injuries should be expected and sought.
• Endotracheal tubes should be large enough to allow ventilation and pulmonary toilet.
• Hypothermia is a major concern, and early, aggressive attempts at prevention are required.
• Modification of the standard lactated Ringer's resuscitation is often necessary in the massive burn or inhalation injury patient or in the very young and old. Additions of colloid, blood, and inotropes are often very useful in restoring hemodynamic stability. Fluid formulas should not be rigid.
• It is important to watch for local perfusion problems and chest wall restriction caused by the burn.
• The burn itself is a low priority for initial care.

Care of the burn patient has improved dramatically over the past 10 to 15 years, resulting in a marked decrease in mortality and morbidity, as well as improved functional outcome. The major reason for this improvement is the multidisciplinary approach by a team that has the clinical decision-making skills, experience, and scientific background to render care in a manner that avoids the predictable pitfalls while also maintaining critical care monitoring. A burn center is the best environment to provide this care.

The burn patient's condition changes dramatically over the course of the injury. The initial postburn period is characterized by cardiopulmonary instability caused by fluid shifts and direct smoke injury to the airways. With the onset of intense wound inflammation, immunosuppression, and infection, physiologic and metabolic parameters change substantially from those seen initially. Treatment therefore must be based on a clear understanding of these changes over time.1,2 This discussion thus will be divided into three time periods—the initial resuscitation period (0 to 36 hours; this chapter), the early postresuscitation period (2 to 6 days; Chap. 99), and the inflammation-infection period, which is usually most evident after the first week (Chap. 100).

Monitoring requirements are no different from those for any other ICU patient. However, vascular access is much more of a problem, and noninvasive measures are often all that are available. A typical burn unit has a procedure room for wound care and often an operating room, but wound care in the ICU is very feasible and actually essential in the unstable patient. Hyperbaric oxygen chambers are not a necessary component and are really only indicated in patients with such severe carbon monoxide exposure that the cytochrome system is saturated with carbon monoxide, which is not readily displaced with 100% oxygen alone (see Chap. 102). It is safe to say that 99% of patients with major burns and some degree of carbon monoxide inhalation do not benefit from hyperbaric oxygen. The secret to a successful patient outcome, however, remains in the knowledge base, judgment, and decision-making skills of the personnel, not in the external environment.1,2

Cardiopulmonary instability characterizes the resuscitation phase. Life-threatening airway and breathing problems are major concerns at this time, with ...

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text:
Topics in Combinatorial Group Theory (for a short talk).

I have started course on combinatorial group theory and supposed to give a short talk/presentation. It would be really helpful if someone can suggest some good/interesting topics to cover. Thanks

• Talk to your professor? – Michael Joyce Feb 25 '14 at 1:21
• @MichaelJoyce that can be done but i was looking for out of box suggestion that may interest anyone, i hope you understand – schzan Feb 25 '14 at 1:22

Combinatorial group theory is a large subject, and is somewhat ill-defined (it is thus called because it uses combinatorics heavily, or because it utilises a combination of techniques? I have heard both argued...). For the purposes of this answer, I shall take it to mean "the study of abstract, discrete infinite groups and their presentations". By discrete, I simply mean we are not considering any topology on the groups. Since the 1980s the more trendy subject of "geometric group theory" has been leading the way, but these subjects are broadly similar and the symmetric difference of the practitioners is very small (by my own observations - please feel free to disagree!).

Dislaimer: I should say that I cite quite a few of my own posts in this post. That is because I am talking about stuff I find interesting so have posted quite a lot of stuff on Math.SE on this!

When working on a talk it is often useful to know the history of the subject you are working on. I stumbled across a wonderful article on the pre-70s history of combinatorial group theory (and really pre-70 is what you are after!) called Some groups I have known by B.H.Neumann. (It is worth pointing out that the "Hanna" he makes reference to is his late wife. Both B.H. and Hanna were formidable group theorists (they are the N and N in HNN-extensions), and two of their sons, Walter and Peter Neumann, have justifiably similar reputations.)

Some Classical problems you may find interesting

Broadly speaking, there were four questions which drove combinatorial group theory in the early days. The first is called Burnside's problem, the last three are Dehn's problems (the word, conjugacy and isomorphism problems).

The Burnside problem A group is called torsion if every element has finite order. Burnside's problem asks if it is possible for a finitely generated infinite torsion group to exist. Note that without the "finitely generated" the question has an obvious answer: just take the direct sum of infinitely many finite groups. The wikipedia article is pretty good on this, and I am not sure that I have anything to add. I would like to point out that 1) a fields medal has been awarded for work on the modified version of this problem 2) the current prize for "best example" goes to Ol'shanskii, and 3) Novikov and Adian (pronounced "Adyyyyyyaaan") play important roles in the story of both this problem and Dehn's problems. Finally, all known examples are infinitely presented. Find a finitely presented infinite torsion group and people will know your name...

Dehn's problems I wrote a long post on Dehn's problems here.

Some topics which I would speak on if I was in your place

If I wanted to give a talk on combinatorial group theory, but didn't just want to point out that free groups have soluble word problem (say what now?!?), I would give an introduction to one of the following areas. But I am not you. These are just some ideas for you to ponder...

Non-Hopfian groups A group is Hopfian if every surjective endomorphism is an isomorphism, so a non-Hopfian group is a group which has a surjective endomorphism which has a non-trivial kernel. For example, consider the infinite (countable) free group and then kill a generator. The resulting group is still infinite (countable) free, so this group is non-Hopfian. A more subtle example is the so-called Baumslag-Solitar group $BS(2, 3)=\langle a, b; b^{-1}a^2b=a^3\rangle$. I wrote a lengthy post on these groups here, and an excellent, and very old, article which talks about their early history is A two-generator group isomorphic to a proper factor group by B.H.Neumann (this is pre-Baumslag-Solitar's example).

van Kampen diagrams van Kampen diagrams give a way of visualising the word problem. If all diagrams satisfy certain conditions (called the small cancellation conditions) then your group has soluble word and (if the conditions are strong enough) conjugacy problem. The classical reference is the last chapter of Lyndon and Schupp's book Combinatorial group theory. See also this post of mine.

Fundamental groups of graphs The fundamental group of a graph is a free group. If you are comfortable with covering spaces and so other stuff from topology then you can prove some remarkable results about free groups by thinking of them as fundamental groups of graphs. You would want to look up something called "Stallings' foldings". The original paper is The topology of finite graphs by J.Stallings, and you will also find Allan Hatcher's book Algebraic Topology helpful. See also this post of HJRW.

Bass-Serre theory Bass-Serre theory is the theory of groups acting on trees. HNN-extensions and free products with amalgamations all act on trees, and if you have ever heard of a "graph of groups" then it is an object from this theory. Bass-Serre theory is extremely powerful, and a wonderful introduction to group actions. The classical text is the book Trees by Serre, although there is a modern book called Groups, graphs and trees by John Meier which is much more readable.

One-relator groups A one-relator group is a group with a presentation of the form $G=\langle X; R^n\rangle$, $n\geq 1$ and $R$ not a proper power of any element. It has torsion if and only if $n>1$, has soluble word problem, every torsion element is conjugate to a power of $R$, and if it is freely indecomposable then every proper subset of $X$ generates a free group. All of these wonderful results can be proven using a standard method, called Magnus' method. The idea is to induct on the length of the word $R^n$. If you have Magnus, Karrass and Solitar's book then the proofs are tricky, employing groups with "staggered" presentations. A chap called Moldovanskii realised that you could use the same idea, but instead embed $G$ into an HNN-extension of a group with a shorter defining relation (this is substantially neater). The best references I have found are an article of Fine and Rosenberger The Freiheitssatz and its extensions in a book called The mathematical legacy of Wilhelm Magnus, and a paper of McCool and Schupp On one-relator groups and HNN-extensions.

The word problem for the fundamental groups of closed, orientable surfaces When Dehn posed his three fundamental problems of group theory he proves that the fundamental groups of closed, orientable surfaces of genus at least two have word problem soluble by "Dehn's algorithm" (not that he called it that, mind!). His proof led to the development of small cancellation theory (mentioned in the "van Kampen diagram" paragraph, above) and ultimately to the development of hyperbolic groups and all that they lead to (I talk more about this in my post on Dehn's problems which I mentioned nearer the top). Because of this pedigree, it would be interesting to go through these proofs and see if you could present them in your talk. I do not know if this is possible, but certainly if I was going to do a talk next week this would be my subject of choice: explain Dehn's original proof! (Or give a modern proof of it. Or something.)

Anyway, I hope you found this all useful. You really should speak to your professor about this, but also you want to think about it by yourself. You want to find something which you find interesting, not just something your professor thinks is "at about your level..."!

• really thanks, this gives me things to work out. – schzan Mar 1 '14 at 14:04

I would add to the list some of the problems from identities among relations. (A good article to consult is

J.-L. Loday, 2000, Homotopical Syzygies, in Une dégustation topologique: Homotopy theory in the Swiss Alps, volume 265 of Contemporary Mathematics, 99 – 127, AMS.

The visual element is good so it makes for a nice presentation. The idea is very simple but then its development requires a bit of care, so again a nice topic to handle. The subtopic of Pictures is also neat.

• It should be pointed out that pictures are dual to van Kampen diagrams (I think Pride came up with them first, and I think actually that these pictures are slightly different from Pride's ones. Hmm...). And I agree that they are very neat! – user1729 Feb 27 '14 at 11:34
• Igusa is credited with them as well and may have the edge on Steve Pride. My main point is that that material is a very nice intro to some of the outward looking links from Comb. Group Theory. It is fun, and easy to present as it does not require that much background. – Tim Porter Feb 27 '14 at 14:42
• Ah, okay, I had never heard of Igusa before, but know something of pictures. I'll look his stuff up. You live and learn :-) – user1729 Feb 27 '14 at 14:53
• Loday's paper is a good one to get those aspects of pictures and has the references to Igusa. – Tim Porter Feb 27 '14 at 19:29

• The free group of rank $2$ acts on the sphere by orthogonal transformations. By carefully dissecting the free group, you can produce paradoxical decompositions. The Wikipedia article explains it all very nicely. Of course, as was already suggested, your instructor can indicate whether the topic is actually suitable for your course. – James Feb 25 '14 at 9:54


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# Assembly and seasonality of core phyllosphere microbiota on perennial biofuel crops

## Abstract

Perennial grasses are promising feedstocks for biofuel production, with potential for leveraging their native microbiomes to increase their productivity and resilience to environmental stress. Here, we characterize the 16S rRNA gene diversity and seasonal assembly of bacterial and archaeal microbiomes of two perennial cellulosic feedstocks, switchgrass (Panicum virgatum L.) and miscanthus (Miscanthus x giganteus). We sample leaves and soil every three weeks from pre-emergence through senescence for two consecutive switchgrass growing seasons and one miscanthus season, and identify core leaf taxa based on occupancy. Virtually all leaf taxa are also detected in soil; source-sink modeling shows non-random, ecological filtering by the leaf, suggesting that soil is an important reservoir of phyllosphere diversity. Core leaf taxa include early, mid, and late season groups that were consistent across years and crops. This consistency in leaf microbiome dynamics and core members is promising for microbiome manipulation or management to support crop production.

## Introduction

The phyllosphere (aerial parts of plants) represents the largest environmental surface area of microbial habitation on the planet1,2,3, and much of that surface area is cultivated agriculture, including an estimated 1.5 × 107 km2 of cropland4. Phyllosphere microorganisms may provide numerous benefits to plants, including increased stress tolerance5,6,7, promotion of growth and reproduction8,9,10, protection from foliar pathogens11, and, with soil microbes, control of flowering phenology12. Phyllosphere microorganisms are also thought to play important roles in Earth’s biogeochemical cycles by moderating methanol emissions from plants13,14 and contributing to global nitrogen fixation15. Despite this importance, knowledge of phyllosphere microbiomes remains relatively modest, especially for agricultural crops3,16,17,18. To leverage plant microbiomes to support productivity and resilience to environmental stress both above and below ground19,20,21, there is a need to advance foundational knowledge of phyllosphere microbiome diversity and dynamics.

Biofuel crops like miscanthus and switchgrass are selected to have extended growing seasons, to produce ample phyllosphere biomass, and to maintain high productivity when grown on marginal lands that are not optimal for food agriculture22,23,24,25. In the field, these grasses provide extensive leaf habitat, with a seasonal maximum leaf area index (LAI) of 6.2 for switchgrass, and 10 m2 leaf surface per m2 land for miscanthus22, as compared to a maximum LAI of 3.2 for corn26. Upon senescence, the aboveground biomass is harvested for conversion to biofuels and related bioproducts. Improved understanding of the phyllosphere microbiome is expected to advance goals to predict or manage changes in biomass quality in response to abiotic stress like drought27,28,29,30,31 or biotic stress like foliar pathogens32,33,34.

Leveraging the Great Lakes Bioenergy Research Center’s Biofuel Cropping System Experiment (BCSE; a randomized block design established at Michigan State’s Kellogg Biological Station in 2008), we ask two questions of the bacterial and archaeal communities (henceforth: microbiomes) inhabiting the leaf surfaces and the associated soils of switchgrass and miscanthus: (1) Are there seasonal patterns of phyllosphere microbiome assembly? If so, are these patterns consistent across fields of the same crop, different crops, and years? (2) To what extent might soil serve as a reservoir of phyllosphere diversity? We find strong seasonal patterns of assembly that is consistent across crops and years, and prioritize a core set of leaf-associated microbiota that are persistent over the season but fluctuate in their relative contributions to the community. Additionally, several lines of evidence suggest that the soil is a key reservoir of leaf microbiota, but also that the leaf habitat selects for particular taxa that generally are not prominent in the soil.

## Results

### Sequencing summary and alpha diversity

In total, we sequenced 373 phyllosphere epiphyte (leaf surface) and soil samples across the two growing seasons in 2016 and 2017. The number of sequences per sample after our 97% OTU (operational taxonomic unit) clustering pipeline ranged from 20,647 to 359,553. The percentage of sequences belonging to chloroplasts and mitochondria per sample range between 0.2–99.8%, but 235 of the samples (63%) had fewer than 10% chloroplasts and mitochondria reads. After removing sequences that were attributed to chloroplasts and mitochondria or that had unassigned taxonomic classification, we filtered samples that contained fewer than 1000 reads and rarefied the remaining samples to 1000 reads for comparative analyses. While this number of reads is not sufficient to fully capture soil diversity, it does capture phyllosphere diversity (Fig. 1a). The majority of the switchgrass and miscanthus phyllosphere communities were exhaustively sequenced, and approached richness asymptotes with their associated soils.

As reported for other plants3,35, switchgrass and miscanthus phyllosphere communities had relatively low richness, with 1480 total taxa observed across both crops and consistently fewer than 150 taxa per time point, though there was modest seasonal variability in richness (Supplementary Fig. 1). Cumulative richness increased most between the two earliest time points, and then tapered gradually upward until senescence (Fig. 1b), showing that the contributions of new taxa to community richness were low but consistent over time.

### Seasonal microbiome dynamics

To perform the most complete temporal analyses of phyllosphere microbiome seasonality, we also subsampled the amplicon sequencing dataset to include the maximum number of time points, resulting in inclusion of 51 discrete leaf and soil samples collected over 18 total time points. The overarching patterns in beta diversity were consistent and statistically indistinguishable from those derived from the same dataset to include more reads per sample but fewer time points (Mantel tests all p < 0.001; Supplementary Table 1, Supplementary Table 2, Supplementary Fig. 2). For consistency, we report the patterns from 1000 reads per sample in the main text, but for transparency and comparison, we report results from the minimum reads per sample, inclusive of the complete time series, in supplementary materials.

There were directional seasonal changes in the structures of switchgrass and miscanthus phyllosphere bacterial and archaeal communities (Fig. 2a, Table 1), and these could be attributed to changes in both soil and leaf properties, as well as to weather (Supplementary Table 3). Over the 2016 season, miscanthus and switchgrass phyllosphere communities were synchronous (changed at the same pace and to the same extent, Procrustes m12 = 0.349, R = 0.807, p = 0.021), and community structure became less variable as the growing season progressed (Supplementary Fig. 3). Switchgrass 2016 and 2017 leaf communities were highly synchronous, suggesting a predictable, interannual assembly (Procrustes m12 = 0.011, R = 0.994, p = 0.008). The switchgrass community structures were overall equivalent between 2016 and 2017, with the exception of the final time points that were collected post-senescence. Together with the species accumulation analysis (Fig. 1b), these data suggest that these phyllosphere communities are not stochastically assembled, nor are they a linear accumulation over seasonal leaf exposure to whatever taxa are dispersed. The communities follow a directional assembly over the growing season, and the assembly was highly consistent over 2 years in the switchgrass.

### Contribution of soil microorganisms to phyllosphere assembly

The major sources of microorganisms to the phyllosphere are soils2, the vascular tissue of the plant or its seed36, and the atmosphere or arthropod vectors3. As several studies have shown that soil microbes contribute to the phyllosphere microbiome35,37, we wanted to understand the potential for soil as a reservoir of microorganisms inhabiting switchgrass and miscanthus phyllospheres. We hypothesized that the intersect of shared soil and phyllosphere taxa would be highest early in the season, after the young grasses emerged through the soil. Our deep sequencing effort also provided the opportunity to investigate differences in taxon relative abundances between soil and leaf communities, and to understand what contributions, if any, the soil rare biosphere has for leaf assembly.

First, we interrogated the 2016 time series to determine the influence of soil-detected taxa on leaf microbial communities for both crops. As expected, the structures of leaf communities were highly distinct from soils (Fig. 2b, Supplementary Fig. 2B, Table 1). Though soil communities also changed seasonally, they experienced less overall change than the phyllosphere (Table 1, Fig. 2b, Supplementary Fig. 2C). While fertilization had no impact on phyllosphere communities, it did have small but significant influence on soil communities (Table 1). These seasonal and fertilization treatment patterns were reproduced in 2017 for switchgrass (Table 1).

To better understand the relationship between soil and phyllosphere communities, including the influence of rare members of the soil, we searched for phyllosphere taxa within the full soil dataset (not subsampled). Approximately 90% of phyllosphere OTUs were present in soil samples, with negligible differences between the two crops and modest variability over time (Fig. 3a). When considering the relative abundances of taxa, the mean fraction of phyllosphere communities found in soil samples was even higher at 98% and exhibited no clear trend over time (Fig. 3b). Our results show that the majority of abundant, commonly detected taxa in the phyllosphere are also present in the soil—albeit often at very low abundances (see below)—highlighting a potentially important role of the soil in harboring phyllosphere taxa between plant colonization events.

Given the large proportion of phyllosphere taxa present in the soil, we explored the potential role that immigration from the soil may have in shaping phyllosphere community composition and seasonal patterns. On balance, many abundant and persistent phyllosphere taxa were in low abundances in the soil, though there was a positive association between soil and leaf abundances for soil taxa > 1 e04 relative abundance (Fig. 3c). This result indirectly supports the presence of an ecological filter operating on the phyllosphere that favors some taxa while disfavoring others. To further investigate how ecological filtering may vary over the growing season, we compared observed trends in OTU richness with those predicted by a source-sink null model which simulated demographic stochasticity and random immigration from the soil between subsequent sampling points (see “Methods”, Fig. 3d–f). Observed phyllosphere communities were dramatically less rich than null model predictions, again supporting the presence of a strong ecological filter. Such a filter could be due to host plant selection, environmental filtering, competitive exclusion among microbial taxa, or a combination of all three. According to this model, the strength of filtering did not trend consistently over the growing season.

Finally, other studies have found that soil microbes contribute more to early season phyllosphere communities38, and we observed similar patterns: the most abundant soil taxa that were also detected on leaves were more prominent in the early season and then became rare and transient on leaves in the late season (Supplementary Fig. 4).

### Core members of the switchgrass and miscanthus phyllosphere

There was high overlap between switchgrass and miscanthus phyllosphere communities and a trend towards increased intra-crop similarity during senescence (Supplementary Fig. 5). There was also a modest influence of host crop in 2016 (Table 1). Therefore, we defined a core microbiome for each crop and season (Supplementary Data 1). We applied an established macroecological approach39 to consider both the occupancy and abundance patterns of these taxa (Fig. 4a–c); abundance-occupancy relationships have been previously explored for microbial communities40,41 and we utilize it here for ecologically informing a core microbiome. Occupancy is an ecological term that considers how consistently a taxon is detected across samples in the dataset, expressed as a proportion of occurrences given the total samples collected (e.g., 1.0 or 100%). Occupancy provides a dataset-aggregated term describing taxon persistence, which can be informative for defining core taxa when datasets include a time series42.

In contrast to the taxa unique to crops and years, which were rare and not persistent, most of the highly abundant and prevalent taxa were shared (Fig. 4a–c). We first quantified the abundance and occupancy distributions of OTUs, and then identified OTUs that were consistently detected across replicate plots at one sampling time (occupancy of 1) to include in the core. We found that these 44, 51 and 42 core taxa (as highlighted in Fig. 4a–c) contribute 84.4%, 79.5% and 79.4% to the total beta diversity in miscanthus 2016, switchgrass 2016 and 2017, respectively (Fig. 4d–f). While these core taxa were highly abundant and persistent on these crops’ leaves, their functions are yet unknown and additional members could also transiently contribute. However, we suggest that the core taxa identified here should be prioritized for follow-up study of functionality and potential plant benefits.

Notably, if we had defined the core as those taxa uniquely detected on each crop (as in a Venn diagram analysis, Supplementary Fig. 6), we would have instead identified rare and transient taxa (Fig. 4a–c). Thus, a core analysis based on presence and absence, instead of on abundance and occupancy, would have provided a different, and arguably less ecologically relevant, core for these perennial crops. The approach used here provides a reproducible and conservative option for longitudinal series, and allows for systematic discovery43,44 of a replicated core over time.

The core taxa included several Proteobacteria (Methylobacterium, Sphingomonas, and Pseudomonas spp.) and Bacteroidetes (Hymenobacter spp.). The taxonomic affiliations of these core taxa are consistent with the literature for other phyllosphere communities2,3,18,35,45,46, providing new support for their seasonal importance in the phyllosphere.

We then performed a hierarchical clustering analysis of standardized (e.g., z-score) dynamics to explore seasonal trends of core taxa (Fig. 4g–i, Supplementary Fig. 7)47. This analysis identified several discrete, seasonally-defined groups of core taxa in switchgrass and miscanthus, respectively. Seasonal groups were taxonomically consistent across crops and years (Fig. 4j–l). This finding suggests potential for functional redundancy because closely related taxa are hypothesized to have substantial overlap in their functional repertoire48. The early-season groups (Supplementary Fig. 7, Fig. 4g–i red traces) included several Gammaproteobacteria (Fig. 4j–l). The late-season groups (Supplementary Fig. 7, Fig. 4g–i blue traces) were comprised of Alphaproteobacteria, Cytophagia and Actinobacteria and were pronounced in switchgrass (Fig. 4j–l). The third groups (Supplementary Fig. 7, Fig. 4g–i gray traces) included taxa that peaked in relative abundance mid-season, including Alphaproteobacteria and few taxa belonging to Beta- and Gamma-proteobacteria, Cytophagia, Sphingobacteria, and Actinobacteria (Fig. 4j–l).

In addition, several Proteobacteria classes exhibited what appear to be compensatory dynamics (Fig. 5a). However, despite similarity in the membership and dynamics of the core microbiota on both crop plants, there were differences in the relative abundances of the same taxa across crops (Fig. 5b).

### Contributions of abiotic variables, space, time, and crop

We summarize our analyses of the contributions of crop (host plant), space, time, and abiotic variables to the assembly of the core phyllosphere community in order of least to most important. There was no explanatory value of the spatial distance between the plots for community beta diversity (assessed by distance-decay of beta diversity using a Mantel test with a spatial distance, r: 0.013, p = 0.256). This finding is different from a recent study of annual crops (common beans, canola, and soybean) that showed an influenced of sampling location on leaf microbiome structure38. Here, among those that variables were significant, crop (switchgrass or miscanthus) had the lowest explanatory value (Table 1). However, our work agrees with previous research that has shown a relationship between plant species/genotype and the leaf microbiota of perennial plants such as wild mustard49, sugar cane37, and tree species like birch, maple, and pine50. Time and measured abiotic factors had highest explanatory value (Table 1, Supplementary Table 3). Related, Copeland et al. 2015 showed that stage in plant development can influence leaf microbiome structure in annual crops.

## Discussion

We found that soil is a major reservoir of leaf microorganisms for switchgrass and miscanthus. Deep sequencing was required of the soils to observe many of the prominent leaf taxa for these perennial crops. This is in contrast to the studies of other plants that have suggested that the phyllosphere is comprised largely of passively dispersed and stochastically assembled microbes from the atmosphere51,52,53, but in agreement with studies in sugarcane37,54, grape55, and perennial mustard49 that have suggested soil origins of leaf microbiota. Notably, our analysis cannot inform directionality or mechanism of dispersal, which could have occurred between soil and leaf via wind, insects, or through grass emergence, etc. While 133 leaf OTUs (9%) observed in the phyllosphere could not be detected in the soil (using the unrarified soil dataset) and may be attributable to non-soil reservoirs, the vast majority of leaf microbes were detectable in local soils and non-neutral assembly patterns suggest both determinism and habitat filtering.

Our data suggest a compensatory relationship between members within the Proteobacteria, where members of Gammaproteobacteria and Alphaproteobacteria replace one another over time (Fig. 5). Such community transitions have been observed on the phyllosphere of crops such as sugarcane37, common beans, soybeans, and canola38. A study of endophytic bacteria of prairie grasses, including switchgrass, showed the same trend in abundance of Gamma- and Alphaproteobacteria56 suggesting that these phyllosphere taxa are facultative endophytes or are similarly affected by the plant development. The benefits plants may gain from these taxa are well characterized (see review from Bringel57), however it remains unknown what drives the exclusion of Pseudomonas and gives rise to Alphaproteobacteria (predominantly Methylobacteria) in the phyllopshere and endopshere. One possible explanation would be nutrient availability regulated by the plant development which would selectively influence the abundances of these taxa. Delmotte and colleagues58 hypothesized that Pseudomonas specialize on monosaccharides, disaccharides and amino acids, whereas Sphingomonas and Methylobacteria are generalist scavengers that can subsist on a variety of substrates present at low amounts.

The crop-specific dynamics of some core taxa suggest their adaptation to or selectivity by the host plant. There were some core OTUs that had consistent dynamics across both crops, but these examples demonstrate, first, that dynamics can be crop specific, and second, that abiotic filtering of an OTU to a particular crop could be manifested as differences in dynamics in addition to the more extreme scenarios of taxon exclusion or crop specificity. Indeed, because the crop-unique taxa were generally rare and transient (Fig. 4), the dynamics of core taxa together with crop-distinctive dynamics may harbor clues as to the competitive landscape and microbially important changes in the hostsʼ leaf environments across crops.

As a point of discussion, we also considered the potential role of priority effects on the community assembly. Priority effects occur when differences in colonization history result in different community assembly outcomes59. While we cannot claim that colonization histories had no effect on phyllosphere successional patterns, the data shown in Supplementary Figs. 3 and 5 suggest that any such effects were relatively minor. Specifically, beta-dispersion among plants of the same species decreased over time (Supplementary Fig. 3), and Bray-Curtis dissimilarity between switchgrass and miscanthus cohorts decreased over time (Supplementary Fig. 5). Both lines of evidence point to phyllosphere community convergence over time, despite early some differences in community composition, suggesting that colonization history per se had little effect on successional trajectories. This is not to say definitively that early colonists did not modify the phyllosphere environment such that particular species were subsequently favored or disfavored, but that early colonists did not modify the phyllosphere environment differentially and/or to a meaningful degree. The majority of the early colonizers were rare or absent by the end of the growing season (Fig. 4g–i), and so they did not modify the phyllosphere environment (i.e., exert priority effects) to ensure and/or enhance their competitive dominance (i.e., niche construction, or niche preemption).

To conclude, we investigated the assembly and seasonal dynamics of the phyllosphere and soil microbes of two perennial grasses, switchgrass and miscanthus, and found consistent community trajectories and memberships across growing seasons, suggesting that their key players are predictable and that most of them can be detected in associated soils. Understanding the seasonal patterns of these key taxa could be used to improve biomass production, plant health, or facilitate conversion. As seen in work by Agler et al.60, the introduction or control of a few key microbial species can have significant impact on the host plant phenotype. Next steps should be to interrogate core members for functionality and direct interactions with the plant, including investigations of the interactions among core members and with the host crop. This exploration lays the foundation for an approach to biofuel grass production that incorporates an understanding of host-microbe and microbe-microbe interactions.

## Methods

### Site description and sampling scheme

Our study system is located within the Great Lakes Bioenergy Research Center (GLBRC), BCSE in Hickory Corners, Michigan (42o23’41.6” N, 85o22’23.1” W). We collected samples from two biofuel crops within the BCSE, switchgrass (Panicum virgatum L. cultivar Cave-in-rock) and miscanthus (Miscanthus x giganteus). Both crops had been continuously grown since 2008, in replicate 30 × 40 m plots arrayed in a randomized complete block design. Within each plot, nitrogen-free (no fertilizer) subplots were maintained in the western-most 3 m of each plot. We sampled replicate plots 1–4 in both the main and the nitrogen-free subplots. We collected leaf and bulk soil samples every three weeks across the 2016 growing season, including bare soil in April through senescence in October and November. In total, we collected 152 soil samples (72 switchgrass and 80 miscanthus) and 136 leaf samples (64 switchgrass and 72 miscanthus). At each sampling time, leaves were collected and pooled at three flags along a standardized path within each plot. Leaves were removed from the plant stem using ethanol sterilized gloves, then stored in sterile whirl-pak bags until processing. Bulk soil cores (2 × 10 cm) were collected at the same three locations within a plot, sieved through 4 mm mesh, then pooled and stored in whirl-pak bags. All samples were kept on wet ice for transport, then stored at −80 °C.

Soil physico-chemical characteristics (pH, lime, P, K, Ca, Mg, organic matter, NO3–N, NH4–N, and percent moisture) were measured by the Michigan State University (MSU) Soil and Plant Nutrient Lab (East Lansing, MI, USA, http://www.spnl.msu.edu/) according to their standard protocols. From each plot, 10 switchgrass leaves or 5 miscanthus leaves were processed for leaf dry matter content according to61. Dried leaves were ground to a fine powder using a Sampletek 200 vial rotator and iron roll bars (Mavco Industries, Lincoln, NE, USA), then carbon and nitrogen were measured on an elemental analyzer (Costech ECS 4010; Costech Analytical Technologies Inc, Valencia, CA, USA). Weather data was collected from the MSU Weather Station Network, for the Kellogg Biological Station location (https://mawn.geo.msu.edu) for each sampling day, and plant height and soil temperature were measured on a per-plot basis.

### Nucleic acid extraction and sequencing

Throughout, we use microbiome to refer to the bacterial and archaeal members as able to be assessed with 16S rRNA gene sequence analysis. Soil microbial DNA was extracted using a PowerSoil microbial DNA kit (MOBio Inc. Carlsbad, California, USA) according to manufacturer’s instructions. Phyllosphere epiphytic DNA was extracted from intact leaves using a benzyl chloride liquid:liquid extraction, followed by an isopropanol precipitation62, using ~5 g of leaves (5–10 switchgrass leaves, or a minimum of 2 miscanthus leaves). Metagenomic DNA from both soil and phyllosphere was quantified using a qubit 2.0 fluorometer (Invitrogen, Carlsbad, CA, USA), and DNA concentrations were normalized between all samples prior to sequencing. Paired-end amplicon sequencing was completed by the Department of Energy’s Joint Genome Institute (JGI) using an Illumina MiSeq sequencer, and using the 16S-V4 primers 515F (5′-GTGCCAGCMGCCGCGGTAA- 3′) and 806R (5′-GGACTACHVGGGTWTCTAAT-3′)63, according to the JGI’s standard operating protocols, and incorporating plastid- and mitochondria-blocking peptide nucleic acids (mPNA: 5′-GGCAAGTGTTCTTCGGA-3′, pPNA: 5′-GGCTCAACCCTGGACAG-3′) to prevent co-amplification of host-derived 16S rRNA genes64.

### Sequence quality control and defining taxa

BBDuk (v 37.96) was used to remove contaminants and trim adaptor sequences from reads. Reads containing 1 or more’N’ bases, having an average quality score of less than ten or less than 51 bases were removed. Common contaminants were removed with BBMap (v 37.96). Primers were trimmed using cutadapt (v1.17). Reads were merged, dereplicated, clustered into 97% identity with usearch (v10.0.240), and classified against version 123 of the Silva Database65 using sintax66. All reads classified as mitochondria, chloroplast or unclassified were removed before the analysis. Additionally, reads from 4371 OTUs assigned only to the domain level were extracted and reclassified using SINA online aligner (https://www.arb-silva.de/aligner/)65. Six hundred and ninety-six unclassified reads subsequently were confirmed to be Bacteria could then be classified to more resolved taxonomic levels. Remaining reads were BLASTed against the entire NCBI nucleotide database and specifically against the switchgrass genome to check for non-specific binding, but no hits could be found. We also performed analyses using OTUs defined at 100% sequence identity (zOTUs) and found that overarching patterns of beta diversity were statistically indistinguishable from those observed using OTUs defined at 97% sequence identity.

### Alpha and beta diversity

For alpha and beta diversity analyses, we performed analyses to datasets subsampled to the minimum observed quality-filtered reads per sample (141), as well as to 1000 reads per sample. We did this to enable comparison of the most complete time series to the most complete comparative view of diversity. We report richness as total number of OTUs clustered at 97% sequence identity. We used the protest function in the vegan package in R67 to test for synchrony in patterns across crops and years. To calculate beta dispersion, we used the betadisper function in the vegan package in R67, which is a multivariate analogue of Levene’s test for homogeneity of variances. PERMANOVA was used to test hypothesis of beta diversity using adonis function in the vegan package in R67.

Though we performed analyses using 97% sequence identity for the OTU definitions, we also checked that beta-diversity patterns were maintained if we have used a 100% sequence identity for clustering, and found them to be statistically indistinguishable by two separate tests (Correlation in a symmetric Procrustes rotation = 0.9075, p-value 0.001 on 999 permutations; Mantel correlation = 0.6966, p-value 0.001 on 999 permutations), as reported for other studies68. Therefore, the strong seasonal patterns observed are robust regardless of using 97% or 100% OTUs.

### Source-sink models and contributions of soil taxa to leaf communities

Given that virtually all phyllosphere taxa were present in the soil, we evaluated the degree to which observed seasonal patterns in phyllosphere community composition could be explained with a null model. The null model assumed functional equivalence among taxa and random source-sink dynamics from the soil. For each crop, we simulated community dynamics between each pair of sequential samples. This involved: (1) calculating the total number of 0.1% incremental increases/decreases in OTU relative abundances observed between the two sampling points; (2) randomly and iteratively selecting OTUs, weighting their probability of selection by their relative abundances, to increase or decrease by 0.1% increments of relative abundance until reaching the total number of observed increases/decreases for the sample pair; (3) counting the number of immigrant OTUs which appeared only in the second sample of the pair; (4) randomly selecting OTUs in the simulated community to decrease by 0.1% increments until the total decrease equaled the observed number of arriving OTUs multiplied by their median initial abundance (0.1%); and then (5) randomly selecting, again weighting their probability of selection by their relative abundance, the predicted number of immigrant OTUs from the soil community, such that the final simulated community abundance was equal to 1000 sequences. The source soil community was generated by pooling all soil samples from both years. We used this process to simulate demographic stochasticity. In the model, it was assumed that 0.1% incremental changes in relative abundance realistically reflects phyllosphere population dynamics, and that an immigration event results in the initial relative abundance of an OTU at 0.1%. Importantly, even if these assumptions are imprecise, the simulation provides a consistent baseline of community composition against which to compare observations over the growing season.

### Core taxa selection

To infer the core phyllosphere taxa and prioritize them for further inquiry, we calculated the abundance-occupancy distributions of taxa, as established in macroecology (e.g., Shade et al.40). For each OTU, we calculated occupancy and mean relative abundance at each time point by crop and year. Only OTUs with occupancy of 100% (found in all samples at a particular time point) were prioritized as core members. Using this conservative threshold for occupancy, we included all OTUs that had strong temporal signatures; these taxa also were in high abundance and were persistent as indicated by their abundance-occupancy distributions. These core taxa also represent potentially important players in plant development, as they were detected at least at one time point in all sampled fields.

We quantified the explanatory value of the core members to community temporal dynamics using a previously published method of partitioning community dissimilarity:69

$${\mathrm{C}} = \frac{{{\mathrm{BC}}_{{\mathrm{core}}}}}{{{\mathrm{BC}}_{{\mathrm{all}}}}}$$
(1)

where C is the relative contribution of community Bray Curtis (BC) dissimilarity attributed to the core OTUs.

To be consistent with all other analyses in this work, we used the 97% sequence identity to define OTUs in our analysis of the core microbiome. We reasoned that 97% OTU clusters would be more conservative relative to 100% OTU clusters, given that any sequencing errors, as well as sequences that had less than perfect match among multiple copies of the 16S rRNA gene from the same genome, would result in inflation and potential overestimation of the core. We provide the representative sequence of each core OTU in Supplementary Data 1 so that the data can be re-analyzed using different OTU definitions and compared to the core detected here.

### Hierarchical clustering

To understand the seasonal abundance patterns of the core taxa we performed hierarchical clustering. We used a z-scored relative abundance matrix subset to contain only core taxa to generate a w complete linkage distance matrix using the R function hclust()47. Groups of core taxa with similar dynamics were defined from the dendrogram using the function cutree() in R with number of desired groups (k=) to be close to the number of sampling time points; 8 for miscanthus 2016, 5 for switchgrass 2016 and 7 for switchgrass 2017.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

## Data availability

The datasets generated and/or analyzed during the current study are available in the Joint Genomes Institute Genome Portal (https://genome.jgi.doe.gov/portal/) with projects designated by year and sample type (Project ID 1139694 [https://genome.jgi.doe.gov/portal/pages/dynamicOrganismDownload.jsf?organism=SwiandphylliTags_FD], and Project ID 1139696 [https://genome.jgi.doe.gov/portal/SwiandmsoiliTags_FD/SwiandmsoiliTags_FD.download.html] for 2016 season phyllosphere and soil; and Project ID 1191516 [https://genome.jgi.doe.gov/portal/SwiandphyiTagsII_FD/SwiandphyiTagsII_FD.download.html] and Project ID 1191517 for 2017 [https://genome.jgi.doe.gov/portal/pages/dynamicOrganismDownload.jsf?organism=SwiandsoiiTagsII_FD] season phyllosphere and soil sequences, respectively).

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## Acknowledgements

We thank S.H. Lee, M. Sleda, S. Wu and M. Nunez for technical assistance in the field and laboratory. This material is based upon work supported by the Great Lakes Bioenergy Research Center, U.S. Department of Energy, Office of Science, Office of Biological and Environmental Research under Award Numbers DE-SC0018409 and DE-FC02–07ER64494, by the National Science Foundation Long-term Ecological Research Program (DEB 1637653) at the Kellogg Biological Station, and by Michigan State University AgBioResearch. The work conducted by the U.S. Department of Energy Joint Genome Institute, a DOE Office of Science User Facility, is supported under Contract No. DE-AC02-05CH11231. This work was supported in part by Michigan State University through computational resources provided by the Institute for Cyber-Enabled Research. N.S. acknowledges support from the Michigan State Plant Resilience Institute.

## Author information

Authors

### Contributions

A.S. designed the study. A.S., K.L.G., J.S. and N.S. conducted field work. K.L.G. executed lab work. J.S., N.S., J.G. and A.S. analyzed the data. All authors discussed and revised the manuscript.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature Communications thanks Isabelle Laforest-Lapoint, Jose Montoya and Andrea Ottesen for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Rights and permissions

Reprints and Permissions

Grady, K.L., Sorensen, J.W., Stopnisek, N. et al. Assembly and seasonality of core phyllosphere microbiota on perennial biofuel crops. Nat Commun 10, 4135 (2019). https://doi.org/10.1038/s41467-019-11974-4

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# Kaplan Review

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01 Jun 2009, 07:06
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Hi Everyone,

I am taking my GMAT on August 13th but I have been studying on and off for about a year. I feel I am pretty close to the 700 level. I just wanted to say that this is a great board - in my opinion the best on the net. I wanted to give a review on what I have done as my time with GMAT comes to a close. I took the Kaplan review last August through October (2008). While it does help with the basics, I feel like it will not get your ready for the upper 700's. It did take my score from a 560 to a 650 but the last 50 to a 100 I have had to do by other resources. Kaplan did however get me in the mode of the GMAT, and made me accountable for studying and got me in the groove so to speak. But my feeling is, if you really want this you will do whatever it takes anyway.

The skinny: If you want to just score up to the mid 600's then pay the $1300 and get it. However, I feel like you dont need to. If you are hell bent on buying one of these courses I feel that Manhatten would serve you better, this coming from buying their practice tests as well as their SC book. You would be better served on quant to buy the practice tests for$75 from this site - they will really bust your ego! But they will get you ready! THEY ARE THE BEST RESOURCE OUT THERE - besides maybe the OG. For verbal, the tests on here are also good. For CR the best thing I have found is the Powerscore LSAT Logical Reasoning bible. If you can master this book, CR will be a breeze. For SC, the Manhatten SC book is the bible.

P.S. I have also purchased the OG Companion......I will write a review on that later and let you know.....
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01 Jun 2009, 19:50
Thank you for your kind words about our tests and your testimonial on Kaplan - I will add you to the list of Reviewers here: gmat-prep-courses-classes-reviews-ratings-and-comparison-78451.html
If I can capture the gist - you felt it did a good job getting your score up 50-100 points but you thought Manhattan would have been a better ROI.

Anything specific you can share about the class? What did you like? Anything that irritated you? How was the teacher?

P.S. Can't wait on the OG Companion review. It is a bit expensive...
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BB,

I have SCOURED these boards and here is basically the magic formula:

Quant:
OG
The OG purple and green books were good too, just more practice.
GMAT Club tests - The hammer, the best.
Manhatten number properties

verbal:
OG
SC - Manhatten SC Guide
CR - Powerscore LSAT Logical Reasoning Bible, the Manhatten GMAT CR Guide is good too - but if you can master the LSAT book - your good to go.
RC - The Kaplan premier online program was good for this, but basically any book that will give you reading practice - Manhatten RC book is good also.

Also, I bought the Kaplan 800 book but the math was not near hard enough - the verbal was pretty good.

I hope this helps and thanks bb.

P.S. As soon as I get into the OG companion I will let you know.....

Last edited by benpack03 on 02 Jun 2009, 15:04, edited 1 time in total.
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02 Jun 2009, 14:38
I also forgot to add, you can also spend about $400 to$500 on the above - maybe, instead of the \$1300 for Kaplan.

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Thank you very much for sharing and for the formula too!
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bb,

Thank you for letting me contribute to this great site. It has helped me out a lot, so its good to give back.

When I get the GMATFix OG Companion and run through it, I will write a review.

Thanks again,

Ben
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